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aberration

is: distortion in an imageoptical image produced by the optical system forming the image and composed of contributions arising from a number of well known causes that include spherical aberration, coma, and chromatic aberration. [PHYS 6.2, PHYS 6.4]

is also: those features of a lens or mirror which cause such distortions. [PHYS 6.4]

absolute error

is: the absolute value (i.e. modulus) of an error or uncertainty in a quantity. [PHYS 1.2]

has: the same dimensions as the quantity itself. [PHYS 1.1]

absolute maximum

See global maximum.

absolute minimum

See global minimum.

absolute temperature

is: a temperature expressed in kelvin (K) on a temperature scale that starts at absolute zero. Such scales include the ideal gas absolute scale, the thermodynamic Kelvin temperature scale and the International Practical Temperature Scale 1990. [PHYS 7.2]

absolute value

See modulus.

absolute zero

is: the lowest possible temperature. [PHYS 7.2]

is defined: as 0 K (i.e. 0 kelvin). [PHYS 7.2]

corresponds: to −273.15 °C (i.e. −273.15 degrees Celsius). [PHYS 7.2]

absorbed dose

is: the amount of energy from ionizing radiation absorbed per unit mass by a body. [PHYS 9.3]

has as its SI unit: the gray (Gy), where 1 Gy = 1 J kg−1 (i.e. 1 joule per kilogram). [PHYS 9.3]

absorption

of: electromagnetic radiation

is: the outcome of any process whereby the energy carried by electromagnetic radiation is transformed and added to the internal energy of the medium through which the electromagnetic radiation is travelling.

should be contrasted: with emission, and reflection.

more generally is: the outcome of any process in which an entity or agency is partly or wholly assimilated into another.

absorption line spectra

is: an absorption spectrum that exhibits absorption lines. [PHYS 8.2]

absorption line

in: the absorption spectrum of a medium (especially a gas, vapour or plasma)

are: characteristic narrow ranges of frequency or wavelength (often treated as single frequencies or wavelengths) at which the spectral brightness is significantly less than the (average) spectral brightness in neighbouring parts of the relevant spectrum. [PHYS 8.2]

correspond individually: to a transition between two bound states of a particular kind of atom, molecule or ion (or to any other process) that causes the absorption of electromagnetic radiation at particular frequencies or wavelengths. [PHYS 8.2]

absorption spectrum

of: electromagnetic radiation, often produced from a continuous emission spectrum (e.g. a source of white light) which has been passed through a specified absorbing medium.

is: the distribution of (relative) spectral brightness with respect to frequency or wavelength. [PHYS 8.2]

may be displayed: as a graph of the (relative) spectral brightness plotted against wavelength or frequency, or (photographically) as a band of varying levels of brightness and darkness. [PHYS 8.2]

may exhibit: (especially for a gas, a vapour or a plasma) characteristic absorption lines, in which case it is often referred to as an absorption line spectrum, or (especially in the case of a solid or a liquid) smoothly varying absorption across a broad range of frequencies or wavelengths. [PHYS 8.2]

absorption transition

in: an atom, molecule or ion

is: a transition in which the atom, molecule or ion absorbs energy from incoming electromagnetic radiation and is thereby excited from one bound state to another bound state of higher energy. Each absorption transition gives rise to an absorption line in an appropriate absorption spectrum. [PHYS 8.2]

usually: involves the ground state as the lower energy state.

AC circuit, a.c. circuit

is: an electrical circuit in which an alternating current flows, or may be presumed to flow. [PHYS 5.4]

AC, a.c.

See alternating current.

acceleration

is: a vector quantity a which specifies the rate of change of velocity with time. [MATH 2.1, MATH 2.4, PHYS 2.1]

in one dimension is: ax = υxux for a particle moving in a straight line with t uniform acceleration ax along the x–axis, where ux and υx are the initial and final velocities respectively and t is the time taken for the change in velocity. [PHYS 2.1]

is defined generally: as a = /dt, the derivative of velocity with respect to time. [MATH 4.1, MATH 5.1]

is often specified: in terms of its scalar components, ax, ay, az by a = (ax, ay, az) = (x/dt, y/dt, z/dt). [MATH 4.1, MATH 5.1]

has as its SI unit: m s−2 (i.e. metre per second squared). [MATH 4.1]

is given graphically: at any particular time, by the gradient of the tangent_to_a_curvetangent to the velocity–time graph of the motion at that time. [MATH 4.1, PHYS 2.1]

See also instantaneous acceleration.

acceleration due to gravity

is: the acceleration with which an object falls near to the surface of the Earth, due to the gravitational force that acts upon it. The magnitude of this acceleration is given the symbol, g and has the approximate value 9.8 m s−2. [PHYS 2.1]

is equal: to the gravitational field at the Earth’s surface. [PHYS 3.2]

may be regarded: as the free fall acceleration of an object at the Earth’s surface, or the surface gravity. [PHYS 3.2]

See magnitude of the acceleration due to gravity.

accommodated (eye)

is: an eye in which the ciliary muscles (which control the lens) are not fully relaxed. [PHYS 6.4]

is focused: somewhere closer than at its far point (usually infinity). [PHYS 6.4]

Contrast with unaccommodated (eye). [PHYS 6.4]

accuracy

of: a measurement or value

is: a measure of the extent to which the measurement (or value) differs from the true value. [PHYS 1.1]

is also: a measure of the extent to which the measurement (or value) is free of systematic error. [PHYS 1.1]

linguistically is: perverse. The greater the accuracy, the smaller is its numerical value. A clearer way of expressing it is to say that a quantity is ‘accurate to within plus–or–minus so–much’. [PHYS 1.1]

Compare with precision.

achromatic doublet

is: a combination of two lenses (glued together), designed to minimize chromatic aberration at two predetermined wavelengths. [PHYS 6.4]

traditionally consists: of a converging lens of crown glass with low dispersion and a weaker diverging lens of flint glass with high dispersion. [PHYS 6.4]

acoustic energy

is: the energy transported by sound. [PHYS 5.7]

acoustic wave

See sound wave.

acoustics

is: the branch of physics concerned with the study of sound.

actinides

are: the fourteen chemical elements with atomic numbers in the range 89-102 inclusive (i.e. from actinium to nobelium). [PHYS 8.4]

are all: radioactive. [PHYS 9.3]

include: uranium and plutonium. [PHYS 8.4]

occur: in a part of the periodic table where the 5f subshell of atoms in their ground state is being progressively filled. [PHYS 8.4]

activity

is: the rate R(t) at which the nuclei of a radioactive substance disintegrate due to radioactive decay. [PHYS 9.2]

is also: a measure of the rate of emission of α–particles, β–particles or γ–radiation from a radioactive isotope. [PHYS 9.2]

is related: to the number N(t) of unstable nuclei of decay constant λ in a pure sample (containing only a single type of radionuclide) by R(t) = −dN/dt = λN(t). [PHYS 9.2]

has as its SI unit: the becquerel (Bq). 1 Bq = 1 decay per second. The non-SI unit of activity, the curie (Ci, 1 Ci = 3.70 × 1010 Bq) is also in common use. [PHYS 9.2]

See activity law.

activity law

is: the law which governs the activity R(t) of a sample of a radioactive isotope, which will remain after a given time t has elapsed. The law is exponential: R(t) = R0eλt, where R0 is the initial activity and λ is the decay constant. [PHYS 9.2]

See radioactive decay and radioactive decay law.

acute angle

is: an angle of less than 90°. [MATH 2.1]

Contrast with obtuse angle and reflex angle.

addition (of vectors)

See vector addition.

addition formulae

are: a class of trigonometric identities. [MATH 1.6]

See trigonometric functions in the Maths For Science handbook.

addition identities

are: a class of hyperbolic function identities. [MATH 4.6]

See hyperbolic functions in the Maths For Science handbook.

adiabat

is: a path representing a quasistatic adiabatic process, usually on a PVT–surface (or some similar surface) or on one of its projections. [PHYS 7.4]

adiabatic

describes: a situation in which no heat enters or leaves a system, so that ΔQ = 0. [PHYS 7.3]

adiabatic condition

for: a fixed quantity of ideal gas

states: that PVγ = constant, where the constant is characteristic of the process, and γ the ratio of specific heats of the gas (CP/CV), is approximately constant for the gas. [PHYS 7.4]

characterizes: an adiabatic process. [PHYS 7.4]

adiabatic process

takes place: without heat entering or leaving the system, so ΔQ = 0. [PHYS 7.3]

See adiabat and adiabatic condition.

adjacent side

of: a right–angled triangle

is: the side (not the hypotenuse) that is adjacent to any specified one of the acute angles. [MATH 1.6]

See trigonometric functions in the Maths For Science handbook.

air friction

is: air resistance. [PHYS 5.2]

air resistance

is: a force that opposes motion through air. [PHYS 2.3]

has magnitude: proportional to the square of the object’s speed, for objects of moderate size and speed, moving through the Earth’s atmosphere close to the Earth’s surface. [PHYS 2.3, PHYS 5.2]

Airy disc

is: the central circular region of an Airy pattern, extending as far as the first minimum. [PHYS 6.4]

Airy pattern

is: the (angular) distribution of radiation diffracted by a circular aperture. [PHYS 6.4]

alcohol–in–glass thermometer

is: a glass capillary with a bulb containing alcohol. Changes in temperature cause the glass and alcohol to expand (or contract) by different amounts, and the result is that the meniscus moves to different positions in the capillary. [PHYS 7.2]

can be calibrated: by marking meniscus positions corresponding to fixed points such as the boiling_pointboiling and freezing points of water, and then interpolating between them. [PHYS 7.2]

algebra

is: the branch of mathematics concerned with symbols and their manipulation according to defined rules.

algebraic

pertains: to algebra, the branch of mathematics concerned with symbols and their manipulation. [MATH 1.1]

algebraic division

is: the application of division to an algebraic expression. [MATH 1.4]

algebraic expression

is: an expression that contains algebraic symbols as well as numbers.

algebraic sum

is: a process of addition that respects a sign convention. [PHYS 2.7]

alkali metals

are: the metallic chemical elementselements lithium, sodium, potassium, rubidium, caesium and francium. [PHYS 8.4]

are so named: because the metals dissolve in water to give solutions that contain significant concentrations of aqueous hydroxide (OH) ions. Materials generating such solutions are said to be alkalis (essentially the opposite of acids). [PHYS 8.4]

occur: in Group I of the periodic table. [PHYS 8.4]

alloy

is: a material with characteristically metallic properties, formed from a combination of element_chemicalelements, of which at least one major constituent is itself a metal. Although specified by a chemical formula, its constituents do not form molecules that correspond to the chemical formula.

α–decay

is: the process in which a nucleus undergoes radioactive decay to form a less massive nucleus with the ejection of an alpha–particleα–particle, e.g. 23892U → 23490Th + 42He (where 42He denotes the α–particle). [PHYS 9.2]

is a type: of radioactive decay. [PHYS 9.2]

α–particle

is: a helium nucleus with positive charge 2e and relative atomic mass 4.0026. [PHYS 8.1, PHYS 9.1, PHYS 9.2]

is ejected: in radioactive α–decay. [PHYS 9.2]

is denoted: α or 42He (or 42He2+ since it is a helium atom stripped of its two electrons). [PHYS 8.1, PHYS 9.1, PHYS 9.2]

alternate angles

See transversal.

alternating current, a.c.

is: an electric current which changes magnitude and direction_of_a_vectordirection in a regular periodic way. [PHYS 5.4, PHYS 5.5]

often is: sinusoidal, i.e. it may be described by the formula I(t) = I0sin(ω t + ϕ), where I0 is the peak value or amplitude of the current, ω is the angular frequency, ϕ is the phase constant and (ωt + ϕ) is called the phase of the current. [PHYS 5.4, PHYS 5.5]

may also be described: using complex quantities, so in the sinusoidal case $I(t) = {\rm Re}[\mathscr{I}_0\exp(\omega t + \phi)]$. [PHYS 5.5]

more generally refers: to other associated electrical quantities whose direction varies with time, e.g. a.c. voltage. [PHYS 5.4]

is abbreviated: AC at the beginning of a sentence, and a.c. elsewhere. [PHYS 5.4]

alternator

is: a device that generates an induced voltage of changing polarity by rotating a coil within a magnetic field. [PHYS 4.4]

is also known: as an alternating current (aca.c.) dynamo. [PHYS 4.4]

ammeter

is: an instrument for measuring electric current that is placed in series (connection)series with other circuit components through which the current to be measured flows. [PHYS 4.1]

ideally has: zero resistance, so that it does not affect the circuit to which it is connected. [PHYS 4.1]

amount of substance

is: a measure of the quantity of substance in a sample, expressed in terms of the number of basic entities (atoms, molecules, etc.) of the substance that are present in the sample.

has as its SI unit: the mole (mol).

ampere, A

is: the SI unit of electric current (i.e. rate of flow of electric charge), one of the seven base units. [PHYS 4.1]

is defined: as that constant current which, if maintained in each of two infinitely long, straight, parallel wires of negligible cross section, placed 1 metre apart, in a vacuum, will cause each wire to experience a force of magnitude 2 × 10−7 newton per metre of its length. [PHYS 4.3]

is equivalent: to the transfer of one coulomb per second, so 1 A = 1 C s−1. [PHYS 4.1]

amplitude

of: an oscillation or a wave

is: the maximum magnitude of displacement from an equilibrium value. [PHYS 5.1, PHYS 5.5, PHYS 6.1]

is represented: by the constant A that appears in the general solution of the simple harmonic motion equation when written in the form y = Asin(ωt + ϕ). [MATH 5.1, PHYS 5.5, PHYS 5.6]

also appears: in similar equations such as that describing damped driven harmonic motion. [MATH 6.3, MATH 6.4]

is exemplified: by the maximum value of the pressure change caused by the passage of a sound wave. [PHYS 5.7]

angle

is: the inclination of one line with respect to another or, equivalently, the amount by which one line must be rotated about a point in order to align it with another line passing through the same point. [MATH 1.6]

is commonly measured: in degrees or radians. [MATH 1.6]

is also called: plane angle.

angle of contact

in: capillarity

is: the angle between a meniscus and a solid surface at their point of contact. [PHYS 7.6]

angle of deviation

in: geometrical optics and acoustics.

is: the angle through which a ray is turned, often by refraction on entering a different material or medium. [PHYS 6.3]

angle of dip

See angle of inclination.

angle of incidence

in: geometrical optics and acoustics.

is: the angle between the incident ray and the normal to the surface or interface at the point of incidence. [PHYS 5.7, PHYS 6.1, PHYS 6.2]

angle of inclination

is: the angle between the (local) Earth’s magnetic field and the horizontal. [PHYS 4.2]

is also called: angle of dip. [PHYS 4.2]

angle of reflection

in: geometrical optics and acoustics.

is: the angle between the reflected ray and the normal to the surface or interface at the point of incidence. [PHYS 5.7, PHYS 6.1, PHYS 6.2]

is equal: to the angle of incidence, according to the law of reflection. [PHYS 5.7, PHYS 6.1, PHYS 6.2]

angle of refraction

in: geometrical optics and acoustics.

is: the angle between the refracted ray and the normal to the surface or interface at the point of incidence. [PHYS 5.7, PHYS 6.1, PHYS 6.2]

is related: to the angle of incidence via Snell’s law (the law of refraction). [PHYS 5.7, PHYS 6.1, PHYS 6.2]

angular acceleration

is: the rate of change of angular velocity, either in magnitude or in direction or in both. [PHYS 2.7]

is defined: as aθ = dω/dt. [PHYS 2.7]

has as its SI unit: rad s−2 (i.e. radian per second squared. [PHYS 2.7]

can be represented: if the direction of the angular velocity does not change, by the scalar quantity aθ = /dt. [PHYS 2.7]

can be determined: if the angular acceleration aθ is uniform, by aθ = (ω2ω1)/t, where ω2 and ω1 are the angular speeds at the end and beginning respectively of the time interval t. [PHYS 2.7]

angular frequency

of: oscillatory motion

is: a measure of the rate at which complete oscillations are executed. [MATH 5.1, PHYS 5.5]

is related: to the frequency f of the oscillation by ω = 2πf. [PHYS 5.1, PHYS 5.4, PHYS 5.5, PHYS 5.6]

is also related: to the period T of the oscillation by T = 2π/ω. [PHYS 5.1, PHYS 5.5]

has as its SI unit: the hertz (Hz), where 1 Hz = 1 s−1 (i.e. per second). [PHYS 5.1, PHYS 5.4, PHYS 5.5]

is represented: by the parameter ω in the formula y = Asin(ωt + ϕ) that describes simple harmonic motion. [MATH 6.3, MATH 6.4, PHYS 5.1]

Compare with angular speed.

angular limit of resolution

See angular resolving power.

angular magnification

is: the ratio of the angle subtended at an observerobserver’s eye by an optical image, to the angle subtended by the object from which it is derived. [PHYS 6.4]

Compare with magnifying power.

angular momentum

of: a particle

about: a chosen origin O, from which the position of the particle is specified by the position vector r,

is: L = r × p, where p is the momentum of the particle. [PHYS 2.8]

is also known as: the moment of momentum of the particle about O. [MATH 2.7]

of: a collection of particles

about: a given point P

is: the (vector) sum of all the moments of momenta of each of the particles about P. [PHYS 2.8, PHYS 11.3]

of: a rigid body

with: angular velocity ω about a single fixed axis of rotation, and moment of inertia I about that axis

is given by: L = Iω. [PHYS 2.8]

has as its SI unit: kg m2 s−1 (i.e. kilogram metre squared per second).

See conservation of angular momentum.

angular position

of: a particle in a plane, with respect to a point O, taken to be the origin of Cartesian coordinates in the plane

is: the angle θ between the particle’s position vector and the positive x–axis. [PHYS 2.7]

equivalently is: the polar angle of the point at which the particle is located, measured in a system of polar coordinates with origin at O.

angular probability density

in: Schrödinger modelSchrödinger’s model of the hydrogen atom

is: the factor |Ylm(θ, ϕ)|2, that arises in calculating the probability density |Ψ(r, θ, ϕ)|2, where Ylm(θ, ϕ) is the angular part of the wavefunction Ψ(r, θ, ϕ). [PHYS 11.3]

angular resolving power

of: an optical system

is: a measure of the systemsystem’s ability to produce or distinguish two separate images of two point–like objects which are, or appear to be, very close together. [PHYS 6.4]

is defined: as the minimum angular separation that the objects must have if their images are to satisfy the Rayleigh criterion. [PHYS 6.4]

is limited: by the ‘diffraction limit’ of the aperture of the optical system, which for a circular aperture of diameter d admitting light of wavelength λ is (1.22 radian)λ/d. [PHYS 6.4]

is also known: as the angular limit of resolution. [PHYS 6.4]

angular speed

of: a particle moving in a plane (taken to be the (x, y) plane) around a point O (taken to be the origin of the (x, y) plane) with an instantaneous angular position θ (measured between the particle’s position vector r and the positive x–axis)

is: the magnitude of the rate of change of θ with respect to time. That is, ω = |dθ/dt|, where θ is normally measured in radians. [PHYS 2.6, PHYS 3.2]

has as its SI unit: rad1s−1 (i.e. radian per second). [PHYS 2.7, PHYS 5.1]

is exemplified: in the case of uniform circular motion about O, at constant speed υ, by the relation ω = υ/r. [PHYS 2.6]

of: a rigid body in uni–axial rotation about a single axis of rotation that is fixed in relation to the body

is: the (positive) angle swept out per second by a line drawn from the axis of rotation to any point in the body that is not on the axis. [PHYS 2.7]

See also instantaneous angular speed.

angular velocity

of: a particle (or rigid body) in uni–axial rotation about a single fixed axis of rotation

is: a vector, usually represented by the symbol ω, whose magnitude is the angular speed ω, about that axis, and whose direction is along the axis, in the sense given by the right–hand grip rule (i.e. if the fingers of the right hand are curled in the direction of rotation of the body, then the extended thumb points in the direction of the angular velocity). [PHYS 2.7, PHYS 2.8]

satisfies: the relation υ = ω × r, where υ is the velocity and r the position vector of the particle (or of any point in the rigid body) measured from an origin O on the axis of rotation. [PHYS 2.7]

has as its SI unit: rad s−1 (i.e. radian per second).

angular wavenumber

for: a periodic wave of wavelength λ

is defined: as k = 2π/λ. [MATH 6.4, PHYS 5.6]

has as its SI unit: m−1 (i.e. per metre). [MATH 6.4, PHYS 5.6]

is widely referred to: as the wavenumber, though this latter term is more properly reserved for σ = 1/λ, i.e. k/2π. [MATH 6.4, PHYS 5.6]

See also angular wave vector and compare with angular frequency. [MATH 6.4, PHYS 5.6]

angular wave vector

is: the generalization of the scalar angular wavenumber to a vector quantity which characterizes waves propagating in two or three dimensions. [PHYS 5.6]

is equal: in magnitude to 2π/λ. [PHYS 5.6]

has direction: parallel to the direction of propagation of the wave. [PHYS 5.6]

usually is denoted: by the symbol k. [PHYS 5.6]

more commonly is referred to: as the wave vector, or the propagation vector. [PHYS 5.6]

anharmonic oscillations

are: oscillations which are not simple harmonic motionsimple harmonic. [PHYS 5.1, PHYS 5.3]

are characterized: by a restoring force which is not proportional to the displacement, and a period which depends on amplitude. [PHYS 5.1, PHYS 5.3]

anharmonic oscillator

is: an oscillator which displays anharmonic oscillations. [PHYS 5.3]

anion

is: a negatively charged ion. [PHYS 8.4]

annulus

is: a region of a plane lying between two concentric circles. [MATH 2.1]

anode

is: an electrode connected to the positive terminal of a supply of electric current. (The term is used especially in the context of a discharge tube or a similar device.) [PHYS 8.1]

antidifferentiation

See inverse differentiation.

antilog

See antilogarithmic function.

antilogarithmic function

is: the function which undoes the effect of the log function f(x) = loga(x), i.e. is the inverse function of loga(x). [MATH 1.5]

is given: by g(x) = ax (where a > 0), since g(f(x)) = aloga(x) which by definition is simply equal to x. [MATH 1.5]

See also exponential function.

antinode

in: a standing wavestanding (stationary) wave

is: one of the positions where the maximum displacement from equilibrium occurs. [PHYS 5.6]

antiparallel (vectors)

are: two vectors which point in exactly opposite directions. [MATH 2.4, PHYS 2.2]

See also parallel (vectors)

antiparticle

is: a particle having the same rest mass as its partner particle but with its other attributes having the opposite sign. For example, the electron (a particle) and the positron (its antiparticle) have equal masses and opposite charges. [PHYS 9.2]

anti–phase

is: the condition in which two oscillations or waves of the same frequency have a phase difference of π (often referred to as π rad or 180°). The maxima of one disturbance then coincide with the minima of the other and vice versa, and the two oscillations or waves are totally out of step. [PHYS 6.1]

is equivalently: the condition of being totally out of phase. [PHYS 5.1]

anti–reflection coating

is: a thin transparent film applied to the surface of an optical component such as a lens in order to reduce (via interference) the amount of light which the surface reflects. [PHYS 6.1]

antisymmetric function

See odd function.

aperture

of: a lens or mirror

is: its effective size (usually expressed as a circular diameter).

more generally is: an opening or gap.

aperture stop

in: an optical system

is: the size of aperture which defines the amount of light entering the system. [PHYS 6.4]

apparatus

is: equipment used in a scientific experiment or investigation.

apparent depth

of: an object viewed by refraction at a plane surface

is: the depth below the surface at which the image appears to be. For near normal viewing the ratio of real depth to apparent depth is equal to the refractive index. [PHYS 6.2]

approximation

of: a number or quantity y by another number or quantity x

is obtained: when x and y have ’similar’ values. The term ’similar’ is not precisely defined but generally means that |xy|/|x| is much less than 1. Such a relationship is shown by writing xy. [MATH 1.2]

also refers: to approximation of a real situation by a model. [PHYS 1.1]

occurs: in ‘orders’, as in a crude ‘first (order) approximation’ or a more accurate ’second (order) approximation’. [PHYS 8.3, PHYS 8.4]

also occurs: in ‘degrees’, as in the approximation of a function by a polynomial (such as a Taylor polynomial of degree n). [MATH 1.7, MATH 4.5]

See also numerical integration and numerical procedures for information on the approximation of definite integrals and roots of equations.

aqueous humour

is: the clear, watery fluid between the cornea and the lens of the eye. [PHYS 6.4]

arbitrary constants

are: constants that arise (as constants of integration) in the solution of differential equations. The general solution of an nthorder linear, ordinary differential equation contains n independent arbitrary constants (which are also known as essential constants). [PHYS 5.5]

arc

is: a part of a curve.

often specifically means: a part of the circumference of a circle, though this should more properly be called a circular arc. [MATH 1.6, MATH 2.1]

arc length

is: a length measured along an arc. [MATH 1.6]

arccos

See inverse trigonometric functions, and the Maths For Science handbook.

arccosh

See inverse hyperbolic functions, and the Maths For Science handbook.

arccosec

See inverse trigonometric functions, and the Maths For Science handbook.

arccosech

See inverse hyperbolic functions, and the Maths For Science handbook.

arccot

See inverse trigonometric functions, and the Maths For Science handbook.

arccoth

See inverse hyperbolic functions, and the Maths For Science handbook.

Archimedes’ principle

states: that an object immersed in a fluid will experience a force due to the fluid which acts upward through the object’s centre of gravity, with a magnitude equal to the weight of the fluid which has been displaced by the object. [PHYS 7.6]

arcsec

See inverse trigonometric functions, and the Maths For Science handbook.

arcsech

See inverse hyperbolic functions, and the Maths For Science handbook.

arcsin

See inverse trigonometric functions, and the Maths For Science handbook.

arcsinh

See inverse hyperbolic functions, and the Maths For Science handbook.

arctan

See inverse trigonometric functions, and the Maths For Science handbook.

arctanh

See inverse hyperbolic functions, and the Maths For Science handbook.

area

is: a measure of the amount of surface within given closed boundaries.

See Table 11 in Section 2 of the Maths For Science handbook for the areas of particular shapes.

area between two graphs

of: the functions f(x) and g(x) which intersect at the points x = a and x = b (where a < b), and for which any other points of intersection lie between x = a and x = b

is given: by the integral $\displaystyle \int_a^b \left\lvert\,f(x)-g(x)\,\right\rvert\,dx$.

area under a graph

of: the function f(x) between a and b

is: a synonym, used in FLAP, for the definite integral of f(x) from a to b, namely $\displaystyle \int_a^b f(x)\,dx$ where b > a. [MATH 5.1,MATH 5.2]

sometimes is referred to: as the signed area since, for b > a it will be negative in any region where f(x) < 0. [MATH 5.2]

can be identified: in graphical terms, with the physical area enclosed by the curve representing f(x) the x–axis, and the lines x = a and x = b provided that a < x < b for all x satisfying a < x < b and the area is measured in the scale units that are appropriate to the graph in question. [MATH 5.1, MATH 5.2]

Argand diagram

is: a plane making use of Cartesian coordinates in which the x–axis represents the real part of a complex number and the y–axis represents the imaginary part. [MATH 3.1, PHYS 5.5]

argument (of a function)

of: a function (e.g. f(x))

is: the independent variableindependent variable(s) e.g. x whose value(s) determines the value of the function. [MATH 1.3]

argument (of a complex number)

of: a complex number in the polar form z = r(cosθ + isinθ), or the exponential form z = reiθ

is: the value of θ. [MATH 3.2, PHYS 5.5]

of: a complex number in the Cartesian form z = a + ib

may be: any value of θ that satisfies the equations

$\sin\theta = \dfrac{b}{\sqrt{\smash[b]{a^2+b^2}}}$

$\cos\theta = \dfrac{a}{\sqrt{\smash[b]{a^2+b^2}}}$ [MATH 3.2, PHYS 5.5]

usually is: the particular value of θ (the principal value) that also satisfies the additional requirement −π < θπ. [MATH 3.2]

is denoted: by arg(z), though some authors use Arg(z) to indicate the principal value of arg(z). [MATH 3.2]

arithmetic

pertains: to the branch of mathematics concerned with numbers and their manipulation. [MATH 1.1]

arithmetic progression

is: a series of the form:

$\displaystyle \sum_{k=0}^{n-1}(a + kh) = a + (a + h) + (a + 2h) + \dots + [a + (n - 1)h] = na + \dfrac{(n - 1)}{2}h$ where the constant, h is known as the common difference. [MATH 1.7]

arithmetic series

See arithmetic progression.

articulated body

is: a body of several defined, jointed parts, which otherwise can be treated as a rigid body. [PHYS 2.8]

aspheric lens

is: a lens whose surfaces are non-spherical. [PHYS 6.4]

aspheric surface

is: a non-spherical surface of a lens or mirror. [PHYS 6.4]

astronomical telescope

is: a telescope which produces a final image that is inverted. [PHYS 6.4]

asymptote

is: a straight line which a curve approaches but does not meet. [MATH 1.3]

more precisely is: a straight line related to a curve in such a way that there is at least one direction of travel along the curve in which the shortest distance between them decreases progressively as the distance from the origin to the point becomes very large. [MATH 4.4]

more formally is: a straight line which is the limit of the tangent to a curvetangents to a curve as the point at which those tangent to a curvetangents touch the curve tends to infinity. [MATH 2.2, MATH 2.3]

asymptotically

means: in the way that a curve approaches, but never meets, its asymptote. [MATH 1.3]

atmosphere, atm

is: a non-SI unit of pressure.

is defined: by 1 atm = 1.013 25 × 105 N m−2. [PHYS 7.2]

is more properly called: standard atmosphere.

more generally is: the layer of air above the Earth’s surface which exerts atmospheric pressure.

atmospheric pressure

is: the pressure due to the weight of the atmosphere. [PHYS 7.2]

is not: a constant, but varies with time and position. [PHYS 7.2]

has a value: at the Earth’s surface varying only by relatively small amounts. [PHYS 7.2]

has as a useful unit: the standard atmosphere (see atmosphereatmosphere, atm) defined by 1 atm = 1.013 25 × 105 N m−2. [PHYS 7.2]

atom

is: the basic building block of all normal solid, liquid or gas matter. [PHYS 7.1]

is: the smallest part of a chemical element that retains the fundamental chemical and physical properties of that chemical elementelement. [PHYS 8.1]

extends: over a diameter of approximately 10−10 m. [PHYS 7.1, PHYS 8.1]

has: a dense, positively charged central nucleus with a diameter of order 10−14 m composed of neutrons and positively charged protons, surrounded by a cloud of negatively charged electrons equal in number to the number of protons, according to nuclear modelRutherford’s nuclear model and all ‘realistic’ models ever since. [PHYS 8.1]

has: zero electrical charge overall. [PHYS 8.1]

Contrast with ion.

atomic force microscope

is: an instrument that measures the vertical displacement of a probe tip, with a diameter of a few nanometers, as it is moved across the surface of a material in such a way that the force it experiences remains constant. [PHYS 7.1]

measures: the profile of the surface with an approximate resolution of 10−10 m. [PHYS 7.1]

can be used: to build a three–dimensional representation of the distribution of atoms on the surface of a material. [PHYS 7.1]

atomic mass

is: the mass of an atom of a chemical element expressed in atomic mass units. It is approximately equivalent to the number of protons and neutrons in the atom (the mass number) or to the average number allowing for the relative abundances of different isotopes.

atomic mass unit, u

is: a non-SI unit of mass. [PHYS 8.1]

is defined: as one twelfth of the mass of one atom of the commonest carbon isotope 126C, so the mass of one carbon–12 atom is exactly 12 u. According to current measurements, 1 u = 1.660154 × 10−27 kg (to six significant figures), or approximately 931 MeV/c2. [PHYS 8.1, PHYS 9.1]

atomic number

is: the number of protons within the nucleus of an atom, usually denoted by the symbol Z [PHYS 7.1, PHYS 9.1]

characterizes: each chemical element uniquely, since the nuclear charge of each atom of a chemical element with atomic number Z is simply Ze. [PHYS 7.1, PHYS 8.1]

also represents: the number of electrons required to balance the nuclear charge in an atom, and therefore determines the chemical behaviour of the atom. [PHYS 8.1]

attenuation coefficient

is: a quantity μ that measures the rate of exponential decrease in intensity, I, of γ–radiation with distance, x, travelled through a material. [PHYS 9.2]

is defined: by I = I0eμx. [PHYS 9.2]

depends for its value: on the material and on the energy of the γ–radiation photons. [PHYS 9.2]

auxiliary equation

of: the differential equation

$a\dfrac{d^2y}{dt^2}+b\dfrac{dy}{dt}+cy+0$

is: the quadratic equation ap2 + bp + c = 0. [MATH 5.5, MATH 6.3]

has the significance: that its root_of_an_equationroots, p1 and p2 appear in the general solution Bexp(p1t) + Cexp(p2t) of the differential equation. [MATH 5.5, MATH 6.3]

may be generalized: (with changed significance) to other differential equations with constant coefficients.

average

means: typical or representative, often describing a condition which, if it persisted, would have the same effect over a specified range as that of which it is an average.

is often used: as a synonym for mean.

average a.c. power

of: an a.c. circuit, or a part of such a circuit,

is: the total energy dissipated in one period of oscillation divided by the duration of that period. [PHYS 5.4]

is given by: $\langle P\rangle = V_{\rm rms}I_{\rm rms}\cos\phi$, where Vrms and Irms are the root–mean-square values of the current I and potential difference V and ϕ is the phase difference between I and V.

has as its SI unit: the watt (W). [PHYS 5.4]

average acceleration

over: a time interval Δt

of: a body moving in one dimension, along the x–axis

is given most simply: by the change of velocity Δυx divided by the time interval Δt. That is, $\langle a_x\rangle = \Delta\upsilon_x/\Delta t$. [PHYS 2.1]

is given more specifically: for a body moving with velocity υx1 at time t1 and velocity υx2 at time t2, by

$\langle a_x\rangle = \dfrac{\upsilon_{x2}-\upsilon_{x1}}{t_2-t_1}$ [PHYS 2.1]

average angular speed

over: a time interval Δt

of: a particle moving in a circle (whose centre is taken to be the origin)

is: the (positive) angle Δθ swept out by the position vector of the particle divided by the time interval Δt, i.e. $\langle\omega\rangle = \Delta\theta/\Delta t$. [PHYS 2.6]

average speed

of: the molecules in a gas with speed distribution f(υ)

is obtained: by dividing the sum of the speeds of all the molecules by the total number of molecules. [PHYS 7.5]

is also obtained: by evaluating the integral $\displaystyle \langle\upsilon\rangle = \int_0^\infty \upsilon f(\upsilon)\,d\upsilon$. [PHYS 7.5]

See applications of integration in the Maths For Science handbook.

average value of a function

over: the interval from a to b

is defined: as $\displaystyle f_{\rm av} = \dfrac{1}{(b-a)}\int_a^b f(x)\,dx$. [MATH 5.4]

average velocity

over: a time interval Δt

of: a body moving in one dimension, along the x–axis

is given most simply: by the change of position Δx divided by the time interval Δt, i.e. $\langle\upsilon_x = \Delta x/\Delta t$. [MATH 4.1, PHYS 2.1]

is given more specifically: for a body with position x1 at time t1 and position x2 at time t2 by

$\langle\upsilon_x\rangle = \dfrac{x_2-x_1}{t_2-t_1}$ [MATH 4.1, PHYS 2.1]

may be similarly expressed: in terms of the displacement sx from a fixed point, rather than the position x. [PHYS 2.1]

of: a body moving in three dimensions

is given most simply: by the change of position Δr divided by the time interval Δt, i.e. $\langle\upsilon\rangle = \Delta {\boldsymbol r}/\Delta t$. [PHYS 2.2]

is given more specifically: if the particle has position r1 at time t1 and position r2 at time t2, by

$\langle{\boldsymbol\upsilon}\rangle = \dfrac{{\boldsymbol r}_2-{\boldsymbol r}_1}{t_2-t_1}$

So, writing r2r1 = Δr = (Δx, Δy, Δz),

$\langle{\boldsymbol\upsilon}\rangle = \left(\langle\upsilon_x\rangle,\langle\upsilon_y\rangle,\langle\upsilon_z\rangle\right) = \dfrac{\Delta{\boldsymbol r}}{\Delta t} = \left(\dfrac{\Delta x}{\Delta t},\,\dfrac{\Delta y}{\Delta t},\,\dfrac{\Delta z}{\Delta t}\right)$ [PHYS 2.2]

Avogadro’s constant

is: the physical constant NA that represents the number of basic entities (atoms, molecules, ions etc.) per mole of any substance, [PHYS 7.1, PHYS 7.2]

has: the value NA = 6.0223 × 1023 mol−1 (to five significant figures). [PHYS 7.1, PHYS 7.2]

Compare with Avogadro’s number (which has no units).

Avogadro’s hypothesis

states: that equal volumes of all gases at the same temperature and pressure contain the same number of atoms or molecules. [PHYS 7.1]

Avogadro’s number

is: the number of basic entities (atoms, molecules, ions, etc.) in one mole of any substance, namely 6.0223 × 1023 (to five significant figures). [PHYS 7.1, PHYS 7.2]

Compare with Avogadro’s constant (which is defined per mole, and consequently has units mol−1).

axes

are: straight lines at an angle to one another, along which and from which we can measure the coordinates of a point. [PHYS 1.3]

usually are: Cartesian coordinate axes, which are at right angles to one another and which intersect at a common point called the origin. [MATH 1.3]

axial ray

is: a light ray which is coincident with the optical axis, before and after refraction or reflection. [PHYS 6.4]

axis of rotation

of: a rotating rigid body

is: the straight line connecting all parts of the body which are at rest. [PHYS 2.8]

bac cab rule

is: a mnemonic reference to the vector identity a × (b × c) = b(a c) − c(a b). [MATH 2.7]

balanced bridge

is: a bridge circuit whose electrical components are arranged so that there is no voltage between its output terminals. [PHYS 4.1]

balanced forces

are: two or more forces whose magnitude_of_a_vector_or_vector_quantitymagnitudes and directions are such that their net force or resultant force is zero. [PHYS 2.3]

ballistic galvanometer

is usually: a type of moving–coil galvanometer. [PHYS 4.4]

is designed: with a weak restoring force and a weak damping force, so that a transient current produces an initial swing whose amplitude is proportional to the total charge passed.

is used: to measure quantities of electric charge, and (in conjunction with a search coil) magnetic fields. [PHYS 4.4]

Balmer series

is: the set of visible lines in the spectrum of atomic hydrogen, whose wavelengths are given by Balmer’s formula. [PHYS 8.2]

Balmer’s formula

is: the formula discovered by Johann Balmer (1825–1898) which gives, to a very high accuracy, the wavelengths of the visible spectral lines emitted by atomic hydrogen:

$\lambda = 364.56\left[\dfrac{n^2}{n^2-4}\right]\,{\rm nanometres}$. [PHYS 8.2]

back e.m.f.

See induced voltage.

band theory

is: the proposal that the energy levels of electrons in (crystalline) solids are distributed in energy bands. [PHYS 11.4]

is also: the theoretical study of energy bands and their consequences. [PHYS 11.4]

bar

is: a non-SI unit of pressure.

is defined: as 1 bar = 105 Pa (i.e. 105 N m−2). [PHYS 7.2]

is slightly smaller: than another non-SI unit of pressure, the standard atmosphere; 1 atm = 1·013 25 bar. [PHYS 7.2]

barrier penetration

See quantum tunnelling.

base (of a number system)

of: a system for specifying numbers

is: a number that takes on the role that 10 plays in the specification of decimal numbers. A base n system uses n digits and is based on power_mathematicalpowers of n. [MATH 1.2]

base (of a logarithm)

is defined: as the value of a in the identity aloga(x) = x. [MATH 1.5]

must be: positive. [MATH 1.5]

is most commonly: e (the base of natural logarithms) or 10 (the base of common logarithms). [MATH 1.5]

basic differentiation

is: an informal term used to denote a range of mathematical skills in the area of differentiation. [MATH 4.2]

includes: the ability to differentiate ’standard’ functions such as sin(kx), cos(kx), exp(kx) and loge(kx), together with constant multiples, sums, products and quotients of such functions. [MATH 4.2]

basic identities

are: a class of trigonometric identities. [MATH 1.6]

See trigonometric functions in the Maths For Science handbook for further details.

basic units

are: seven SI units. [PHYS 1.1]

comprise: the metre, kilogram, second, ampere, kelvin, mole and candela. [PHYS 1.1]

battery

consists: of two or more electric cells connected together to act as a single current source. (Colloquially, a single cell is also called a battery.) [PHYS 4.5]

beam

is: a collection of waves or particles travelling along closely parallel paths.

is also: a bundle of closely parallel rays.

beat frequency

between: two oscillations or waves of similar frequency that are superposed

is: the frequency of the (modulated) amplitude of the superposed waves. [PHYS 5.1]

is equal: to the difference between the frequencies of the two oscillations or waves. [PHYS 5.1, PHYS 5.3, PHYS 5.7]

is also equal: to the reciprocal of the beat period. [PHYS 5.7]

beat period

is: the time interval between successive beats in situations where two waves (e.g. sound waves) of slightly different frequency are superposed. [PHYS 5.7]

is equal: to the reciprocal of the beat frequency. [PHYS 5.7]

beating

between: two oscillations or waves of similar frequency that are superposed

is: the periodic variation of the total amplitude that gives rise to beats. [PHYS 5.1]

occurs: at the beat frequency. [PHYS 5.1]

beats

are: periodic variations in intensity due to beating. [PHYS 5.1, PHYS 5.7]

are produced: when two waves of nearly equal frequency and similar amplitude are superposed. [PHYS 5.1, PHYS 5.7]

becquerel, Bq

is: the SI unit of activity.

is defined: as an activity of 1 decay per second. is related: to a common non-SI unit, the curie (Ci), by 1 Ci = 3.70 × 1010 Bq. [PHYS 9.2]

β–decay (beta–decay)

is: the process in which a nucleus undergoes radioactive decay to form a less massive nucleus of a different element_chemicalelement with the emission of a β–particle. [PHYS 9.2]

is classified: in two types: β–decay and β+–decay. [PHYS 9.2]

if β–decay, is: radioactive decay with the ejection of an electron (a β–particle) and an electron antineutrino, e.g. 156C → 157N +   0−1e + ν_e. A neutron in the original nucleus is transformed into a proton, an electron and an electron antineutrino: n → p + e + ν_e. [PHYS 9.2]

if β+–decay, is: radioactive decay with the ejection of a positron and an electron neutrino, e.g. 116C → 155B +   0+1e + νe. A proton in the original nucleus is transformed into a neutron, a positron and an electron neutrino: p → n + e+ + νe. [PHYS 9.2]

β–particle

is: a particle that is emitted in β–decay. [PHYS 9.2]

is classified: in two types: the β–particle (an electron) which is emitted in beta_decayβ–decay, and the β+–particle (a positron) which is emitted in beta_decayβ+–decay. [PHYS 9.2]

biconcave lens

is: a lens having two surfaces which curve inwards into the material. The centre is thinner than the edges. [PHYS 6.3]

often is called simply: a concave lens. [PHYS 6.3]

biconvex lens

is: a lens having two surfaces which curve outwards from the material. The centre is thicker than the edges. [PHYS 6.3]

often is called simply: a convex lens. [PHYS 6.3]

bimetallic strip

is: a thermally sensitive device consisting of two thin strips of different metals soldered, or otherwise attached, face to face. [PHYS 7.2]

bends: with any change in temperature, since the extent to which the two metals expand in response to a given change of temperature will generally differ. [PHYS 7.2]

can be used: to measure temperature or as a means of temperature–sensitive control. [PHYS 7.2]

binding energy (of a nucleus)

of: a nucleus

is: the minimum energy required to break a nucleus apart into its free constituent nucleons. [PHYS 9.1]

more generally is: the minimum energy required to separate any system into appropriately specified components.

binding energy (of an electron)

of: an electron

in: an atom

is: the minimum energy required to remove the electron from the atom. [PHYS 8.1]

binomial coefficient

is: any one of the coefficients, nCr, that arise in the binomial expansion. [MATH 1.7]

is defined: as

${}^nC_r = \dfrac{n!}{r!(n-r)!} = \dfrac{n(n-1)(n-2)\dots(n-r+2)(n-r+1)}{r(r-1)(r-2)\dots2\times1}$

(See factorial for the definition of n!) [MATH 1.7]

See summations and series in the Maths For Science handbook. where nr.

binomial expansion

is: a polynomial expression for (a + b)n, where n is a positive integer:

$\displaystyle (a+b)^n = \sum_{k=0}^n {}^nC_{n-k}a^{n-k}b^k$

where nCr is a binomial coefficient and Σ is the summation symbol. [MATH 1.7]

See binomial series, binomial theorem.

See also summations and series in the Maths For Science handbook.

binomial series

is: an infinite series for (1 + x)r, where r is any real number and −1 < x < 1:

$(1+x)^r = 1 + \dfrac{rx}{1!} + \dfrac{r(r-1)x^2}{2!} + \dfrac{r(r-1)(r-2)x^3}{3!} + \dots$ [MATH 1.7]

is equivalent: to the corresponding binomial expansion when r is an integer.

See summations and series in the Maths For Science handbook.

binomial theorem

is: an alternative expression for the binomial expansion or the binomial series. [MATH 1.7]

bisection method

for: locating a root_of_an_equationroot of an equation

works: by constructing a sequence of intervals of decreasing length, such that the associated function changes sign on each interval. [MATH 1.4]

bisector

is: a line drawn in such a way that it cuts a specified angle into two equal parts. [MATH 2.1]

black body

is: an idealized object that absorbs all the electromagnetic radiation that falls upon it. [PHYS 8.2, PHYS 10.1]

reflects: absolutely no radiation. [PHYS 8.2, PHYS 10.1]

is also: an ideal emitter of radiation. [PHYS 8.2, PHYS 10.1]

emits: black–body radiation - which has a spectrum that depends only on the temperature of the black body. [PHYS 8.2, PHYS 10.1]

has: spectral brightness which is given by Planck’s function. [PHYS 7.3]

is approximated roughly: by a matt black surface. [PHYS 7.3]

is approximated well: by a cavity maintained at a well–defined temperature and connected to its environment by a small aperture. The spectrum of radiation inside such a cavity is described quite accurately by Planck’s function, and the radiation emitted from the small hole closely approximates black–body radiation irrespective of the material of the container or the state of its inner surface. [PHYS 7.3, PHYS 8.2, PHYS 10.1]

black–body radiation

is: electromagnetic radiation emitted by a black–body. [PHYS 8.2, PHYS 10.1]

has: a characteristic spectrum whose spectral brightness at wavelength λ is given by Planck’s function:

$R = \dfrac{2hc^2}{\lambda^5(\exp(hc/\lambda kT)-1)}$

with an overall shape, a wavelength for peak emission, and a total radiation_thermalradiated power per unit surface area all determined entirely by the temperature of the black–body. [PHYS 7.3, PHYS 8.2, PHYS 10.1]

is also found: within a cavity in thermodynamic equilibrium. [PHYS 8.2, PHYS 10.1]

therefore can be realized in practice: by using a cavity with a small aperture. [PHYS 8.2, PHYS 10.1]

black–body spectrum

See black–body radiation.

body

is: a collection of interacting particles which extends throughout a particular region of space.

Bohr model

of: the hydrogen atom

is: now supplanted but remains historically important as the first theoretical account of atomic structure to make use of quantum physics. [PHYS 8.2]

was formulated: by Niels Bohr (1885–1962) in 1913. [PHYS 8.2]

postulates: (1) that the negatively charged electron is held in a circular orbit around the positively charged nucleus by the Coulomb force between them; (2) that the range of allowable orbits is restricted by the requirement that the angular momentum of the orbiting electron is quantized in units of h/2π, where h is Planck’s constant; (3) that, contrary to classical physics, the orbiting electron does not continuously lose energy through the emission of electromagnetic radiation; (4) that electromagnetic radiation is emitted when the electron makes a transition from an initial orbit of energy Ei to a final orbit of energy Ef and that the frequency of that radiation is given by the Planck–Einstein formula as f = (EiEf)/h. [PHYS 8.2]

explains: many features of the spectrum of atomic hydrogen, including Balmer’s formula. [PHYS 8.2, PHYS 11.3]

may be: extended to atoms other than hydrogen, but only with limited success.

See Bohr orbit, Bohr radius, Bohr’s quantization conditionBohr’s quantization, Bohr’s quantum number.

Bohr orbit

in: the Bohr model of the hydrogen atom

is: one of the allowed orbits for the electron. An electron in such an orbit moves with a definite speed and has a constant energy; contrary to classical physics, it does not continuously emit electromagnetic radiation.

corresponds: to a definite energy level of the atom. [PHYS 8.2] [PHYS 8.2]

Bohr radius

in: the Bohr model of the hydrogen atom

is: the radius of the smallest Bohr orbit for the electron. [PHYS 8.2, PHYS 11.3]

is given: by $a_0 = \dfrac{\varepsilon_0h^2}{\pi m_{\rm e}e^2}$ where ε0 is the permittivity of free space, me is the mass of the electron, e the charge on the proton, and h is Planck’s constant. [PHYS 8.2]

therefore is: quantized by Bohr’s quantum number n. [PHYS 8.2]

Bohr’s quantization condition

in: the Bohr model of the hydrogen atom

states: that the magnitude_of_a_vector_or_vector_quantitymagnitude L of the angular momentum of the electron as it orbits the nucleus must be a positive integer multiple of Planck’s constant h divided by 2π. Thus:

$L = \dfrac{nh}{2\pi}$ for n = 1, 2, 3, ...

where n is called Bohr’s quantum number. [PHYS 8.2]

Bohr’s quantum number

in: the Bohr model of the hydrogen atom

is: an integer n that may take any positive value starting from 1, and which determines the (quantized) angular momentum magnitude_of_a_vector_or_vector_quantitymagnitude L of the electron in the nth Bohr orbit around the nucleus (see Bohr’s quantization). [PHYS 8.2]

also determines: the radius of the nth Bohr orbit and the associated energy level: En = −(13.6 eV)/n2 for n = 1, 2, 3, ... [PHYS 8.2]

boiling point

of: a liquid subjected to a specified external pressure (usually standard atmospheric pressure)

is: the temperature at which the saturated vapour pressure of the liquid is equal to the external pressure.

Boltzmann’s constant

is: the physical constant k that has the value k = 1.380 × 10−23 J K−1 (to four significant figures). [PHYS 7.5]

is expressible: in terms of two other physical constants, the molar gas constant R and Avogadro’s constant NA, by k = R/NA. From this, Boltzmann’s constant is seen to act as the gas constant per molecule. [PHYS 7.5]

appears: in equations which relate microscopic properties to macroscopic parameters of physical systems; e.g. in an ideal gas at temperature T, the mean translational kinetic energy of a particle is 3kT/2. [PHYS 7.5]

bond

between: atoms in a molecule or molecules in a solid (more particularly between specified states of those atoms or molecules)

is: a quantum physical phenomenon associated with a specific bonding energy that causes the atoms or molecules that have bonded to act as a single entity. [PHYS 11.4]

is fundamentally explained: by electromagnetic forces between the atoms or molecules. [PHYS 11.4]

may be classified: according to the number of electrons involved in maintaining the bond.

bonding electron

is: an electron involved in forming or maintaining a bond between atoms or molecules.

bonding energy

is: the minimum energy required to break a specific bond.

Born probability interpretation (hypothesis)

is: the association between the wavefunction of a particle and the probability of finding that particle in a given region of space at a particular time.

states: that if a particle moving in one dimension has the wavefunction Ψ(x,t), then the probability of finding the particle in a small region Δx around x at time t is proportional to |Ψ(x,t)|2Δx. If the wavefunction is normalized, then the probability is equal to |Ψ(x,t)|2Δx. [PHYS 10.4, PHYS 11.1]

bound state

of: a quantum system

is: a state of a composite system in which a finite amount of energy is required to separate the components of the system.

is: in Schrödinger modelSchrödinger’s model of the hydrogen atom, a state in which the probability that the electron will escape infinitely far from the proton, is zero.

is: in the Bohr model of the hydrogen atom, any one of an infinite number of possible states, corresponding to the allowed Bohr orbits for the electron, each with its own definite energy corresponding to one of the energy levels. [PHYS 8.2, PHYS 11.3]

boundary conditions

for: differential equations

are: conditions which specify the value of the dependent variable or its derivatives, for specific values of the independent variable. [MATH 6.1, PHYS 11.1, PHYS 11.2]

can be used: to determine (or help to determine) any arbitrary constants that arise in the general solution of a differential equation. [PHYS 5.4, PHYS 5.5, PHYS 11.1, PHYS 11.2]

often arise as: conditions imposed on a wave at the boundary of a medium, usually involving the value of either the displacement of the medium or the derivative of the displacement with respect to position. [PHYS 5.6, PHYS 10.3]

Boyle’s law

states: that at constant temperature, the pressure P and volume V of a fixed amount of ideal gas are related by PV = constant. [PHYS 7.2]

See ideal gas equation of state.

brackets

take the form: (),[],or{}. [MATH 1.1]

have a hierarchy: {[( )]}. [MATH 1.1]

are used: to separate one part of an expression from the rest. In a calculation, the part of an expression enclosed in brackets must be evaluated before being combined with other terms. [MATH 1.1]

Bragg’s law

for: diffraction of monochromatic electromagnetic radiation of wavelength λ

from: parallel planes of atoms separated by a distance d in an orderly array of atoms (such as a crystal)

determines: the values of the angle θ, (measured between the incident ray and the plane of atoms) at which local maxima of intensity are formed in the diffraction pattern by constructive interference of the reflected rays from adjacent planes of atoms. [PHYS 7.1]

is normally expressed: as = 2dsinθ, where n is an integer. [PHYS 7.1]

branchies

of: a hyperbola

refers: to the two separate parts of a hyperbola that are produced when a plane intersects a double cone. [MATH 2.3]

breaking point

of: a given material

is: the point on the loading curve of the material at which the material breaks apart. [PHYS 7.6]

corresponds: to the maximum tensile stress that the material can sustain. [PHYS 7.6]

breeder reactor

is: a nuclear fission reactor whose reaction products include material that can be used as fuel for further reactions. [PHYS 9.3]

bremsstrahlung

is: the electromagnetic radiation emitted when an electrically charged particle is accelerated, in particular, when it is slowed down. For example, when high- energy electrons collide with a target, X–rays are produced with a continuous spectrum. [PHYS 8.3]

linguistically is: German for ‘braking radiation’. [PHYS 8.3, PHYS 10.1]

bridge circuit

is: a circuit consisting of four electrical components (generally resistors) connecting four points (A, B, C, D, say) to form a closed loop. [PHYS 4.1]

produces: an output voltage between two non–adjacent points (A and C say) when a voltage source is connected across the other two points (B and D). [PHYS 4.1]

is used: to compare resistances. [PHYS 4.1]

is balanced: when the resistances are such that the output voltage is zero.

bridge circuit balance condition

is: the equation which relates the four resistances in a balanced bridge circuit. [PHYS 4.1]

brittleness

is: the property of a material which causes it to fracture without appreciable plasticity, before or soon after the elastic limit is reached. [PHYS 7.6]

Brownian motion

is: the microscopic random motion of pollen grains and other small particles suspended in gases or liquids. [PHYS 7.1, PHYS 8.1]

was first observed: by the botanist Robert Brown (1773–1858). [PHYS 7.1, PHYS 8.1]

was explained: as the result of numerous unseen molecular collisions, by Albert Einstein (1879–1955) in 1905. [PHYS 7.1, PHYS 8.1]

bulk modulus

of: a material (solid, liquid or gas)

is: an elastic modulus, conventionally denoted K. [PHYS 5.7, PHYS 7.6]

is defined: as the ratio of the applied volume stress σvol to the resulting volume strain εvol:

$K = \dfrac{\sigma_{\rm vol}}{\varepsilon_{\rm vol}} = \dfrac{-\text{pressure change}}{\text{fractional volume change}}$ (note the − sign) [PHYS 5.7]

has as its SI unit: N m−2 or Pa (i.e. pascal). [PHYS 5.7, PHYS 7.6]

buoyancy

is: the phenomenon by which a fluid tends to reduce the apparent weight of a body through the buoyancy force. [PHYS 7.6]

buoyancy force

is: the vertical upward force exerted on a body by a static fluid in which it is submerged or floating. [PHYS 7.6]

is quantified: by Archimedes’ principle. [PHYS 7.6]

is also called: the upthrust. [PHYS 7.6]

caesium atomic clock

is: a device that uses an atomic resonance in caesium of very narrow resonance absorption bandwidth and very high Q–factor, to provide a time or frequency standard. [PHYS 5.3]

is used: to establish the SI unit of time, the second. [PHYS 5.3]

calculation

is: a sequence of mathematical operations performed with the objective of determining the answer to a question.

calculus

is: a branch of mathematics which is concerned with the way in which (small) changes in one quantity determine or are determined by changes in related quantities. [MATH 4.1, PHYS 2.1]

is more properly called: infinitesimal calculus. [MATH 4.1, PHYS 2.1]

includes: differentiation and integration. [MATH 4.1, PHYS 2.1]

calibration

is: the process of checking one measuring instrument against another, more accurate one. [PHYS 1.1]

calibration points

for: a thermometer

are: two or more fixed points which can be used to calibrate the scale of the thermometer. [PHYS 7.2]

are usually: triple points or boiling_pointboiling or freezing points. In the case of the Kelvin temperature scale one of the two points is the unattainable absolute zero, the other is the triple point of H2O. [PHYS 7.2]

permit between or beyond them: interpolations or extrapolations, often using polynomial thermometric relations. [PHYS 7.2]

calorimeter

is: a container of known heat capacity used in calorimetry experiments. [PHYS 7.4]

calorimetry

is: the branch of physics concerned with the measurement of heat and its effects. [PHYS 7.4]

camera

is: a device for producing a record of an image, either on photographic film or via some other means (e.g. electronic). [PHYS 6.4]

See also pinhole camera. [PHYS 6.4]

cancelling

is: a term used to describe the mathematical process in which (a) a factor appearing on both sides of an equation is eliminated by dividing both sides of the equation by that factor; or (b) a factor appearing in both the numerator and denominator of a fraction (arithmetic or algebraic) is eliminated by dividing both the numerator and the denominator by that factor. [MATH 1.1]

candela, cd

is: the SI unit of luminous intensity, one of the seven base units. (Not used in FLAP .)

capacitance

of: an isolated electrical conductor

is: the ratio of the charge q stored on the electrical_conductorconductor, to the potential difference V between it and some selected reference point. [PHYS 4.5]

is given: by C = q/V. [PHYS 4.5, PHYS 5.5]

more generally is: the charge stored between two points per unit potential difference between those points.

is exemplified: by the capacitance between the terminals of a capacitor, which for parallel plates of area A separated by a dielectric with permittivity ε and thickness d is C = εA/d. [PHYS 4.5]

has as its SI unit: the farad, (F), where 1 F = 1 C V−1. [PHYS 4.5, PHYS 5.5]

capacitive reactance

of: a capacitor with capacitance C, when passing alternating current of angular frequency ω

is: the ratio of the peak voltage to the peak current V0/I0.

is given: by XC = 1/ωC. [PHYS 5.4, PHYS 5.5]

has as its SI unit: the ohm (Ω). [PHYS 5.4, PHYS 5.5]

See complex capacitive reactance, impedance, reactance. [PHYS 5.4, PHYS 5.5]

capacitive time constant

is: the time for the current, charge or voltage across a capacitor to decay exponentially by a factor e. [PHYS 4.5]

is given: for a circuit in which a capacitor of capacitance C discharges through a resistance R, by τ = RC. [PHYS 4.5]

capacitor

is: a device for storing electric charge. [PHYS 4.5, PHYS 5.5]

usually consists: of two parallel metal surfaces (not necessarily flat) separated by a dielectric. [PHYS 4.5]

generally has: in practical electronic circuits, a capacitance very much less than 1 farad (1 F) so its capacitance might well be expressed in microfarad (μF) or picofarad (pF).

capillarity

is: the elevation or depression of the surface of a liquid in contact with a solid due to the relative attraction of the liquid molecules for each other as compared to their attraction to those of the solid. [PHYS 7.6]

See meniscus.

capillary

is: a tube of narrow internal diameter. [PHYS 7.6]

See capillarity.

Carnot cycle

in: thermodynamics

is: a reversible closed cycle consisting of four steps, two isothermal processes linked by two adiabatic processes. [PHYS 7.4]

See Carnot engine.

Carnot engine

is: a reversible heat engine that utilizes the Carnot cycle. [PHYS 7.4]

has: efficiency η = 1 − Tcold/Thot when operating between temperatures Thot and Tcold. (Any reversible heat engine operating between those temperatures must have the same efficiency.) [PHYS 7.4]

is: the most efficient possible heat engine operating between two fixed temperatures. [PHYS 7.4]

Cartesian axes

See Cartesian coordinate system.

Cartesian component vectors

of: a vector υ, with respect to a given Cartesian coordinate system

are: the vectors υx, υy, υz directed along the Cartesian axes such that υx + υy + υz = υ. [MATH 2.5]

are therefore: individually proportional to the corresponding Cartesian unit vectors i, j and k. [MATH 2.5]

should not be confused with: the Cartesian scalar components (υx, υy, υz) of υ which are individually the scalars by which a Cartesian unit vector must be scaling_of_a_vectorscaled to produce the corresponding component vector (e.g. υx = υxi). [MATH 2.5]

Cartesian coordinate system

is: a coordinate system that uses Cartesian coordinates, measured along mutually perpendicular axes from a point of common intersection called the origin. In three dimensions, the three axes are conventionally labelled as the x–axis, y–axis and z–axis, and it is conventional to perform the labelling so as to produce a right–handed coordinate system rather than a left–handed coordinate system.

can be generalized: to any number of dimensions.

Cartesian coordinates

are: coordinates measured from a common origin along axes that intersect (at the origin) at right angles. The horizontal axis normally is used to represent values of x. In two dimensions, the vertical axis is used to represent values of y. In three dimensions, the second horizontal axis is used to represent values of y, and the vertical axis to represent values of z. The convention is to refer to these as the x–axis, y–axis and z–axis. [MATH 1.3, MATH 2.2]

can be used: for any number of dimensions. [MATH 1.3, MATH 2.2]

Cartesian form (of a complex number)

represents: a complex number as a + ib with a and b real. [MATH 3.2]

Compare and contrast with exponential form and polar_form_of_a_complex_numberpolar form, and see complex numbers in the Maths For Science handbook for the relationship between these forms.

Cartesian form (of a vector)

is: the form in which a vector υ is represented as a vector sum of Cartesian component vectors: υ = υx + υy + υz or of scaled Cartesian unit vectors: υ = υxi + υyj + υzk or, equivalently, as an ordered triple of Cartesian scalar components: υ = (υx, υy, υz). [MATH 2.5]

See scalars and vectors in the Maths For Science handbook.

Cartesian representation (of a complex number)

See cartesian_form_of_a_complex_numberCartesian form.

Cartesian scalar components

of: a vector υ

are: the scalar quantities υx, υy and υz which appear in the expression for υ when given in the cartesian_form_of_a_vectorCartesian form υxi + υyj + υzk. [MATH 2.5]

are individually equal: to the projection of υ onto the corresponding Cartesian unit vector, so υx = υ i, etc. [MATH 2.6]

Cartesian sign convention

in: optics

is: a sign convention which takes the pole of a surface or the centre of a lens as the origin of a Cartesian coordinate system, ascribing positive signs to positions measured to the right or upwards, and negative signs to positions measured to the left or downwards of this origin. [PHYS 6.3]

Cartesian unit vectors

are: unit vectors in the mutually perpendicular directions of the Cartesian coordinate axes. Two such vectors are required in two dimensions, usually denoted by i and j in the directions of the x–axis and y–axis respectively. In three dimensions the three unit vectors are usually denoted i, j and k. [MATH 2.5]

cathode

of: a discharge tube or a similar device

is: an electrode connected to the negative terminal of a supply of electric current. [PHYS 8.1]

cathode rays

are: the ‘rays’ emanating from the cathode of a discharge tube containing gas at a sufficiently low pressure. [PHYS 8.1]

are in fact: high–speed flows of electrons, as shown by J.J. Thomson (1856–1940). [PHYS 8.1]

cation

is: a positively charged ion. [PHYS 8.4]

caustic curve

is: the curve formed by the superposition of rays from a lens or mirror which suffers from spherical aberration. [PHYS 6.4]

Cavendish’s experiment

is: an experiment to determine Newton’s universal gravitational constant, G, first performed by Henry Cavendish (1731–1810) in 1798. [PHYS 3.2]

cell

See electric cell, and (in the context of crystals) unit cell.

Celsius temperature scale

is: a nearly centigrade temperature scale which tracks the Kelvin temperature scale precisely. [PHYS 7.2]

is defined: in terms of the Kelvin temperature scale by TC/°C = T/K − 273.15, where T is an absolute temperature and TC is the corresponding Celsius temperature. [PHYS 7.2]

is named: after Anders Celsius (1701–1744). [PHYS 7.2]

centigrade

is: the description given to a temperature which is measured on a centigrade temperature scale. [PHYS 7.2]

centigrade temperature scale

is: any temperature scale based on a thermometric property X that uses a thermometric relation of the form

$T_{\rm cen} = \dfrac{X - X_0}{X_{100}-X_0} \times 100°{\rm centigrade}$ [PHYS 7.2]

will agree: with another centigrade scale at any fixed points (normally the freezing_pointfreezing and boiling points of water) that are common to both scales, but will not necessarily agree at any other points because different physical properties X may vary differently with temperature. [PHYS 7.2]

central force

is: a force that is always directed towards a fixed point (sometimes called the force centre) and which has the property that its magnitude_of_a_vector_or_vector_quantitymagnitude depends only on the distance from that point. [PHYS 2.4, PHYS 2.7, PHYS 2.8]

centre

of: a circle (or sphere)

is: the unique point that is at the same distance from every point on the circumference (or surface). [MATH 2.1, MATH 2.3]

is also: the unique point at which any two different diameters intersect. [MATH 2.1]

is more generally: the mid–point of a body or system.

centre of gravity

of: a rigid body in a gravitational field

only exists: if the gravitational field is uniform, or if the body has a sufficiently high degree of symmetry.

is: the point (fixed with respect to the body, but not necessarily within the body) at which the entire mass of the body can be considered to be concentrated for the purpose of determining the effect of gravitational forces on the body. [PHYS 2.3, PHYS 2.7]

is therefore: the point about which the gravitational forces produce no resultant torque irrespective of the orientation of the body. [PHYS 2.7]

is determined: by the gravitational forces acting on the body as well as the distribution of mass within the body, but will always coincide with the centre of mass for a body in a uniform gravitational field.

centre of mass

of: a rigid body

is: the point (not necessarily within the body) at which the entire mass of the body can be considered to be concentrated for the purpose of determining the translational motion of the body under an applied force. If the body is entirely free to move and the line of action of the force passes through the centre of mass, that force will cause translation of the centre of mass but not rotation about the centre of mass. [PHYS 2.3, PHYS 2.7, PHYS 2.8]

is determined: by considering the body to consist of (infinitesimal) mass elements Δmi at positions ri and then finding the point specified by rc, such that

$\displaystyle {\boldsymbol r}_c = \dfrac{\sum_i \Delta m_i{\boldsymbol r}_i}{\sum_i \Delta m_i}$ [MATH 5.4]

should not be confused: with the centre of gravity.

centrifugal force

is: a fictitious force with no physical basis in fact, invented to allow Newton’s laws of motion to be applied in a rotating frame of reference, which is a non-inertial frame of reference where Newton’s laws are otherwise invalid. [PHYS 2.3]

centripetal acceleration

of: a particle in uniform circular motion

is: an acceleration directed towards the centre of the circle

has magnitude: 2, where r is the radius of the circle and ω is the particleparticle’s angular speed. [PHYS 2.6, PHYS 3.2]

centripetal force

on: a particle in uniform circular motion

is: the force which is necessary to maintain the uniform circular motion. [PHYS 2.3]

is directed: towards the centre of the circle. [PHYS 2.3]

has magnitude: mrω2, where r is the radius of the circle, m is the mass of the particle and ω is its angular speed. [PHYS 2.6, PHYS 3.2]

chain rule

is: a rule used for differentiating a function of a function, such as f(g(x)). The rule states that if u = g(x) and y = f(u) so that y = f(g(x)) then

$\dfrac{dy}{dx} = \dfrac{dy}{du}\times\dfrac{du}{dx} = f'(u)\times g'(x)$ [MATH 4.3]

See the chain rule and its uses in the Maths For Science handbook.

change of phase

is: a process in which a substance changes from the solid phase, liquid phase or gaseous phase to one of the others. [PHYS 7.3]

changing the (dependent) variable

is: a technique used to transform a first–order differential equation into one that can be solved by a standard method such as separation of variables or use of an integrating factor. A new dependent variable is defined as an appropriate function of the old dependent variable and the independent variable. [MATH 6.2]

chaos

is: a property exhibited by deterministic systems which are described by certain non–linear differential equations (or sets of non–linear equations).

occurs: when two systems governed by the same non–linear differential equation but with slightly different initial states subsequently develop in completely dissimilar ways. [MATH 6.1]

characteristic emission spectrum

of: a chemical element

is: the emission spectrum from that chemical element and is unique to that chemical element. [PHYS 8.2]

often contains: prominent emission lines and is then referred to as the emission line spectrum of the chemical element. [PHYS 8.2]

characteristic X–ray spectrum

of: a heavy atom

is: the characteristic emission spectrum in the X–ray wavelength range from that atom and is unique to that kind of atom. [PHYS 8.3]

is produced: when an ejected inner shell (comparatively low energy) electron is replaced by an outer shell (comparatively high energy) electron, provided that the spacing between the energy levels is at least several thousand electronvolts. [PHYS 8.3]

charge

See electric charge.

charge carriers

are: mobile charged particles (e.g. electrons and ions) that can move within a material. [PHYS 4.1]

See hole.

charge sharing

is: the process by which a body can be charged by receiving some of the charge from another charged object with which it makes contact. [PHYS 3.3]

charge–to–mass ratio

for: a particle of charge q and mass m

is equal: to q/m. In the case of the electron the quantity e/m. is often referred to as the charge–to–mass ratio, even though the charge of the electron is actually q = −e. [PHYS 8.1]

Charles’ law

states: that at constant pressure, the volume V and absolute temperature T of a fixed quantity of ideal gas are related by V/T = constant. [PHYS 7.2]

chemical bonding

is: the binding together of chemical elements by forces that are fundamentally electromagnetic_forceelectromagnetic. [PHYS 8.4]

See covalent bonding, ionic bonding, metallic bonding.

chemical compound

is: a substance that consists of more than one element_chemicalelement, the atoms being bound together in a fixed ratio that is characteristic of the substance. [PHYS 8.1]

is also: a substance which can be broken down into more elementary substances by a process such as heating or the passing of an electric current. [PHYS 7.1]

chemical element

traditionally is: a substance which cannot be divided or separated by chemical means, including heating and passing of electrical current. [PHYS 8.1]

currently, is more appropriately defined: as matter consisting of atoms characterized by a single atomic number Z, which consequently contain a definite number of protons. (The atoms may be bound together to form molecules, as in the case of the diatomic oxygen molecule O2.) [PHYS 7.1, PHYS 8.1]

chemical formula

is: a formula such as H2O which uses chemical symbols to indicate the chemical elements involved in a chemical compound and subscripts to show the relative numbers of atoms of those chemical elements. [PHYS 8.1]

chemical reaction

is: a process in which bonds between atoms and molecules are made or broken with the result that materials are transformed.

chemical symbol

is: a symbol consisting of one or two letters that may be used to represent the name of a chemical element. The first letter is always upper case while the second, if there is one, is lower case. [PHYS 8.1]

is exemplified: by H for hydrogen, He for helium and Na for sodium. (See a copy of the periodic table for a complete list.) [PHYS 8.1]

chord

is: a straight line that cuts a curve at two points. [MATH 2.1, MATH 4.1, MATH 4.2]

chromatic aberration

is: aberration caused by the variation of the focal length of a lens with wavelength, as a result of dispersion. [PHYS 6.4]

appears as: coloured fringes seen on images. [PHYS 6.4]

ciliary muscles

make up: the ring of muscles surrounding the lens of the human eye. The focal length of the lens is changed as these muscles contract or relax. [PHYS 6.4]

circle

of: radius R

centred: on a point P

is: the locus of all points in a plane that are located at a distance R from P. [MATH 2.1, MATH 2.3, PHYS 3.2]

See equation of a circle.

circle of least confusion

is: the minimum but finite image size of a point object, which results from spherical aberration − in which the focal length of the lens varies with the radial distance of rays from the optical axis. [PHYS 6.4]

circuit

is: a continuous closed pathway, or network of pathways, along which electric charge may flow. [PHYS 4.1, PHYS 5.5]

circuit components

is: a general term for any of the many devices (e.g. capacitors, inductors, resistors) that might form part of a circuit.

circular

in: geometry

means: pertaining to a circle. [MATH 2.1]

circumference (of a circle)

is (1): the distance 2πR around a circle of radius R. [MATH 2.1]

is (2): the circle itself (as in ‘a point on the circumference’). [MATH 2.1]

See also perimeter.

classical mechanics

See Newtonian mechanics.

classical physics

is: that part of physics which includes and builds on Newtonian mechanics, Maxwell’s theory of electromagnetism, the laws of thermodynamics and (usually) relativity, but which specifically excludes quantum physics. [MATH 6.4, PHYS 10.2]

Clausius–Clapeyron equation

is: an equation that relates the slope (dP/dT) of the boundary curve between two phases on a PT diagram to the latent heat (ml) and change of volumeV) involved in an isothermal crossing of that boundary at temperature T:

$\dfrac{dP}{dT} = \dfrac{ml}{T\Delta V}$ [PHYS 7.4]

closed cycle

is: any succession of processes (which may be reversible or irreversible) which restores a system to its initial state. [PHYS 7.4]

codomain (of a function)

of: a function

is: that set within which can be found the range of values of the dependent variable which are generated by the function over its domain. [MATH 1.3]

coefficient

is: any one of the constants, a0, a1, a2, ... an−1 and an, that appear in a polynomial expression of the form a0 + a1x + a2x2 + ... + an−1xn−1 + anxn. [MATH 1.3, MATH 1.4]

is exemplified: by the coefficient of x3 in x4 − 5x3x2 + 4x + 2, which is −5.

coefficient of friction

See coefficient of sliding friction, coefficient of static friction.

coefficient of mutual inductance

of: a pair of coils (or circuits), or of a transformer,

is: the quantity M that relates the magnitude of the induced voltage in one coil to the rate of change of current, dI2/dt, in the other coil, through the equation

$V_1 = M\left\lvert\,\dfrac{dI_2}{dt}\,\right\rvert$. [PHYS 4.4]

has as its SI unit: the henry (H), where 1 H = 1 V s A−1.

often is abbreviated: to mutual inductance. [PHYS 4.4]

See also ‘mutual induction’. [PHYS 4.4]

coefficient of self inductance

of: a coil (or circuit)

is: the quantity L that relates the magnitude of the self induced voltage Vind in the coil to the rate of change of current dI/dt in the coil, through the equation

$V_{\rm ind} = L\left\lvert\,\dfrac{dI}{dt}\,\right\rvert$. [PHYS 4.4, PHYS 4.5]

has as its SI unit: the henry (H), where 1 H = 1 V s A−1. [PHYS 4.4, PHYS 4.5]

often is abbreviated: to self inductance or inductance. [PHYS 4.4, PHYS 4.5]

See also self–induction and inductance.

coefficient of sliding friction

for: an object sliding over a solid surface

is denoted: by μslide. [PHYS 2.3]

is: the ratio of the magnitude of the sliding frictional force on the object to the magnitude R of the reaction force on the object. [PHYS 2.3]

depends: on the surfaces involved and their state of lubrication. [PHYS 2.3]

is largely independent: of other factors, including the area of contact and the speed of the object. [PHYS 2.3]

usually is: smaller than the coefficient of static friction μstatic. [PHYS 2.3]

coefficient of static friction

for: an object on a solid surface, being prevented by friction from moving

is denoted: by μstatic. [PHYS 2.3, PHYS 2.6]

is: the ratio of the magnitude of the maximum frictional force on the object before it moves, to the magnitude R of the reaction force on the object. [PHYS 2.3, PHYS 2.6, PHYS 7.6]

depends: on the surfaces involved and their state of lubrication. [PHYS 2.3, PHYS 2.6]

is largely independent: of other factors, including the area of contact. [PHYS 2.3, PHYS 2.6]

usually is: larger than the coefficient of sliding friction μslide. [PHYS 2.3, PHYS 2.6]

coefficient of thermal conductivity

of: a substance (under strictly specified conditions of temperature and pressure)

is: the quantity κ that describes the relative ease with which heat is transferred through the material between points at different temperatures. [PHYS 11.4]

is defined: as κ in the relation (a special case of Fourier’s law)

$\dfrac{dQ}{dt} = -\kappa A\dfrac{T_2-T_1}{l}$

where dQ/dt is the rate of flow of heat along a well insulated bar of length l and uniform cross–sectional area A from an end at temperature T1 to an end at temperature T2. [PHYS 11.4]

has as its SI unit: W m−1 K−1.

See conduction (of heat) and Fourier’s law.

coefficient of viscosity

is: the quantity η that describes the relative difficulty with which a fluid may flow. [PHYS 7.6]

is defined: by the relation (a special case of Newton’s law of viscosity)

$\sigma_x = -\eta\dfrac{d\upsilon_x}{dy}$

where σx is the shear stress applied in a given direction, x/dy is the velocity gradient in a perpendicular direction, and the minus sign indicates that the velocity decreases with distance from the plane over which the shear stress is applied. [PHYS 7.6]

is sometimes called: the viscosity of the fluid. [PHYS 7.6]

has as its SI unit: kg m−1 s−1, or equivalently N s m−2 or Pa s.

coherence

between: waves

is: the property that enables phase differences known at one position or time to determine phase differences at other positions and times. [PHYS 5.3, PHYS 6.1]

coherent

describes: two waves related in such a way that knowing the phase of one at some particular time and position enables the phase of the other to be predicted at some position (if spatially coherent) or time (if temporally coherent) [PHYS 6.1]

may also be applied: in its temporal sense, to two oscillations. [PHYS 5.3]

coherent fibre bundle

is: an organized or stacked array of optical fibres, such that the relative position of each optical fibrefibre in the bundle is the same at either end of the bundle. [PHYS 6.2]

can be used: to transfer image information. [PHYS 6.2]

coil

is: a structure consisting of several loops (called turns) of wire wound in a similar sense to form a simple geometric shape, most typically a circular prism (cylinder) or a helix (solenoid), but possibly some other shape such as a rectangle.

coincident roots

of: an equation

are: repeated roots. (As, for example, the roots of the equation (x − 1)2 = 0 are repeated_rootrepeated and are therefore coincident at x = 0.) [MATH 1.4]

colinear

means: acting along the same line. [PHYS 5.1]

collimator

is: a device used to produce a parallel beam of radiation from a lamp or other source. An optical collimator usually consists of a converging lens with an illuminated slit or circular aperture placed at its focus. [PHYS 6.4]

forms: the first stage of a spectrometer. [PHYS 8.2]

collision

is: a brief but strong interaction between two particles or bodies which come into close proximity. [PHYS 2.4, PHYS 2.5]

coma

in: an image

is: the aberration which appears as a comet–like flaring at the edge of an extended image. It is the result of the focal length for non–axial rays varying with their point of incidence on a lens. [PHYS 6.4]

common denominator

of: two or more fractions

is: any number that is exactly divisible (without remainder) by the denominator of each of the fractions. [MATH 1.1]

can be obtained: by multiplying together the denominators of each of the fractions (though the result will not necessarily be the lowest common denominator).

common difference

See arithmetic progression.

common factor

of: two of more numbers or algebraic expressions

is: any number or algebraic expression which is a factor of each. [MATH 1.1]

common logarithm

is: a synonym for the logarithm to the base 10, i.e. log10. [MATH 1.5]

common ratio

See geometric progression.

common tangent

is: a straight line that is a tangent_to_a_curvetangent to two (or more) given curves. [MATH 2.1]

commutator

is: a device used to periodically reverse the current in a rotating coil, in order to maintain the direction of a magnetic torque on the coil. [PHYS 4.3]

complementary angles

are: two angles whose sum is 90°. [MATH 2.1]

complementary function

forms: part of the general solution to a second–order differential equationsecond–order linear_differential_equationlinear inhomogeneous differential equation with constant coefficients, of the form

$a\dfrac{d^2y}{dt^2}+b\dfrac{dy}{dt}+cy=f(x)$. [MATH 6.3]

is: the general solution to the corresponding linear homogeneous differential equation

$a\dfrac{d^2y}{dt^2}+b\dfrac{dy}{dt}+cy=0$. [MATH 6.3,PHYS 5.5]

completed square form

is: the form y = a(xp)2 + q of a quadratic function, y = ax2 + bx + c that makes clear the location of the vertex at (p, q) = (b/(2a), [cb2 /(4a)]). [MATH 1.3]

completely inelastic collision

is: a collision in which the maximum amount of kinetic energy is converted into other forms of energy, consistent with the principle of conservation of momentum. [PHYS 2.5]

completing the square

is: the procedure by which a quadratic function is expressed in completed square form. [MATH 1.3, MATH 1.4]

complex

means: pertaining to complex numbers.

complex capacitive reactance

of: a capacitor with capacitance C when passing alternating current of angular frequency ω

is given: by ZC = −i/ωC. [PHYS 5.5]

See complex impedance, capacitive reactance.

complex conjugate

of: a complex number, z = x + iy, (where x and y are real numbers)

is: xiy. [MATH 3.1, PHYS 5.5]

is denoted: by z*. [MATH 3.1, PHYS 5.5]

complex impedance

of: an electrical component or a network of such components subject to an alternating voltage of angular frequency ω

is: a complex quantity $\mathcal{Z}$ that determines the complex current $\mathscr{I}$ that flows in response to the complex voltage $\mathscr{V}$ through the relation $\mathscr{V} = \mathcal{Z}\mathscr{I}$. (It therefore determines the peak value and the phase lag of the sinusoidally varying current that flows in response to a sinusoidally varying voltage. [PHYS 5.5]

is given: for n (complex) impedances connected in series, by

$\mathcal{Z} = \mathcal{Z}_1 + \mathcal{Z}_2 + \dots + \mathcal{Z}_n$ [PHYS 5.5]

is given: for n (complex) impedances connected in parallel, by

$\dfrac{1}{\mathcal{Z}} = \dfrac{1}{\mathcal{Z}_1} + \dfrac{1}{\mathcal{Z}_2} + \dots + \dfrac{1}{\mathcal{Z}_n}$ [PHYS 5.5]

is given: for a single resistance by $\mathcal{Z} = R$; for a single inductance by $\mathcal{Z}_L = i\omega L$ and for a single capacitance by $\mathcal{Z}_C = -i/\omega C$. [PHYS 5.5]

See complex capacitive reactance and complex inductive reactance

complex inductive reactance

of: an inductor with inductance L when passing alternating current of angular frequency ω

is given: by $\mathcal{Z}_L = i\omega L$. [PHYS 5.5]

See complex impedance, inductive reactance.

complex number

is: an expression that may be written in the form x + iy, where x and y are real numbers and i is a symbol satisfying the algebraic rule i2 = −1, i.e. $i = \sqrt{-1\os}$. [MATH 1.4, MATH 3.1, PHYS 5.5, PHYS 10.3, PHYS 11.1]

complex plane

is: the set of all complex numbers or the representation of them on an Argand diagram. [MATH 3.1]

complex variable

is: a variable that may take on complex values.

component vectors

of: a vector

are: a number of vectors (usually orthogonal) whose vector sum is the original vector. [MATH 2.4, MATH 2.5]

should not be confused with: (scalar) components of a vector.

components of a vector

are: n scalar quantities (υx, υy, υz) that can be used to specify an n–dimensional vector in Cartesian form.

are sometimes referred to: as the scalar components, in order to emphasize their distinction from component vectors. [MATH 2.4, PHYS 2.1, PHYS 2.2]

should not be confused with: component vectors.

See projection.

composite function

is: a function obtained through the combination of two or more functions. Given two functions f(x) and g(x), the composite function f(g(x)) is obtained by replacing each occurrence of x in f(x) by g(x). [MATH 1.3, MATH 4.3]

is also called: a function of a function. [MATH 1.3, MATH 4.3]

compound

See chemical compound.

compound microscope

is: a microscope which consists of an objective lens and an eyepiece lens, although each of these may consist of several component lenses. [PHYS 6.4]

compression

is: the process of making something smaller in size.

is also: the force within the body of a compressed elastic spring, acting along the axis of the spring in order to restore the spring’s natural length. [PHYS 2.3]

also can mean: the externally applied force acting to compress such a spring. [PHYS 2.3]

also can mean: the difference in length between the uncompressed and the compressed spring. [PHYS 2.3]

also can mean: a region where pressure and hence density are higher than average. [PHYS 5.7]

Contrast with expansion and rarefaction.

Compton effect

is: the phenomenon involving the scattering of photons by an electron, which shows that each quantum of electromagnetic radiation has both energy and momentum. [PHYS 10.1]

Compton wavelength

for: a particle of mass m

is defined: as h/mc, where h is Planck’s constant and c is the speed of light. [PHYS 10.1]

appears: in the theory of the Compton effect. [PHYS 10.1]

is of the same order of magnitude: as the change in wavelength of the scattered photons. [PHYS 10.1]

concave downwards

describes: a function whose second derivative is less than zero throughout an interval. [MATH 4.4]

concave lens

is: a lens, shaped so that at least one of its surfaces curves inwards into the material. The centre is thinner than the edges. Usually the surfaces are spherical. [PHYS 6.3]

is also called: a diverging lens or a negative lens. [PHYS 6.3]

concave meniscus lens

is: a lens having two concave surfaces of different radii when viewed from one side and with the centre of the lens thinner than the edges. [PHYS 6.3]

concave mirror

is: a mirror shaped so that its reflecting surface curves inwards, away from the incoming light rays. [PHYS 6.3]

concave surface

is: a surface which bulges away from the object position, when viewed from that position. [PHYS 6.3]

concave upwards

describes: a function whose second derivative is greater than zero throughout an interval, i.e. a function where slope increases continually throughout the interval. [MATH 4.4]

concentric

describes: any two objects which have the same centre, used especially of circles and spheres. [MATH 2.1]

condensation

is: the process whereby a gas or vapour is converted into a liquid.

Contrast with evaporation.

conductance

of: a body of (electrical) resistance R

is: the reciprocal of the resistance, i.e. 1/R.

conduction (of electricity)

is: the process whereby electric charge flows from one part of a material to another

takes place: at the atomic level, mainly through the movement of electrons from atom to atom.

therefore is: a transport process.

conduction (of heat)

is: one of three processes (the other two being convection and radiation) in which heat can be transferred. [PHYS 7.3]

is operative: only in materials (gases, liquids and solids), i.e. not in a vacuum. [PHYS 7.3]

takes place: at the atomic level, through energy being passed from atom to atom by vibration and/or collision. [PHYS 7.3]

is driven: at the macroscopic level, by a temperature gradient, with heat being transferred from high temperature to low temperature. [PHYS 7.3, PHYS 7.5]

therefore is: a transport process. [PHYS 7.5]

sometimes is quantified: by Fourier’s law. [PHYS 7.3]

conduction band

in: the band theory of solids

is: the lowest energy band that would be completely unoccupied at absolute zero. [PHYS 11.4]

conduction electrons

in: the band theory of solids

are: those electrons that are relatively free to move through the solid and may therefore give rise to electrical conduction. [PHYS 11.4]

conductivity

of: a material

is: the reciprocal of the resistivity ρ of that material. [PHYS 4.1, PHYS 7.3]

has as its SI unit: (Ω m)−1, though S m−1 (i.e. siemens per metre) are also used. [PHYS 4.1, PHYS 7.3]

conductor (electrical)

See electrical conductor.

conductor (thermal)

is: a substance with a moderate to high coefficient of thermal conductivity, typically a metal, and usually also an electrical conductor.

cone

is: the shape formed by rotating a triangle about one of its sides. [MATH 2.3]

cones (of the eye)

are: one of two types of light sensor present in the eye, the other type being rods. PHYS 6.4]

provide: colour vision, being mainly sensitive to either red, green or blue light but being ineffective at low light levels. [PHYS 6.4]

confinement

See plasma confinement.

congruent

describes: two geometric figures which are identical in shape and size. [MATH 2.1]

conic section

is: the intersection of a cone with a plane. [MATH 2.3, PHYS 3.2]

can be defined: as the locus of all points P, such that the ratio of the distance from P to a fixed point (the focus), to the distance from P to a fixed line (the directrix), is constant. The value of this constant is known as the eccentricity e. The conic section is:

an ellipse if e < 1,
a parabola if e = 1,
an hyperbola if e > 1. [MATH 2.3]

also can be defined: as the shape described by any second degree equation of the form:

ax2 + 2hxy+by2 + 2gx + 2fy + c = 0

The conic section is:

an ellipse if h2 < ab,
a parabola if h2 = ab,
an hyperbola if h2 > ab. [MATH 2.3]

See conic sections in the Maths For Science handbook for further information.

conical pendulum

is: a mechanical system consisting of a mass, suspended from a point by a thread, undergoing uniform circular motion in a horizontal plane. [PHYS 2.3]

conics

See conic section.

conjugate equation

is: an equation which links object and image points for an optical element. [PHYS 6.3]

See conjugate equation for a single spherical surface and conjugate equation for a thin lens.

conjugate equation for a single spherical surface

is: an equation which links together the object distance and image distance and the radius of curvature of the spherical surface at which refraction occurs. [PHYS 6.3]

conjugate equation for a thin lens

is: an equation which links together the object distance and image distance and the radii of curvature of the lens surfaces at which refraction occurs. [PHYS 6.3]

conjugate planes

are: planes perpendicular to the optical axis, containing conjugate points. [PHYS 6.3]

conjugate points

are: object and image points linked by a conjugate equation. [PHYS 6.3]

conservation of angular momentum

is a principle which states: that when no unbalanced external torque acts on a body or a system of bodies, the total angular momentum of that body or system stays constant. [PHYS 2.8]

conservation of (electric) charge

is a principle which states: that the total net charge in the Universe is constant. Charges can be created and destroyed but only if the amounts of positive and negative charge involved are identical so that the net change is zero. [PHYS 3.3]

conservation of energy

for: an isolated system (which is therefore not subjected to unbalanced external forces)

is a principle which states: that the total amount of energy in the system is always constant (i.e. energy cannot be created or destroyed), although some or all of the energy may be converted from one form into another. [PHYS 2.4, PHYS 2.5]

See conservation of relativistic energy.

conservation of mass

for: a system that does not exchange any matter with its environment

is a principle which states: that the mass of the system is constant and is unaffected by position, velocity, temperature or any other factor. [PHYS 2.3]

is approximately true: when the velocity of the system is much less than the velocity of light. [PHYS 2.3]

See conservation of relativistic energy.

conservation of mechanical energy

for: an isolated system in which only conservative forces act

is a principle which states: that the total mechanical energy (i.e. the sum of the kinetic and potential energies) stays constant. [PHYS 2.4]

conservation of momentum

for: an isolated system (which is therefore not subject to unbalanced external forces)

is a principle which states: that the total momentum of the system is constant. [PHYS 2.5]

implies: that the total momentum of the system of objects does not change due to mutual interactions between the objects within the system. [PHYS 2.5]

conservation of nucleon number

is a principle which states: during radioactive decay, nuclear fusion and nuclear fission, the number of nucleons (sum of protons and neutrons) is constant.

conservation of relativistic energy

is: simply the conservation of energy, but named in this way to emphasize that quantities such as kinetic energy should be specified in the form required by Einstein’s special theory of relativity, and that contributions arising from mass energy should be included. [PHYS 9.1]

conservation principle (or law)

is: a law or principle which states that, at least under certain conditions, the value of a physical quantity remains fixed and does not vary in time. [PHYS 2.4, PHYS 9.1]

is exemplified: by conservation of mass, conservation of charge, conservation of energy, conservation of momentum and conservation of angular momentum. [PHYS 2.4, PHYS 9.1]

conservative force

is: a force which may be associated with a unique value of potential energy at each point in space and for which the work done between any two points is independent of the path chosen. As a result, the work done by the force around any closed path is zero. [PHYS 2.4, PHYS 11.2]

is exemplified by: gravitational forces, and electrostatic forces. [PHYS 2.4, PHYS 11.2]

conserved quantity

describes: any quantity that has the same value at the beginning and end of a wide class of processes, so that it might be made the subject of a suitably formulated conservation law. [PHYS 2.5]

constant

means: independent of time.

is also: a quantity whose value does not change in the course of a calculation. [MATH 1.1, MATH 1.3]

may be: a physical constant, e.g. Planck’s constant or the speed of light in a vacuum.

may be: a mathematical constant, e.g. π or e.

Contrast with variable.

constant acceleration

See uniform acceleration.

constant acceleration equations

See uniform acceleration equations.

constant addition rule (for summation)

for: any constant a and any positive integer N

is: $\displaystyle \sum_{i=1}^N (x_i+a) = \sum_{i=1}^N x_i + Na$ [MATH 1.7]

constant field

is: a field that does not change with time. [MATH 2.6, PHYS 3.3]

constant multiple rule (for integration)

for: any constant a

is: $\int af(x)\,dx = a\int f(x)\,dx$. [MATH 5.2]

constant multiple rule (for summation)

for: any constant a and any positive integer N

is: $\displaystyle \sum_{i=1}^N ax_i = a\sum_{i=1}^N x_i$ [MATH 1.7]

constant multiple rule (for differentiation)

for: any constant a

is: $\dfrac{d}{dx}\left(af(x)\right) = a\dfrac{d}{dx}\left(f(x)\right)$ [MATH 4.2]

constant of integration

is: the arbitrary constant introduced by the process of indefinite integration. [MATH 5.1, MATH 5.2]

is exemplified: by the constant C in the equation $\int x\,dx = \dfrac{x^2}{2} + C$

constant of proportionality

between: two variables x and y which are proportional (i.e. xy )

is: the constant k such that x = ky. [MATH 1.1, PHYS 1.3]

does not depend: on the values of x and y though it may depend on the values of other variables that are independent of x and y. [MATH 1.1, PHYS 1.3]

constant speed

See uniform speed.

constant velocity

See uniform velocity.

constant–volume gas thermometer

is: a thermally sensitive device in which the pressure of a gas, constrained to a constant volume, is used as a thermometric property. [PHYS 7.2]

is: not particularly convenient to use, but occupies a central role in defining precise scales for the measurement of temperature. [PHYS 7.2]

defines: a gas scale which is intimately related to the thermodynamic Kelvin scale, which is the most fundamental of all temperature scales because it is totally independent of the material (gas, liquid, or solid) and the thermometric property chosen. [PHYS 7.2]

construction line

is: an imaginary line added to a diagram to help in explanation, proof or problem solving. [PHYS 2.7]

constructive interference

is: the condition in which the superposition of two oscillations or waves produces a resultant with larger amplitude than either of the original oscillations or waves. When the two oscillations or waves are in phase, the amplitude of their resultant is the sum of their amplitudes. [PHYS 5.1, PHYS 5.6, PHYS 5.7, PHYS 6.1]

constructive superposition

See constructive interference.

continuous spectrum (emission or absorption)

of: electromagnetic radiation (usually from a specified source)

is: a spectrum that is (relatively) smooth and unbroken over a wide continuous range of wavelengths. [PHYS 8.2]

is typical: of the emission spectrum from a solid or liquid heated to a high temperature. [PHYS 8.2]

is exemplified: by white light, which can be dispersed by a diffraction grating or a prism into all the colours of the rainbow. [PHYS 8.2]

is also exemplified: by the black–body spectrum. [PHYS 8.2]

continuous flow method

is: a standard calorimetry procedure that can be used to measure specific heats of fluids. [PHYS 7.4]

involves: a fluid flowing at a constant known rate past a heater delivering a known power which produces a rise in temperature between the inlet and outlet. [PHYS 7.4]

continuous function

is: a function whose graph has no breaks. [MATH 4.4]

continuous refraction

is: a phenomenon that can occur in a region of a medium where the refractive index varies smoothly with position. [PHYS 6.2]

can cause: an appropriately directed ray to change its direction continuously. [PHYS 6.2]

continuous variable

is: a variable that changes only in a smooth fashion (with no sudden jumps in its value). [MATH 1.3]

continuous X–ray spectrum

is: the spectrum of X–rays that results when electrons are accelerated through a potential difference of several thousand volts and then strike a target. [PHYS 8.3]

is created: as the electrons come to rest. Because the energy of the electrons in the target ranges from zero to a maximum value, the energy of the X–rays emitted will also vary continuously from zero up to a maximum. [PHYS 8.3]

also known as: bremsstrahlung Contrast with characteristic X–ray spectrum.

continuum

is: the continuous range of available energies for an electron moving under the influence of an atom or ion to which it is not bound. The electron is sometimes said to be in an unbound state of the atom or ion. [PHYS 8.2]

can be contrasted: with the discrete energy levels of the bound states of the atom which the electron might otherwise occupy. [PHYS 8.2]

is reached: by a bound electron which is given sufficient energy to exceed the ionization level of the atom or ion and therefore to escape from it. [PHYS 8.2]

continuum level

See ionization level.

contraction

is: the process of making something smaller is size.

control rod

is: a rod of a material that readily absorbs thermal neutrons. [PHYS 9.3]

is lowered: into a nuclear fission reactor to control or stop the nuclear chain reaction. [PHYS 9.3]

convection

is: one of three processes (the other two being conduction and radiation) in which heat can be transferred. [PHYS 7.3]

operates: only in fluids (i.e. gases and liquids), where the relative movement of parts of the fluid at different temperatures is the means by which heat is carried from hot regions to cold regions. [PHYS 7.3]

is classified: in two broad categories: ‘forced convection’, in which the fluid is being moved by external means (a breeze blowing across your face, or a coolant being pumped past a hot object), and ‘free convection’, in which the flow is induced by buoyancy caused by thermal expansion of hotter regions of the fluid relative to cooler regions (around fins designed to cool the electronics in your hi–fi amplifier, in central heating by electric convectors or, despite their common name, by water–filled radiators). [PHYS 7.3]

involves: a generally very complicated relationship between heat flow and temperature difference, depending on temperature difference in a non-linear way and on other factors including many thermal properties of the fluid and the geometry and orientation of the object exchanging heat with the fluid. There are many empirical formulae employed by engineers for situations commonly encountered, but when in doubt, or when information is lacking, the best one can do is to use Newton’s law of cooling dQ = hA ΔT where dQ/dt is the rate of heat dt flow between two surfaces of area A that differ in temperature by an amount ΔT, and h is an appropriately chosen convective heat transfer coefficient. [PHYS 7.3]

convective heat transfer coefficient

See convection.

converge

See convergent series and convergent sequence.

convergent integral

is: an improper integral with a finite value. [MATH 5.2]

convergent sequence

is: a sequence, S1, S2, S3, S4, ... all of whose members, beyond some particular member, are as close as we please to some particular number. This number is called the limit of the sequence. [MATH 1.7]

convergent series

is: a series whose partial sums form a convergent sequence. The limit of a sequence of partial sums is known as the sum of the series. [MATH 1.7]

converging lens

is: a lens which increases the convergence or reduces the divergence of light rays passing through it. [PHYS 6.3]

is also called: a convex lens or a positive lens. [PHYS 6.3]

conversion factor

is: a dimensionless factor, such as (103 m/km), which is actually equal to one, but which is expressed as a ratio of two quantities which have different units. [PHYS 1.1]

can be used: to convert a quantity expressed in terms of certain units into an equivalent quantity expressed in terms of other units. [PHYS 1.1]

convex lens

is: a lens, shaped so that at least one of its surfaces curves outwards, away from the centre of the material. The centre is thicker than the edges. Usually the surfaces are spherical. [PHYS 6.3]

is also called: a converging lens or a positive lens. [PHYS 6.3]

convex meniscus lens

is: a lens having two convex surfaces of different radius of curvature when viewed from one side, and with the centre of the lens thicker than the edges. [PHYS 6.3]

convex mirror

is: a mirror shaped so that its reflecting surface curves outwards, towards the incoming light rays. [PHYS 6.3]

convex surface

is: a surface which bulges towards the object position, when seen from that side. [PHYS 6.3]

coolant

in: a nuclear fission reactornuclear reactor

is: a fluid (liquid or gas) that keeps a reactor cool and transfers the energy released in the reactor so that it may be used to produce steam and hence drive electricity generators. [PHYS 9.3]

coordinate axes

See Cartesian coordinates.

coordinate system

is: a system for associating a set of values, called coordinates, with points in space so that each point may be uniquely identified and distinguished from every other point.

See Cartesian coordinates, polar coordinates and spherical polar coordinates.

coordinates

of: a point

are: the (unique) set of values associated with that point by a coordinate system that distinguish that point from other points.

are exemplified by: the x- and y–coordinates of a point on a graph. [PHYS 1.3]

Copenhagen interpretation

is: the most commonly accepted view of quantum physics. [PHYS 10.2]

holds that: the Universe operates according to probabilistic laws which tell us as much as can be known, even in principle, about future events. [PHYS 10.2]

was formulated: by a group of scientists (including Heisenberg) who worked in Copenhagen in the 1920s. [PHYS 10.2]

contrasts: with the many universe interpretation.

coplanar

means: in the same plane. [PHYS 2.7]

correspondence principle

states: that in the classical limit the predictions of quantum mechanics are in agreement with those of (non-relativistic) classical physics. [PHYS 11.2, PHYS 11.3]

corkscrew rule

is: a rule for working out the direction of a vector product such as a × b.

states that: if the handle of a (right–handed) corkscrew is aligned with the vector a and oriented in such a way that its handle may be twisted into alignment with b by turning it through an angle less than 180°, then the direction of a × b is the direction in which the corkscrew would advance.

more briefly states: the direction of a × b is the direction of advance of a corkscrew as its handle is rotated from a to b. [MATH 2.7, PHYS 4.3]

Compare with the right–hand screw rule and the (preferred) right–hand rule.

cornea

is: the transparent protective outer covering to the eye. [PHYS 6.4]

is: the first surface at which refraction takes place for light entering the eye. [PHYS 6.4]

corresponding angles

See transversal.

cosecant, cosec

See trigonometric function.

cosech

See hyperbolic function.

cosh

See hyperbolic function.

cosine rule

states: that given a triangle with angles A, B and C opposite to sides a, b and c then c2 = a2 + b2 − 2abcosC. Likewise a2 = b2 + c2 − 2bccosA and b2 = a2 + c2 − 2accosB. [MATH 1.6]

reduces: to Pythagoras’s theorem when the chosen angle is 90°.

See trigonometric functions in the Maths For Science handbook for further details.

cosine, cos

See trigonometric function.

cosmic rays

are: high energy particles (mainly protons) which enter the Earth’s upper atmosphere from space. They may collide with nuclei in the atmosphere, producing radioactive isotopes. [PHYS 9.3]

cotangent, cot

See trigonometric function.

coth

See hyperbolic function.

Coulomb force

See electrostatic force and Coulomb’s law. [PHYS 3.3]

Coulomb’s law

is: the law, first formulated by Charles Augustin de Coulomb (1736–1806), which describes the electrostatic force between charged particles. [PHYS 3.1]

states that: for two particles of charge q1 and q2 separated by a distance r, the force on particle 2 due to particle 1 is

$F_{\rm el} = \dfrac{q_1q_2}{4\pi\varepsilon_0r^2}\hat{\boldsymbol r}$

where ε0 is the permittivity of free space, q1 and q2 are signed quantities, and r^ is a unit vector pointing from q1 to q2. The direction of the force is therefore along the line joining the charges, and like charges repel while unlike charges attract. [PHYS 3.3]

coulomb, C

is: the SI unit of charge.

is defined: as the amount of charge transferred when a current of 1 ampere flows for 1 second, so 1 C = 1 As. [PHYS 3.3]

couple

is: a pair of forces of equal magnitude acting in opposite directions along different lines of action. [PHYS 2.7, PHYS 4.3]

may be characterized: by a non–zero torque about any point, the magnitude of which is equal to the magnitude of either one of the forces multiplied by the perpendicular distance between their lines of action. [PHYS 2.7]

causes: rotation but not translation, when applied to rigid body that is entirely free to move [PHYS 2.7]

coupled oscillators

are: two oscillators connected in such a way that the displacement of one oscillator affects the restoring force acting on the other. [PHYS 5.1, PHYS 5.3]

exhibit: normal modes. [PHYS 5.1, PHYS 5.3]

may be generalized: to a system of many oscillators.

covalent bond

is: a bond in which one or more electrons is shared between two (or more) atoms. [PHYS 11.4]

covalent bonding

is: a type of chemical bonding in which the chemical bonds are created by electron pairs shared between atoms. [PHYS 8.4]

has typical energy: of 1 to 5 eV. [PHYS 7.1]

is characterized: by an increased electron density between the nuclei of the atoms. [PHYS 11.4]

creep

is: the condition in which the strain in a material exhibits a slow time- dependence under constant stress in the region of plasticity. [PHYS 7.6]

critical

describes: the condition inside a nuclear reactor (or similar device) in which a nuclear chain reaction is just able to self–sustain at a steady rate, i.e. where, on average, exactly one neutron released in the fission of one nucleus goes on to produce fission in one further nucleus. [PHYS 9.3]

Contrast with subcritical, supercritical.

critical angle

for: light rays passing from a medium of given refractive index into a medium of lesser refractive index

is: the minimum angle of incidence that corresponds (via Snell’s law) to an angle of refraction of 90°. A ray meeting the interface at a greater angle of incidence will suffer total internal reflection unless special steps are taken to frustrate the process. [PHYS 5.7, PHYS 6.2]

critical damping

is: the condition in which a damped oscillator just fails to oscillate and comes to rest in the shortest possible time following release from a given position. It is the intermediate condition between light damping (i.e. underdamping) and heavy damping (i.e. overdamping). [PHYS 5.2]

is accompanied by: no more than one overshoot of the equilibrium value before coming to rest.

is exemplified electrically: by a series a.c. circuit containing a capacitor of capacitance C, an inductor of inductance L, and a resistor of resistance R, wherein the damped oscillations of stored charge (or current) are critically damped when $R = 2\sqrt{L/C}$. [PHYS 5.4]

is exemplified mechanically: by a damped mechanical oscillator containing an oscillating body of mass m, a spring of spring constant k, and a linear damping force with damping coefficient b, wherein oscillations are critically damped when $b = 2\sqrt{km}$. [PHYS 5.4, PHYS 5.5]

is described by: x(t) = (H + Jt)eγt/2 where γ = b/m for a mechanical oscillator, and γ = R/L for an electrical oscillator. H and J are constants determined by the initial conditions.

critical mass

is: the mass of a fissile material that is just capable of maintaining a nuclear chain reaction. [PHYS 9.3]

therefore is: the mass of a fissile material that is just capable of keeping a nuclear chain reaction at the critical condition. [PHYS 9.3]

critical opalescence

is: a phenomenon displayed by normally transparent fluids under the conditions that define the critical point. Illuminated by a beam of light, the substance takes on an intensely white, diffuse cloudy appearance. [PHYS 7.4]

critical point

of a substance

is: the unique point on a PVT–surface (or some similar surface), or on one of its projections, representing the state in which the liquid and vapour phases of a substance become indistinguishable. [PHYS 7.4]

See also critical opalescence.

critical pressure

is: the pressure of a substance at its critical point. [PHYS 7.4]

critical temperature

is: the temperature of a substance at its critical point.

is also: the maximum temperature at which a gas can be liquefied by an isothermal process. [PHYS 7.4]

critical volume

is: the volume of a substance at its critical point. [PHYS 7.4]

critically damped

See critical damping.

cross product

See vector product.

cross–sectional area

generally is: the area of intersection of a geometrical solid and a plane. Usually the plane is normal to an axis of symmetry, but could be some other specified direction. [MATH 2.1]

See also prism.

crown glass

is: a glass of relatively low refractive index and thus low dispersive power. [PHYS 6.4]

is used as a component: in an achromatic doublet. [PHYS 6.4]

crystal

is: any material with a crystalline structure.

crystalline structure

is: a regular array of atoms in three–dimensional space that can be described by associating the same arrangement of one or more atoms with every point of a given three–dimensional lattice. [PHYS 11.4]

cubic equation

is: a polynomial equation of degree 3. [MATH 1.4]

cubic function

is: a polynomial function of degree 3. [MATH 1.3]

cuboid

is: any rectangular block. [MATH 2.1]

current

See electric current.

current balance

is: a device designed to measure the force between two current–carrying coils or wires. [PHYS 4.3]

can be used: to measure currents accurately and hence to determine the current of magnitude one ampere. [PHYS 4.3]

current divider equations

are: a pair of equations which describe the way in which an electric current is divided between two resistors in parallel. [PHYS 4.1]

curve

is: a continuous set of points, often (though not necessarily) in a plane.

cut–off wavelength

of: a continuous X–ray spectrum.

is: the sharply defined wavelength, below which there is no continuous spectrum. [PHYS 8.3]

corresponds to: the situation in which the maximum kinetic energy of an incident electron is entirely radiated away as a single X–ray photon. [PHYS 8.3]

cycle

of: a periodic motion (or a more general oscillation)

is: the motion or behaviour which occupies exactly one period. [PHYS 5.1]

cyclotron

is: a device which can accelerate charged particles by applying a periodic electric field to the particle as it moves, constrained in a circular or spiral path, by an applied magnetic field. [PHYS 4.3]

cyclotron frequency

is: the frequency of the circular or helical motion of a charged particle in a uniform magnetic field. [PHYS 4.3]

is dependent: only on the particleparticle’s charge–to–mass ratio q/m and on the magnetic field strength B:

$f_{\rm cyclotron} = \dfrac{\left\lvert\,q\,\right\rvert B}{2\pi m}$. [PHYS 4.3]

cyclotron motion

of: a charged particle

in: a magnetic field

is: the periodic motion of the particle in the plane perpendicular to the magnetic field. [PHYS 4.3]

cyclotron period

is: the time to complete one period of cyclotron motion and the reciprocal of the cyclotron frequency. [PHYS 4.3]

d’Alembert’s ratio test

is: one of several tests for the convergence or divergence of a series. If an is the nth term in the series, the test consists of calculating:

$\displaystyle R = \lim_{n\to\infty}\left(\dfrac{a_{n+1}}{a_n}\right)$

There are three possible outcomes:

R < 1 implying convergence,
R > 1 implying divergence,
R = 1 implying that the test is incapable of providing a definite answer.

[MATH 1.7]

DC circuit, d.c. circuit

is: an electrical circuit in which a direct current flows, or may be presumed to flow. [PHYS 4.1]

DC isolation, d.c. isolation

of: two circuits

is: their separation such that they may have independent d.c. potentials but yet may be mutually influenced by each other’s a.c. currents. [PHYS 4.4]

can be achieved: via the mutual inductance between the circuits, through a transformer or via a capacitor. [PHYS 4.1, PHYS 4.4, PHYS 5.4]

damped (electrical) oscillator

is: an electrical system in which a quantity such as charge or current exhibits oscillatory behaviour while energy is dissipated to the environment.

is exemplified: by a circuit in which an inductance L, capacitance C, and resistance R are connected in series, so that the charge q stored in the capacitor at time t obeys the differential equation:

$L\dfrac{d^2q}{dt^2} = -\dfrac1Cq - R\dfrac{dq}{dt}$

and is consequently described, in the case of light damping (R2 < 4L/C), by an oscillation with an exponentially decaying amplitude:

q(t) = q0eγt/2cos(ωt + ϕ)

where γ = R/L, $\omega = \sqrt{\dfrac{1}{LC}-\dfrac{R^2}{4L^2}}$ and q0 and ϕ are arbitrary constants. [PHYS 5.4, PHYS 5.5]

See critical damping. [PHYS 5.4, PHYS 5.5]

damped oscillator

See damped (electrical) oscillator, damped (mechanical) oscillator.

damped (mechanical) oscillator

is: a mechanical system in which a quantity such as displacement exhibits oscillatory behaviour while energy is dissipated to the environment.

is exemplified: by a particle of mass m on a spring of spring constant k, moving subject to a damping force with damping coefficient b so that its displacement from equilibrium, x, at time t satisfies the equation of motion:

$m\dfrac{d^2x}{dt^2} = -kx -b\dfrac{dx}{dt}$

and is consequently described in the case of light damping (b2 < 4mk) by an oscillation with an exponentially decaying amplitude:

x(t) = x0eγt/2cos(ωt + ϕ)

where γ = b/m, $\omega = \sqrt{\dfrac km - \dfrac{b^2}{4m^2}}$ and x0 and ϕ are arbitrary constants. [PHYS 5.2, PHYS 5.5]

See critical damping and heavy damping.

damped oscillation

See damped (electrical) oscillator, damped (mechanical) oscillator.

damping

is: any phenomenon involving dissipation (such as friction, viscosity or electrical resistance) that causes a system (particularly an oscillating system) to lose energy. [MATH 6.3, PHYS 5.2, PHYS 5.4]

See damping force, damping constant.

damping coefficient

is: the constant b that appears in the equation for a linearly damped harmonic oscillator: $m\dfrac{d^2x}{dt^2}+b\dfrac{dx}{dt}+kx=0$

damping constant

for: an oscillating particle of mass m subject to a dissipative force of magnitude , where υ, is the speed of the particle

is given: by γ = b/m. [PHYS 5.2]

is equal: to twice the decay constant α for the amplitude of the oscillation. [PHYS 5.2]

See damping force, damped mechanical oscillator.

damping force

in: a mechanical oscillator.

is: a dissipative force which opposes the motion and which therefore causes damping. [MATH 6.3, PHYS 5.2, PHYS 5.4]

See damping constant.

data

is: recorded information, particularly numerical or statistical information that can be used in an analysis or calculation.

daughter isotope

See daughter nucleus.

daughter nucleus

is: an isotope produced in the radioactive decay of a parent nucleus. [PHYS 9.2]

de Broglie hypothesis

states: that the propagation of all matter is determined by an associated de Broglie wave, from which the diffraction and interference behaviours may be predicted. [PHYS 10.2]

de Broglie wave

is: a wave associated with the propagation of matter. [PHYS 10.2]

can be used: to predict the diffraction and interference behaviours of matter. [PHYS 10.2]

See de Broglie wavelength.

de Broglie wavelength

of: a particle or, more generally, of a free quantum

is given: by λdB = h/p, where p is the magnitude of the momentum of the particle and h is Planck’s constant. [PHYS 10.2, PHYS 11.1, PHYS 11.2]

determines: the diffraction when the quantum meets an obstacle. [PHYS 11.1, PHYS 11.2]

Debye model

is: a model of the specific heats of solids

postulates: that the solid behaves like an elastic body capable of exhibiting quantized oscillations characterized by a specific distribution of classical frequencies. [PHYS 11.4]

predicts: that near absolute zero the specific heat is proportional to T3, where T is the absolute temperature. [PHYS 11.4]

decay

is: a general term describing the tendency to decrease with time.

See decay constant.

decay channels

are: the different ways in which a particular radioactive nucleus may decay. [PHYS 9.3]

decay constant

is: the constant of proportionality, α that relates the rate of radioactive decay, R to the number, N of unstable nuclei present: R = αN. [PHYS 9.2]

is: a property of radionuclides, unaffected by the physical or chemical environment. [PHYS 9.2]

more generally is: the reciprocal of the time constant τ in any exponential decay process: A(t) = A0eαt = A0et/τ. [PHYS 5.2]

deceleration

is: the slowing down of an object, and an associated reduction in speed. [MATH 4.1, PHYS2.1]

is commonly misconstrued: as negative acceleration. This may be, but is not necessarily, the case, since acceleration is a vector quantity and has an associated sign. [PHYS 2.1]

decibel, dB

is: a unit of (acoustic) intensity level. [PHYS 5.7]

permits representation: of intensity level in terms of a reference intensity level: given a sound of intensity I (measured in W m−2), its intensity level is given by

$\beta = 10 \times \log_{10}\left(\dfrac{I}{I_0}\right)$ decibel

where I0 = 1 × 10−12 W m−2. Audible, non–painful sounds usually have intensity levels in the range 0 to 120 dB. [PHYS 5.7]

decimal number

is: a number expressed in base ten notation, so that 345.6 means 3 × 102 + 4 × 101 + 5 × 100 + 6 × 10−1. [MATH 1.2]

decimal notation

is: a way of representing integer and real numbers. [MATH 3.2]

consists: of a string of one or more base ten digits in the case of an integer number.

consists: of a string of one or more base ten digits, a decimal point and then another string of base ten digits in the case of an real number. The total number of digits after the decimal point is the number of significant figures, and is often used to denote the precison of a numerical value [MATH 1.2, MATH 1.5, PHYS 1.1]

may be: preceeded by a minus (-) or a plus (+) symbol to indicate whether the number is less than or greater then zero, respectively.

compare with: scientific notation.

decimal places

describes: the number of digits which a decimal number has after the decimal point. [MATH 1.2]

decreasing function

is: a function f(x) for which f(a) > f(b) for all a < b. [MATH 4.4]

exists: on an interval if f′(x) is negative at all points of the interval. [MATH 4.4]

definite integral

of: a function f(x) defined on an interval from x = a to x = b

is denoted: $\displaystyle \int_a^b f(x)\,dx$

where the values a and b are known as the lower and upper limits of integration, f(x) is called the integrand, and the symbol dx is the element of integration which shows that x is the integration variable with respect to which the integration is to be performed. [MATH 5.1, MATH 5.2, PHYS 2.4]

is defined: by the limit of a sum:

$\displaystyle \int_a^b f(x)\,dx = \lim_{\Delta x\to0}\left(\sum_{i=1}^n f(x_i)\,\Delta x_i\right)$ with Δxi = xi+1xi

where the sequence of values x1, x2, ... xn+1 is such that a = x1 < x2 < ... < xn+1 = b, and Δx is the largest of the Δxi. [MATH 5.1, MATH 5.2,PHYS 2.4]

may be interpreted: for a given function between given limits, as the area under a graph of that function between the given limits, provided that due regard is paid to signs (areas of regions below the horizontal axis must be treated as negative quantities). [MATH 5.1, MATH 5.2, PHYS 2.4]

can be evaluated: according to the fundamental theorem of calculus using

$\displaystyle \int_a^b f(x)\,dx = \left[F(x)\right]_a^b = F(b) - F(a)$

where F(x) is any indefinite integral of f(x) (i.e. any function F(x) that satisfies dF/dx = f(x)). [MATH 5.1, MATH 5.2, PHYS 2.4]

also can be evaluated: by means of numerical integration. [MATH 5.1, MATH 5.2, PHYS 2.4]

degeneracy

is: the phenomenon in which different quantum states of a system (e.g. the states of electrons in an atom) have the same characteristic energy and therefore belong to the same energy level of the system. [PHYS 8.3]

therefore is also: the existence of more than one independent wavefunction, characterized by different sets of quantum numbers, corresponding to the same energy level. [PHYS 10.3]

degenerate

describes: an energy level or a wavefunction, when degeneracy is present. [PHYS 10.3]

degree, °

is: the unit of plane angle corresponding to 1/360th of a circle, written as 1°. In other words, a rotation through 360° is a full rotation.

is equal: to 0.01745 radian, (to five decimal places). [MATH 1.6] [MATH 2.1]

degree Celsius, °C

is: a non-SI unit of temperature and temperature difference.

is defined: to be equal in size to the SI unit of absolute temperature, the kelvin (K), but the zeros of the thermodynamic Kelvin temperature scale and the Celsius temperature scale are different (0 °C = 273.15 K).

degree (of a differential equation)

is: the highest power_mathematicalpower to which the highest order of derivative in the differential equation is raised. [MATH 6.1]

for: a linear differential equation is equal to 1. [MATH 6.1]

degree (of a polynomial)

is: the integer n that appears in a polynomial expression of the form a0 + a1x + a2x2 + ... + an−1xn−1 + anxn = 0, that is, the highest power_mathematicalpower of the variable in the polynomial expression. [MATH 1.3, MATH 1.4]

degrees of freedom

of: a system

are: the characteristics of a system’s configuration that can be varied independently. [PHYS 5.1]

are exemplified: by the three position coordinates that determine the location of a particle in three–dimensional space.

correspond: to the independent variables required to describe the motion of the system fully. [PHYS 7.5]

are reduced: by constraints in the system which limit the possible motions. For instance, a system consisting of two independent particles has six degrees of freedom, but a ‘dumb–bell’ in which two particles are separated by a fixed distance has only five degrees of freedom (these can be thought of as three translational and two rotational degrees of freedom). [PHYS 7.5]

Demoivre’s theorem

states: that for any real number, n

[cos(θ) + isin(θ)]n = cos() + isin() [MATH 3.3, PHYS 5.5]

denominator

is: the number or expression at the bottom of a fraction. [MATH 1.1]

density

of: a uniform body of mass M and volume V

is: the mass per unit volume of the body, M/V

is defined more generally: at a point in a (possibly non-uniform) body by

$\displaystyle \rho = \lim_{\Delta V\to 0}\left(\dfrac{\Delta m}{\Delta V}\right)$

where Δm is the mass of a small element of the body, of volume ΔV centred on the specified point.

dependent error

in: a measurement

when: the errors arising in the measurement are being analysed

is: any error whose size is determined, wholly or partly, by the size of another. [PHYS 1.2]

See uncertainty.

dependent variable

in: an experiment (or a calculation)

is: the quantity whose value is monitored by the experimenter (or by the person doing the calculation). [PHYS 1.3]

is controlled by: the value of the independent variable to which it is connected by a set of experimental observations (or by a mathematical function). [MATH 1.3]

on graphs is plotted: conventionally along the vertical axis. [PHYS 1.3]

depth of field

is: the range of distances of an object from a lens, for which the image will appear to be sharp for a particular lens position. [PHYS 6.4]

increases: as the lens aperture is reduced in size. [PHYS 6.4]

Contrast with depth of focus.

depth of focus

is: the range of lens positions for which the image of an object will appear to be sharp for a particular distance of the object from the lens. [PHYS 6.4]

increases: as the lens aperture is reduced in size. [PHYS 6.4]

Contrast with depth of field.

derivative

of: a function y = f(x)

is: its rate of change with respect to x at any particular value of x

is given by:

$\displaystyle f'(x) = \dfrac{dy}{dx} = \lim_{\Delta x\to0}\left(\dfrac{\Delta y}{\Delta x}\right) = \lim_{\Delta x\to0}\left[\dfrac{f(x+\Delta x)-f(x)}{\Delta x}\right]$

where f′(x) is known as the first derivative or derived function.

is defined: over any domain in which a unique limit exists for all values of x. [MATH 4.1, MATH 4.2, PHYS 2.1]

derived function

See derivative.

derived units

are: SI units created by specified combinations of the base units. [PHYS 1.1]

See Table 2 in Section 0 of the Maths For Science handbook for a detailed listing.

destructive interference

is: the condition in which the superposition of two oscillations or waves results in an oscillation or wave with smaller amplitude than either of the original oscillations or waves. When the two oscillations or waves are in anti–phase, the amplitude of their resultant is the difference of their amplitudes. [PHYS 5.1, PHYS 5.6, PHYS 5.7, PHYS 6.1]

also known as: destructive superposition.

destructive superposition

See destructive interference.

determinism

is: a belief that the Universe operates according to laws whose nature is such that the state of the Universe at one time completely determines its state at any later time. [PHYS 10.2]

deterministic system

is: a system for which a complete knowledge of the laws governing it and of its initial state allows its subsequent evolution in time to be predicted exactly. [MATH 6.1]

deuterium

is: the isotope of hydrogen that has mass number A = 2. [PHYS 9.3]

is also called: heavy hydrogen. [PHYS 9.3]

deuteron

is: a deuterium nucleus, 21H. [PHYS 9.3]

is also represented: as D or sometimes d. [PHYS 9.3]

deviation

is: the difference between a particular measurement xi (from a set of measurements) and the mean $\langle x\rangle$ of that set. The deviation of the ith measurement is therefore $d_i = x_i - \langle x\rangle$. [PHYS 1.2]

See also standard deviation.

diameter

of: a circle, sphere or ellipse.

is: a line segment passing through the centre of the circle, sphere or ellipse. [MATH 2.1]

touches: the boundary at two ‘diametrically opposite’ points. [MATH 2.1]

is also: the length of such a line segment, which will be twice the radius in the case of a circle or sphere, but will depend on orientation in the case of an ellipse. [MATH 2.1]

diatomic ideal gas

is: an ideal gas in which the internal energy is a function of temperature T that (classically) rises from 3nRT/2 at low temperature, to 5nRT/2 at moderate temperature (due to the excitation of the rotational degrees of freedom), to 7nRT/2 at high temperature (due to the excitation of vibrations). [PHYS 7.4]

can be used: to model the behaviour of a real gas with two atoms per molecule at low density. [PHYS 7.4]

diatomic molecules

are: molecules made of two atoms chemically bonded together. The atoms can be of the same element (homonuclear molecules), or of different elements (heteronuclear molecules).

are exemplified by: the five gaseous state diatomic elements: Cl2, F2, H2, N2, O2 and at room temperatures Br2 (liquid) and I2 (solid).

dielectric

is: a term used to describe an insulator in situations where its dielectric constant is (or may be) of significance (e.g. between the plates of a capacitor). [PHYS 4.5]

dielectric constant

of: a medium

is: the ratio of the permittivity of the medium to the permittivity of free space, ε0. [PHYS 4.5]

is synonymous: with relative permittivity, εr.

difference

See operation.

differential equation

is: an equation which involves the first derivative and/or higher derivatives of a quantity. [PHYS 5.3, PHYS 5.4, MATH 6.1]

has as its order: the order of the highest derivative appearing in the equation. [MATH 6.1, PHYS 5.3, PHYS 5.4]

has as its degree: the highest power_mathematicalpower of the derivative of highest order appearing in the equation. [MATH 6.1, PHYS 5.3, PHYS 5.4]

has a general solution: which involves one or more arbitrary constants with values that have to be determined by boundary conditions which are characteristic of the problem being considered. [MATH 6.1, PHYS 5.3, PHYS 5.4]

See differential equations in the Maths For Science handbook for further details.

differential operator

is: an operator (i.e. a symbolic instruction to carry out a mathematical operation) that involves the process of differentiation. [MATH 4.3]

usually acts: on whatever is immediately to its right. [MATH 4.3]

is exemplified: by $\hat{\rm p}_x = -i\hbar\dfrac{d}{dx}$ which, in quantum mechanics, corresponds to the x–component of momentum. [PHYS 10.4]

is also exemplified: by $\hat{\rm E}_{\rm kin} = -\dfrac{\hbar^2}{2m\vphantom{^0}}\dfrac{d^2}{dx^2}$ which, in quantum mechanics, corresponds to the kinetic energy of a particle moving in one dimension. [PHYS 10.4]

See also eigenfunction, eigenvalue and eigenvalue equation.

differentiation

is: the process of finding the derived function, or derivative, of a function. [MATH 4.1, MATH 4.2]

diffraction

is: the ability of waves to bend around obstacles or to be spread by apertures. [PHYS 5.7, PHYS 6.1, PHYS 6.2]

depends for its amount: on the relationship between the wavelength of the wave and the size of the obstacle or aperture. [PHYS 5.7, PHYS 6.1, PHYS 6.2]

is negligible: when the wavelength is much less than the size of the obstacle or aperture. [PHYS 5.7, PHYS 6.1, PHYS 6.2]

is greatest: when the wavelength is about the same size as the obstacle or aperture. [PHYS 5.7, PHYS 6.1, PHYS 6.2]

diffraction grating

is: an optical device consisting of a flat plate with a series of equally spaced, parallel slits on its surface. The distance between the slits is usually a few wavelengths of the radiation involved, and is called the grating spacing. The plate may be transparent (a transmission grating) or reflecting (a reflection grating) and the slits may have been produced by ruling them with an appropriate machine (ruled grating), or by taking a cast of an existing ruled grating (replica grating). [PHYS 6.1]

produces: when illuminated by normally incident monochromatic light of wavelength λ an interference pattern which has primary intensity maxima at angles θn from the straight–through position given by

$\sin\theta_n = \dfrac{n\lambda}{d}$

where n is the order of diffraction and d is the grating spacing. [PHYS 5.5, PHYS 6.1]

diffraction pattern

is: an interference pattern from an identifiable obstruction, for example a circular aperture or slit, or a pair of slits (as in Young’s experiment), or an array of slits (as in a diffraction grating). [PHYS 5.7, PHYS 6.1, PHYS 6.2]

See diffraction.

diffuse reflection

is: reflection from a rough surface, so that rays incident from the same direction are reflected in different directions by different parts of the surface. [PHYS 5.7]

diffusion

is: the process by which molecules spread from regions of high to low concentration. [PHYS 7.5]

therefore is: a transport process. [PHYS 7.5]

digit

is: a symbol used in the specification of a number 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are the ten digits used to specify decimal numbers. [MATH 1.2, PHYS 1.1]

dimension

of: a coordinate system (e.g. a system of Cartesian coordinates)

is: a ‘direction’ in which measurements may be made (usually) independently of measurements in other dimensions. In the case of Cartesian coordinates the directions of the x–axis, y–axis and z–axis each represent one of three independent dimensions. The number of dimensions (the dimensionality of the system) is therefore the minimum number of coordinates needed to uniquely identify any point in the region covered by the system of coordinates.

See also dimensional analysis and dimensions for a different meaning.

dimensional analysis

is: the process of assigning appropriate combinations of dimensions to physical quantities and using such assignments to test the plausibility of proposed relationships between physical quantities. [MATH 1.3, PHYS 1.1]

dimensionless

refers: to a quantity with no overall dimensions, such as a pure number or a ratio of two quantities which have the same dimensions. [MATH 1.2, PHYS 1.1]

dimensionless ratio

is: a ratio of two quantities which have the same dimensions. [MATH 1.2]

dimensions

are: basic measurable quantities such as mass (M), length (L) and time (T). [MATH 1.2]

can be used: singly or in appropriate combinations to characterize physical quantities. Speed, for example, can be measured in the same units as the ratio of a length to a time and is therefore said to have the same dimensions as length/time, a relationship shown by writing [speed] = [length/time] = L T−1. Quantities with units that differ only by a dimensionless conversion factor are said to have the same dimensions. [MATH 1.2, PHYS 1.1]

diminished

means: made smaller – as for an image formed by a lens or a mirror, when the image is smaller than the object. [PHYS 6.3]

dioptre

is: the unit of optical power of a lens, being the reciprocal of the focal length of the lens and expressed in m−1. [PHYS 6.3]

dipole

See electric dipole, magnetic dipole.

dipole moment

See electric dipole moment, magnetic dipole moment.

direct current, d.c.

is: an electric current whose direction does not vary with time. [PHYS 4.1]

more generally refers: to other associated electrical quantities whose direction or polarity does not vary with time, e.g. d.c. voltage. [PHYS 4.1]

is abbreviated: DC at the beginning of a sentence, and d.c. elsewhere. [PHYS 4.1]

direct integration

is: a method of solution which can be applied to differential equations of the form $\dfrac{dy}{dx} = f(x)$. [MATH 6.1, MATH 6.2]

See inverse differentiation.

directed line segment

is: a line of finite length with an arrow head drawn on it. The length and orientation of such a line can be used to represent the magnitude_of_a_vector_or_vector_quantitymagnitude and direction of a vector or a vector quantity in a diagram or illustration. [MATH 2.4]

direction (of a vector)

is: a characteristic property of a vector which determines its orientation with respect to a coordinate systemsystem of coordinates. [PHYS 2.2]

usually is specified: in two dimensions relative to a two–dimensional Cartesian coordinate system, by quoting the angle (measured in the anticlockwise sense) from the positive x–axis to the vector. [PHYS 2.2]

may be more generally specified: by expressing the vector in terms of its components of a vectorcomponents relative to a given Cartesian coordinate system.

See scalars and vectors in the Maths For Science handbook.

direction (of propagation)

is: the direction of motion of a wave. [PHYS 5.6, PHYS 6.1]

See transverse wave and longitudinal wave.

direction cosines

of: a straight line relative to a three–dimensional system of Cartesian coordinates.

are: three numbers that represent the cosines of the angles between the line and the coordinate axes. [MATH 2.2]

are: in the same ratio as the direction ratios of the line.

direction ratios

for: a straight line

in: three dimensions

are: the constants l, m, n in the equation for the straight line:

$\dfrac{x-a}{l} = \dfrac{y-b}{m} = \dfrac{z-c}{n}$

where (a, b, c) is a point on the line. [MATH 2.2]

directly proportional

describes: two variables x and y, if their ratio x/y remains constant as x and y are varied. [MATH 1.1]

is symbolized: by xy. [MATH 1.1]

generally is abbreviated: to ‘proportional’. [MATH 1.1]

See constant of proportionality.

Contrast with inversely proportional.

directrix

See conic section.

disc

is: a circle together with the points enclosed by its circumference. [MATH 2.1]

discharge tube

is: a device used to investigate the conduction of electricity through a gas. [PHYS 8.1]

consists: in its simplest form, of a gas–filled glass tube containing an anode and a cathode, in which the pressure can be reduced by means of a pump. [PHYS 8.1]

discrete (variable)

is: a variable that only takes certain separated values and is therefore not a continuous variable. [MATH 1.3]

discriminant

for: a quadratic equation ax2 + bx + c = 0

is: the quantity b2 − 4ac. [MATH 1.3, MATH 1.4]

determines: the number of times that the graph of the quadratic function will intersect the x–axis, i.e., the number of roots that the equation has. [MATH 1.3, MATH 1.4]

dispersion

is: the phenomenon in which a wave travels through a material with a phase speed that depends on its frequency. [PHYS 5.6, PHYS 6.1, PHYS 6.2, PHYS 6.3, PHYS 10.3]

arises from: variation of the refractive index of the material with the frequency of the wave, for an electromagnetic wave. [PHYS 5.6, PHYS 6.1, PHYS 6.2, PHYS 6.3, PHYS 10.3]

therefore causes: light of different frequencies to be refracted by different angles on entering the material, and hence enables light of different frequencies to be refracted in different directions. [PHYS 5.6, PHYS 6.1, PHYS 6.2, PHYS 6.3, PHYS 8.2, PHYS 10.3]

dispersion relation

of: a given type of wave in a specified medium

is: an expression which describes the variation of the wave’s wavelength (or some related quantity such as wavenumber) with the frequency of the wave. [PHYS 10.3]

is exemplified: for an electromagnetic wave of wavelength λ travelling through a medium with a frequency–dependent refractive index μ(x), by λ = c/fμ(f) where c is the speed of light in a vacuum.

is also exemplified: by the dispersion relation for the de Broglie wave of a free particle $\omega = \dfrac{\hbar k^2}{2m}$, where ω is the angular frequency and k is the corresponding angular wavenumber.

dispersive power

is: the ability of an optical medium to produce dispersion for a given optical power or focal length. High or low dispersive power corresponds to high or low refractive index, respectively. [PHYS 6.4]

displacement

from: one point in space to another

is: the change in position from the first point to the second. [PHYS 2.1]

is represented: by a vector. The displacement s from a point with position vector r1 to a point with position vector r2 is given by s = r2r1. [PHYS 2.2]

has magnitude: equal to the distance between the two points. [PHYS 2.2]

has direction: along the line from the first point to the second. [PHYS 2.2]

may be measured: from any selected reference point, unlike a position vector. [PHYS 2.2]

has as its SI unit: the metre (m). [MATH 2.4]

in one dimension can be represented: by a single scalar component sx. If the selected reference point is at the initial position of the particle, then the displacement of the particle at time t is sx = x(t) − x(0). [MATH 4.1, PHYS 2.1]

in linear motion is given: for displacement of an object from its position at time t1 to its position at time t2 by the area under a grapharea under the corresponding velocity–time graph between t1 and t2. [MATH 5.1]

displacement–time graph

for: a particle moving in one dimension

is: a graph of the displacement (from an agreed reference point) of the particle against time. The convention is to plot the displacement vertically and the time horizontally. The gradient of the displacement–time graph is the velocity in that dimension. [PHYS 2.1]

dissipation

is: the irreversible loss of energy by a system to its environment as a result of the action of dissipative forces.

dissipative forces

are: forces arising from friction, viscosity or similar effects that cause a reduction in relative motion, and are usually accompanied by the production of heat. [PHYS 5.2]

dissociation

is: the process of breaking a molecule (or part of a molecule) into its constituent atoms. [PHYS 8.2]

distance

from: one point to another

is: the magnitude_of_a_vector_or_vector_quantitymagnitude of the displacement from the first point to the second. [MATH 4.1]

therefore is: a positive quantity. [PHYS 2.1, PHYS 2.2]

has as its SI unit: the metre. [PHYS 2.2]

See basic coordinate geometry in the Maths For Science handbook.

See also path length.

distance–time graph

is: a graph used in the analysis of one–dimensional linear motion, where the distance of an object from a reference point is plotted against the time. [PHYS 2.1]

distant–action force

is: a force that always exists between two particles without their being in contact and regardless of any intervening matter.

is exemplified: by the gravitational force. [PHYS 3.1]

distribution

of: values of a given physical quantity x

over: a number of particles or entities.

is: a function f(x) which specifies the fraction of the total number of particles which have values of x lying within the small interval between x and x + Δx. [MATH 5.4]

is defined: so that this fraction is equal to f(xx. [MATH 5.4]

divergent (integral)

is: an improper integral with no finite value. [MATH 5.2]

divergent sequence

is: a sequence that does not converge. [MATH 1.7]

divergent series

is: a series that does not converge. [MATH 1.7]

diverging lens

is: a lens which increases the divergence or reduces the convergence of light rays passing through it. [PHYS 6.3]

is also called: a concave lens or a negative lens. [PHYS 6.3]

divisor

See operation.

domain (of a function)

of: a function

is: the range of values of the independent variable over which the function is defined. [MATH 1.3]

Doppler effect

is: the effect in which the observed frequency of a wave (such as an acoustic wave or an electromagnetic wave) is changed when the source of the wave and the observer are moving with respect to each other. [PHYS 5.7]

causes: an increase in the observed frequency of the wave if the source and observer are moving closer together, and a decrease in the observed frequency of the wave if the source and observer are moving apart. [PHYS 5.7]

dose equivalent

is: a quantity that quantifies the biological hazard of ionizing radiation [PHYS 9.3]

is defined: as the product of the absorbed dose and the appropriate radiation weighting factor. [PHYS 9.3]

has as its SI unit: the sievert, Sv. [PHYS 9.3]

dot product

See scalar product.

dots (...)

See ellipsis.

double–angle formulae

are: a class of trigonometric identities. [MATH 1.6]

See trigonometric functions in the Maths For Science handbook for details.

double bond

is: a chemical bond between two atoms, which is equivalent to two single bonds. [PHYS 8.4]

arises: in electronic theories of bonding, from the sharing of two pairs of electrons. [PHYS 8.4]

double cone

is: the surface produced by extending to infinity (in both directions) every straight line on the surface of a cone. [MATH 2.3]

double–argument identities

are: members of a class of hyperbolic function identities. [MATH 4.6]

See hyperbolic functions in the Maths For Science handbook.

doublet

in: a line spectrum

consists: of two spectral lines whose wavelengths are almost equal. [PHYS 8.2]

arises: when two transitions have almost the same energy difference.

appears: if at all, in each order of diffraction from a diffraction grating (except in the zeroth order). [PHYS 8.2]

driven oscillations

describes: the behaviour exhibited by a driven oscillator. [PHYS 5.4, PHYS 5.5]

driven oscillator

is: an oscillating system that is supplied with energy (continuously or periodically) by an externally applied driving force.

is exemplified: by a mechanical oscillator consisting of a particle of mass m moving in one dimension along the x–axis subject to a restoring forcekx a damping forcex and a driving force F0sin(Ωt), so that its displacement from equilibrium, x at time t satisfies the equation of motion:

$m\dfrac{d^2x}{dt^2} = -kx - b\dfrac{dx}{dt} + F_0\sin({\it\Omega}t)$

and consequently will eventually exhibit forced oscillations described by

$x(t) = A_0\sin({\it\Omega}t+\phi)$

where $A_0 = \dfrac{F_0/m}{\sqrt{(\omega_0^2-{\it\Omega}^2)^2+(\gamma{\it\Omega})^2}}$ and $\phi = \arctan\left(\dfrac{-\gamma{\it\Omega}}{\omega_0^2-{\it\Omega}^2}\right)$ with $\omega = \sqrt{k/m}$ and γ = b/m. [PHYS 5.2, PHYS 5.3]

is also exemplified: by an electrical oscillator consisting of an inductance L in series with a capacitance C and a resistance R driven by an applied voltage V0sin(Ωt). In such a system the charge q stored on the capacitor at time t is described by the same equations as the driven mechanical oscillator, subject to the replacement of m, k, b and F0 by L, (1/C), R and V0, respectively. [PHYS 5.4]

has angular frequency: Ω which is completely independent of the natural frequency ω of the oscillating system in the absence of driving or damping forces. [PHYS 5.4]

displays amplitude: A0, which is generally dependent on the angular frequency (Ω) of the driver and which may exhibit resonance at a particular driving frequency. [PHYS 5.4]

driving force

is: one of a trio of forces that determine the behaviour of a driven oscillator: restoring force, damping force and driving force. [PHYS 5.2, PHYS 5.3, PHYS 5.5]

ductile region

is: the part of the loading curve (the graph of stress against strain) of a material over which it exhibits plasticity.

is also called: the plastic region. [PHYS 7.6]

dummy variable

is: the variable of integration which is used in a definite integral. [MATH 5.2]

is named: ‘dummy’ since it does not appear in the final answer, so its identity is unimportant. [MATH 5.2]

more generally is: in a particular calculation, any variable that does not appear in the final result of that calculation.

dynamic equilibrium

is: a state of a multi–member system in which there is no time–dependence in the average properties of the system as a whole, but in which there are changes and fluctuations in the states of the individual members of the system. [PHYS 7.6]

dynamic friction

See sliding friction.

dynamics

is: the study of how forces give rise to changes in motion. [PHYS 2.3]

Compare with kinematics.

dynamo

is: a device that generates an induced voltage by rotating a coil within a magnetic field. [PHYS 4.4]

produces: depending on the arrangement of the connections to the external circuit, an output which may be either a.c. or d.c. An a.c. dynamo is also known as an alternator. [PHYS 4.4]

e

is: a numerical constant, whose value to eight decimal places is 2.718 281 83 [MATH 1.5]

can be defined: by $\displaystyle {\rm e} = \lim_{n\to\infty}(1+1/n)^n$. [MATH 1.5]

equivalently can be defined: by $\displaystyle {\rm e} = \lim_{m\to0}(1+m)^{1/m}$. [MATH 1.5]

is the basis: of the exponential function ex. [MATH 1.5]

is used: as the base of natural logarithms. [MATH 1.5]

is: an irrational number. [MATH 1.5]

Contrast with the (italic) e used to represent the charge on the proton.

e

is: the symbol used to represent the electric charge on a proton, one of the fundamental physical constants.

has the value: 1.602 × 10−19 C, to three decimal places.

is equal in magnitude: to the negative charge carried by the electron. [PHYS 3.3]

See quantization of charge.

Contrast with the (non–italic) e used to represent the base of natural logarithms.

Earth satellite

is: any object in orbit around the Earth, whether natural (the Moon) or artificial (e.g. communication or meteorological satellites). [PHYS 2.6]

must have: an orbit that is circular or elliptical (to a first approximation). [PHYS 2.6]

earth potential

is usually defined: to be at zero potential and is used as a reference potential in conventional circuit measurements. [PHYS 4.1]

earthed

describes: a conduction_of_electricityconducting body, or a point on a body, that is connected to the Earth by an electrical_conductorelectrically conducting pathway. [PHYS 4.1]

implies: that the conduction_of_electricityconducting body or point is at earth potential. (The Earth may be regarded as an enormous reservoir of mobile charge at a fixed potential (earth potential), so any conduction_of_electricityconducting body (or point) that is earthed will quickly acquire earth potential.) [PHYS 4.1]

earthing

is: the process of connecting a body to the Earth by a conduction_of_electricityconducting pathway so that it is earthed. [PHYS 4.1]

allows: charge on a charged electrical_conductorconductor to flow to the Earth until the electric potential of the electrical_conductorconductor is equal to that of the Earth, i.e. is at earth potential. [PHYS 4.1]

is a special case: of charge sharing. [PHYS 3.3]

eccentricity

of: a given conic section

is: the ratio of the distance PF from any point P on the conic section to a focus F of the conic section, to the perpendicular distance PD from the point P to the directrix (i.e. e = PF/PD). [MATH 2.3]

is exemplified: by the eccentricity e of an ellipse for which 0 ≤ e < 1, and the lengths of the semi–major axis a and the semi–minor axis b are related by $b = a\sqrt{1-e^2}$.

eddy current

is: an induced current which circulates entirely within the body of a electrical_conductorconductor. [PHYS 4.4]

effective area

of: a (current–carrying) coil of N turns, all in the same plane and each of geometrical area A

is equal: to NA [PHYS 4.3]

See magnetic dipole moment.

efficiency

of: a piece of equipment

generally is: the dimensionless ratio of the amount of a physical quantity extracted from the equipment to the amount of the same physical quantity supplied to the equipment.

efficiency (of a heat engine)

is: the ratio of the useful work delivered from the heat engine, to the heat supplied to the heat engine, η = ΔW/(Q1Q2). [PHYS 7.4]

efficiency of a reversible heat engine

operating: between two fixed temperatures Thot and Tcold

is: η = 1 − Tcold/Thot. [PHYS 7.4]

eigenfunction

of: a mathematical operator as used in quantum mechanics.

is: a function ψ(x) which, when operated on by the operator, produces a real number multiplied by ψ(x). The real number is the eigenvalue of the operator. [PHYS 10.4, PHYS 11.1, PHYS 11.2, PHYS 11.3]

See eigenvalue, eigenvalue equation and spatial wavefunction.

eigenvalue

of: a mathematical operator as used in quantum mechanics.

is: the real number which appears when the operator acts on one of its eigenfunctions to produce the eigenfunction multiplied by a real number. [PHYS 10.4, PHYS 11.1, PHYS 11.2, PHYS 11.3]

See eigenfunction, eigenvalue equation and energy level.

eigenvalue equation

is: an equation in which an operator acts on an eigenfunction to produce the eigenfunction, multiplied by an eigenvalue. That is, for an operator $\hat{\rm O}$,

$\hat{\rm O}f = \lambda f$

where f is an eigenfunction of $\hat{\rm O}$, and λ is the eigenvalue of $\hat{\rm O}$ belonging to the particular eigenfunction. [PHYS 10.4, PHYS 11.1, PHYS 11.2, PHYS 11.3]

permits: more than one (and possibly an infinite number) of eigenvalues and eigenfunctions for a given operator. In physical problems $\hat{\rm O}$ is most commonly a differential operator, but it can take other forms. In quantum physics, f is commonly a spatial wavefunction (i.e. an eigenfunction of the energy operator, the Hamiltonian). [PHYS 10.4, PHYS 11.1, PHYS 11.2, PHYS 11.3]

Einstein model

is: a model of the specific heat of a solid.

postulates: that a solid behaves as though composed of independent quantum harmonic oscillators characterized by a common classical frequency. [PHYS 11.4]

predicts: that the specific heat will be small near absolute zero. [PHYS 11.4]

See Debye model.

Einstein’s mass–energy equation

is: the equation, E = mc2, which gives the mass m associated with an amount of energy E, where c is the speed of light in a vacuum. [PHYS 2.4, PHYS 9.1]

is one of the consequences: of Einstein’s special theory of relativity. [PHYS 2.4, PHYS 9.1]

Einstein’s photoelectric equation

is: an equation that relates the maximum kinetic energy of electrons released in the photoelectric effect to the frequency f of the incident light, the work function ϕ of the surface and Planck’s constant h:

$hf-\phi = \frac12m_{\rm e}\upsilon_{\rm max}^2$. [PHYS 10.1]

Einstein’s special theory of relativity

is based: on two postulates:

Postulate 1: The laws of physics can be written in the same form in all inertial frames of reference.

Postulate 2: The speed of light (in a vacuum) has the same constant value, c in any inertial frame of reference.

has deep consequences: among which are these:

1. If two spatially separated events are measured as simultaneous in one inertial frame, they will not generally be measured as simultaneous in another inertial frame which is moving relative to the first frame.

2. If a clock is measured as moving in an inertial frame, it will also be measured as running slow (losing time) in that inertial frame.

3. If an object is measured as moving in an inertial frame, it will also be measured as contracted in the direction of its motion in that inertial frame. Moreover, its mass will be measured as greater than if it were at rest.

has been confirmed: repeatedly by experiment.

elastic

describes: the ability of a body to recover fully from a distortion and to store energy (as strain potential energy) while distorted, so long as it is not strained beyond its elastic limit. [PHYS 2.4, PHYS 5.2, PHYS 5.7]

elastic body

is: a deformable body that returns to its original shape when the cause of any deformation is removed, unless the amount of deformation exceeds the elastic limit of the body. [PHYS 2.4]

elastic collision

is: a collision during which the total kinetic energy of the system of interacting bodies is conserved. [PHYS 2.4, PHYS 2.5]

elastic limit

of: an elastic body.

is: the maximum change in length under which the body still obeys Hooke’s law. [PHYS 2.3]

is also: the maximum stress that a solid can sustain without undergoing permanent deformation. [PHYS 7.6]

equivalently is: the point on the loading curve which marks the end of the elastic region and the start of the plastic region. [PHYS 7.6]

is also called: the yield point. [PHYS 7.6]

elastic material

is: a material which fully recovers its previous physical and mechanical state, with zero strain, when the stress is removed. [PHYS 7.6]

elastic modulus

See modulus of elasticity.

elastic region

is: the part of the loading curve of a material, over which the material behaves as an elastic material. [PHYS 7.6]

extends: from zero stress to the elastic limit or yield point. [PHYS 7.6]

electric cell

is: a device essentially consisting of two dissimilar electrodes dipping into an electrolyte solution. Chemical reactions between the electrodes and electrolyte produce ions. When the cell is connected to an external circuit, there is a flow of charge within the electrolyte and around the external circuit, i.e. the cell is a source of direct current. [PHYS 4.5]

electrical charge

is: a fundamental property of matter which determines whether or not particles or bodies experience electrical interactions. [PHYS 3.3]

is classified: into two types: positive and negative. Charges of the same type repel each other, charges of opposite types attract each other. [PHYS 3.3]

is carried: by some fundamental particles, e.g. the electron carries a charge of −e, the proton a charge of +e. Some others carry none, e.g. the neutron is uncharged. [PHYS 3.3]

has as its SI unit: the coulomb (C), where 1 C = 1 A s (i.e. 1 ampere second).

See quantization of charge.

electric current

through: a surface

is: the rate dq/dt at which (net) charge q is transferred across that surface. [PHYS 4.1, PHYS 5.5]

is due: in metallic conductors, to the movement of electrons. In other media, it can be due to the movement of other charged particles (e.g. ions in solution_chemicalsolution). [PHYS 4.1]

has direction: which is defined conventionally as the direction in which positive charge would move, though in many cases the current is actually a flow of negatively-charged particles in the opposite direction. [PHYS 4.1]

has as its SI unit: the ampere (A). [PHYS 4.1]

electric dipole

consists: of equal and opposite electric charges +q and −q separated by a distance d [PHYS 3.3]

can be found: in molecules containing a variety of atoms, where the electrons forming the bonds between atoms of different chemical elements are not shared equally between the two atoms involved. The result is equivalent to a dipole, in which one atom has a slight positive charge and the other a slight negative charge. [PHYS 3.3]

See electric dipole moment. [PHYS 3.3]

electric dipole moment

is: the product of the charge magnitude and charge separation in an electric dipole. For a dipole consisting of charges +q and −q separated by a distance d, the dipole moment is qd. [PHYS 3.3]

is strictly: a vector quantity whose magnitude_of_a_vector_or_vector_quantitymagnitude is as defined above, and whose direction is the same as for the displacement from the negative to the positive charge.

electric field

throughout: a region of space

is: a vector field that gives rise to an electrical force on a test charge placed at any point in the region. [PHYS 3.1]

is defined: at any point specified by a position vector r, as the electrostatic force per unit positive charge that would act on a test charge placed at that point. So, generally,

${\boldsymbol E}({\boldsymbol r}) = \dfrac{{\boldsymbol F}_{\rm el}(\text{on }q\text{ at }{\boldsymbol r})}{q}$

whether the test charge q is positive or negative. [PHYS 3.1, PHYS 3.2]

is related: to the electric potential by the requirement that it points in the direction of most rapid decrease of the potential, and has a magnitude given at every point by the magnitude of the rate of change of the potential in that direction (e.g. in the radial direction from an isolated point charge, so that Er = −dVel/dr). It therefore always points in a direction at right angles to lines or surfaces of equipotential surfaceequal potential, and from high potential towards low potential. [PHYS 3.1, PHYS 3.3]

has as its SI unit: the newton per coulomb (N C−1) or, equivalently, the volt per metre (V m−1). [PHYS 3.1, PHYS 3.3]

electric field lines

are: a means of representing an electric field. [PHYS 3.3]

are drawn: so that at any point the tangent_to_a_curvetangent to the line represents the direction of the field at that point. [PHYS 3.3]

therefore are directed: away from a positive charge and towards a negative charge. [PHYS 3.3]

have spacing: which is related to the electric field strength, i.e. where the lines are close together the field is strong and where they are further apart the field is weaker. [PHYS 3.3]

always cut: equipotential surfaces at right angles. Where these are closest together, their rate of change is greatest, and so there the electric field is strongest. [PHYS 3.1, PHYS 3.3]

electric field strength

at: any point

is: the magnitude of the electric field at that point. [PHYS 3.1]

electric force

See: electrostatic force.

electric potential

at: a given point in space

is: the electric potential energy per unit positive charge at that point. [PHYS 3.1, PHYS 3.3]

is also: the electric potential difference (i.e. voltage difference) between the given point and a point at which the electric potential energy is defined to be zero. In an electrical circuit the earth, or the negative terminal of a power supply, is usually taken to be at zero potential. [PHYS 3.1, PHYS 3.3]

has as its SI unit: the volt, (V). [PHYS 4.1]

electric potential difference

between: point A and point B in an electric field

is: the difference VBVA, in electric potential energy per unit positive charge between the two points (i.e. ΔVel = ΔEel/q). [PHYS 2.6, PHYS 4.1]

is therefore: the negative of the work done per unit charge by an electric field when a unit charge is moved from A to B. [MATH 2.6]

is also called: voltage difference. [PHYS 4.1]

has as its SI unit: the volt, (V), where 1 V = 1 J C−1 (i.e. 1 joule per coulomb). [PHYS 4.1]

electric potential energy

is: the energy a charged particle has by virtue of its position in an electric field. [PHYS 3.1, PHYS 3.3, PHYS 4.1]

requires for its full definition: a position of zero electric potential energy to be arbitrarily chosen, since only differences in electric potential energy are physically meaningful. [PHYS 3.1, PHYS 3.3]

changes: in going from point A to point B, by an amount equal to the negative of the work done by the electric field when the charged particle is moved from A to B. [PHYS 3.1]

is exemplified: by the electric potential energy of a particle of charge q2 in the electric field of a particle of charge q1, when the distance between the two particles is d. Subject to the conventional choice that Eel = 0 when r → ∞, this is given by

$E_{\rm el} = \dfrac{q_1q_2}{4\pi\varepsilon r}$

where ε is the permittivity of the medium between the charges. [PHYS 3.1, PHYS 3.3]

is related: to the electric potential Vel in a region by Eel = qVel, so when a charge q moves through a voltage difference (i.e. an electric potential difference) ΔVel, the change in electric potential energy ΔEel, is given by ΔEel = qΔVel. [PHYS 4.1]

often is referred: to as ‘electrical energy’ or electrostatic potential energy. [PHYS 3.1, PHYS 3.3]

has as its SI unit: the joule (J).

electrical

means: pertaining to electricity.

See also electrostatics and electromagnetism.

electrical breakdown

in: an electrical insulator which is subjected to an electric field above a certain threshold

occurs: when some of the electrons become detached from their parent atoms and flow through the material − which thus becomes, temporarily, an electrical conductor. [PHYS 3.3]

electrical components

is: a general term for electrical devices, particularly those that are used in circuits.

electrical conductor

is: a material containing an abundance of mobile charged particles that are free to move throughout the whole of the material. [PHYS 3.3, PHYS 4.1]

has: a low resistivity. [PHYS 4.1]

has typically: in terms of the band theory of solids, a partly filled valence band at absolute zero. [PHYS 11.4]

is exemplified: by any metal. [PHYS 3.3, PHYS 4.1, PHYS 11.4]

is the opposite: of an electrical insulator. [PHYS 3.3, PHYS 11.4]

electrical energy

is: energy supplied by an electrical power supply.

See also electric potential energy.

electrical insulator

is: a material containing a negligible number of mobile charged particles. [PHYS 3.3, PHYS 4.1]

has: an extremely high resistivity. [PHYS 4.1]

has typically: in terms of the band theory of solids, an empty conduction band separated by a substantial gap (e.g. 5 eV) from a full valence band at absolute zero. [PHYS 11.4]

is the opposite: of an electrical conductor. [PHYS 3.3]

can be used: to prevent the flow of current between points at different potential. [PHYS 4.1]

See also electrical breakdown.

electrical interaction

See electromagnetic interaction.

electrical oscillator

is essentially: an inductor connected across a capacitor to form a simple circuit in which charge stored on the capacitor may oscillate, possibly also containing a resistor (to provide damping) and possibly subject to an externally supplied voltage to make it a driven oscillator.

See simple harmonic oscillator, damped electrical oscillator, driven oscillator, as appropriate.

electricity

is: a general term for electric charge, whether static or moving, as in an electric current.

electrochemical series

is: a listing of chemical elements in order of their electrode potential. The further apart two element_chemicalelements are in the series, the greater is the open circuit voltage (e.m.f.) produced when they form the two electrodes in a simple electric cell. The element_chemicalelement with the greater (more positive) electrode potential forms the positive terminal of the cell. [PHYS 4.5]

electrode

is: an electrically conducting structure used to emit or collect charge, often (though not always) a metal plate or grid.

electrode potential (of an element)

is: the open circuit voltage (e.m.f.) obtained by using the element to make one terminal of an electric cell, whose other terminal is a hydrogen electrode. The (theoretical) magnitude of the open circuit voltage (e.m.f.) of any simple cell is found by subtracting the two electrode potentials one from the other. [PHYS 4.5]

electrolyte

is: a substance, usually in the form of a solution_chemicalsolution, which allows the conduction_of_electricityconduction of electricity by the movement of positive and negative ions. [PHYS 4.5]

electrolytic capacitor

is: a capacitor whose plates are made from two different materials separated by an electrolyte.

must be connected: the correct way round in a d.c. circuit. [PHYS 4.5]

electromagnet

is: a coil or solenoid would around a core of ferromagnetic material and which then exhibits strong magnetic induction when a current flows. [PHYS 4.2]

electromagnetic force

is: the total force on a charged particle in an electric field and/or magnetic field, found by adding the separate electrostatic force and magnetic force that would be produced by each field acting independently. [PHYS 4.3]

is described: by the Lorentz force law

${\boldsymbol F} = q({\boldsymbol E}+{\boldsymbol\upsilon}~{\boldsymbol\times} ~{\boldsymbol B})$. [PHYS 4.3]

is also called: the Lorentz force. [PHYS 4.3]

arises: from the electromagnetic interaction, one of the four known fundamental interactions in nature. [PHYS 9.2]

electromagnetic induction

is: the phenomenon that results in the production of an induced voltage in a electrical_conductorconductor by changing a magnetic field near the electrical_conductorconductor, or by moving the electrical_conductorconductor within a magnetic field (motional induction). [PHYS 4.4]

See Faraday’s law and Lenz’s law.

electromagnetic interaction

is: the fundamental interaction that gives rise to electromagnetic force. [PHYS 9.2]

comprises: together with the weak_interactionweak, strong_interactionstrong and gravitational_interactiongravitational interactions, the four known fundamental interactions of nature. [PHYS 9.2]

See gravitational force, strong nuclear force, weak_interactionweak nuclear force.

electromagnetic pick–up

is: the induced voltage caused in a circuit by magnetic field fluctuations near the circuit. [PHYS 4.4]

electromagnetic radiation

is: radiation consisting of fluctuating electric_fieldelectric and magnetic fields that can propagate through space, or through suitable media, as electromagnetic waves characterized by a wavelength λ and a frequency f. Many aspects of the interaction of electromagnetic radiation with matter require the use of quantum theory for their accurate description.

is exemplified: by familiar phenomena such as visible light, radio waves and X–rays, which are all parts of the electromagnetic spectrum, corresponding to different wavelengths of electromagnetic radiation.

can transfer: energy and momentum. [PHYS 7.3]

See radiation pressure.

electromagnetic spectrum

is: the complete range of electromagnetic waves. [PHYS 6.1, PHYS 7.3]

extends: from long-wavelength radio waves, through microwaves, infrared, visible light, ultraviolet and X–rays to short-wavelength γ–rays. [PHYS 6.1, PHYS 7.3]

electromagnetic wave

is: a pattern of mutually perpendicular, oscillating electric_fieldelectric and magnetic fields that can travel through a vacuum at the speed of light, c. [PHYS 6.1]

is a form: of transverse wave. [PHYS 6.1]

is characterized: in the simplest case (a linearly polarized, monochromatic, plane wave), by its direction of propagation, plane of polarization, amplitude, wavelength and frequency. (In a vacuum the wavelength and frequency are related by c = fλ). [PHYS 6.1]

has speed: c/μ in materials other than a vacuum, where μ is the refractive index of the material. [PHYS 6.1]

electromagnetism

is: the branch of physics that encompasses all electrical and magnetic phenomena, including the interactions of charges and magnets with electric and magnetic fields and the production and propagation of electromagnetic waves. [PHYS 4.2]

electromotive force (e.m.f.)

is: an alternative term for the open circuit voltage of a voltage generator. [PHYS 4.1]

is not: a force in the sense defined by Newton’s second law.

electron

is: an elementary particle that is a constituent of every atom. [PHYS 3.3, PHYS 8.1]

has: chargee = −1.602 × 10−19 C and mass m = 9.109 56 × 10−31 kg, approximately 1/1836 times the mass of a proton. [PHYS 3.3, PHYS 8.1]

is liberated: from atoms when the atoms are ionized in a discharge tube, as deduced by its discoverer J.J. Thomson (1856–1940). [PHYS 8.1]

has: no known internal structure at the time of this writing. [PHYS 8.1]

electron antineutrino

is: an elementary particle, the antiparticle of the electron neutrino. [PHYS 9.2]

always accompanies: the electron emitted in β_decayβ–decay. [PHYS 9.2]

electron band

See energy band.

electron cloud

in: the quantum model of the atom

is: the concept that replaces the electron orbits of more primitive models, such as the Bohr model.

has: for a given stationary state of the atom, a density at every point that is proportional to the probability density |Ψ(r, θ, ϕ)|2 of the associated wavefunction. [PHYS 11.3]

electron diffraction

is: the diffraction of electrons by a regular array of atoms (as in a crystal). [PHYS 7.1]

is a consequence: of the wave–like behaviour of electrons, as described by quantum physics. [PHYS 7.1]

results in: a diffraction pattern with sharp local maxima of intensity in directions determined by Bragg’s law. [PHYS 7.1]

See de Broglie wave.

electron microscope

is: a microscope that uses the (short wavelength) wave–like behaviour of beams of electrons to produce images with much better resolution than those possible with optical microscopes. [PHYS 7.1]

electron neutrino

is: an elementary particle that has zero charge and such a small mass (if any) that it is currently indistinguishable from zero.

always accompanies: the positron which is emitted in β_decayβ+–decay. [PHYS 9.2]

electron pair

is: two electrons that occupy the same quantum state apart from having opposed spin angular momentumspins.

electron shell

See shell.

electron spin

is: the intrinsic angular momentum of an electron. [PHYS 8.3]

is described: by an electron spin quantum number s = 1/2 and hence permits two possible values for the spin magnetic quantum number, ms = 1/2 or ms = −1/2, implying that the z–component of the spin must be either $+\hbar/2$ or $-\hbar/2$ when measured along an arbitrarily chosen z–axis. [PHYS 8.3]

creates: electron spin magnetism. [PHYS 4.2]

helps to account: for the magnetic properties of the electron and those of atoms that contain unpaired electrons. [PHYS 8.3]

electron spin magnetism

is: an intrinsic property of an electron (like electric charge), such that the electron behaves as a magnet with a measurable magnetic dipole moment. [PHYS 4.2]

electron subshell

See subshell.

electron tunnelling

is: a special case of quantum tunnelling, in which an electron tunnels through a potential barrier whose height exceeds the total energy of the electron. [PHYS 10.4]

is important: in various electronic devices, including the tunnel diode.

electronegativity

is: a numerical measure of the ability of an atom to attract electrons to itself during chemical reactions. [PHYS 8.4]

is highest: (~4.0) in the region of the periodic table occupied by fluorine and chlorine. [PHYS 8.4]

electronic configuration

is: a description of the distribution of electrons within shells and subshells in an atom, using the quantum numbers that describe the quantum states of the electrons. [PHYS 8.3, PHYS 8.4]

often is presented: in shorthand form using the s–p–d–f notation for subshells. For example, the ground state configuration of sodium is represented as 1s22s22p63s1, meaning that

electronic structure

is: a synonym for electronic configuration. [PHYS 8.3]

electronvolt, eV

is: a non-SI unit of energy.

is defined: as the kinetic energy gained by an electron when it is accelerated through a potential difference of 1 volt. [PHYS 8.3, PHYS 9.1]

is equal: to 1.602 × 10−19 J (to four significant figures). [PHYS 3.3]

is commonly used: in large multiples such as MeV (1 MeV = 106 eV) and GeV (1 GeV = 109 eV) in nuclear physics and elementary particle physics. [PHYS 9.1]

electrostatic constant

is: the physical constant 1/(4πε0) that appears in Coulomb’s law. [PHYS 3.1]

has the value: 1/(4πε0) = 8.988 × 109 N m2 C−2 (to four significant figures). [PHYS 3.1]

See Coulomb’s law, permittivity of free space (ε0) [PHYS 3.1]

electrostatic force

is: the force that acts on a charged body due to its location in a static electric field. For a test charge q located at a point with position vector r, where the electric field is E(r), the electrostatic force is

Fel(on q at r) = qE(r). [PHYS 3.3]

is exemplified: by the force (described by Coulomb’s law) that one charged particle exerts on another by virtue of the electric field that it creates. Two particles with charge of the same sign repel one another, and two particles with charge of the opposite sign attract one another. [PHYS 3.1]

is given: for a positive unit charge by the negative derivative of electric potential energy in the direction of maximum change (e.g. in the radial direction from an isolated point charge, Fr = −dEel/dr). [PHYS 3.1, PHYS 3.3]

electrostatic induction

is: the process by which a region of an initially electric_chargeuncharged object can become charged due to the influence of an electric field (usually due to another charged object) which causes a rearrangement of charge on the original object. [PHYS 3.3]

electrostatic potential energy

See electric potential energy.

electrostatic screening

is created: by a perfectly conduction_of_electricityconducting shell containing no free charges. [PHYS 3.3]

ensures: that no electric field can exist inside the shell. [PHYS 3.3]

electrostatics

is: the study of the electrical interaction between charged particles which are not moving in relation to one another, or in relation to the observer. [PHYS 3.3]

element

is: a small part of something, often of a given solid body, or a volume of fluid. For example, a body of mass M may be considered to be composed of many separate elements of mass Δmi such that $\displaystyle M = \sum_i m_i$

element (chemical)

See chemical element.

element (of a set)

is: an entity that is a member of a set.

element of integration

is: an infinitesimal increment in the variable with respect to which an integration is to be performed. [MATH 5.1, MATH 5.2]

is exemplified: by the dx which appears at the end of the definite integral $\displaystyle \int_a^b f(x)\,dx$. [MATH 5.1,MATH 5.2]

elementary entity

See mole.

elementary functions

are: a slightly ill–defined class of functions including the common (and ‘uncomplicated’) functions, such as sine, logarithm and arctangent. [MATH 1.7]

See the Maths For Science handbook, which includes graphs of many of these functions.

elementary particles

are: subatomic particles believed, or formerly believed, not to have any constituents. Examples include electrons, protons, neutrons and photons. It is now widely believed that protons and neutrons are in fact composed of constituents called quarks, and a modern listing of ‘truly’ elementary particles would consist of three families: the leptons (including the electron), the quarks (including the charged constituents of many other ‘elementary particles’), and the exchange particles (including the photon and the various other particles that are responsible for the fundamental interactions between quarks and leptons).

elementary particle physics

is: the sub-branch of physics that deals with the structure and properties of elementary particles.

elimination (of a variable)

is: the process of manipulating given equations to obtain an equation which does not involve the specified variable, especially in the context of simultaneous linear equations. [MATH 1.4]

is exemplified: by eliminating y between the equations x + y = 1 and xy = 2 to yield 2x = 3. [MATH 1.4]

ellipse

is: a conic section shaped like a flattened circle, that may be described by an equation of the form

$\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$, where $b = a\sqrt{1-e^2}$ with 0 ≤ e < 1, the longest diameter of which (2a) is called the major axis, and the shortest diameter of which (2b) is called the minor axis. [MATH 2.3, PHYS 3.2]

See conic sections in the Maths For Science handbook for further details.

ellipsis

consists: of three dots, thus ...

is often used: to indicate that an expression or sequence continues in a similar fashion, as in 1, 2, 3, 4, ... [MATH 1.1, MATH 2.3, PHYS 3.2]

emission

of: electromagnetic radiation

is: the outcome of any process whereby the internal energy of a system is wholly or partly transformed into energy carried away by electromagnetic radiation.

should be contrasted: with absorption and reflection.

more generally, is: the process of giving out.

emission lines

are: characteristic frequencies or wavelengths that are particularly prominent in an emission spectrum. [PHYS 8.2]

correspond individually: to the radiation emitted in a transition between two bound states of an atom or molecule. [PHYS 8.2]

emission line spectrum

is: an emission spectrum consisting of emission lines. [PHYS 8.2]

emission spectrum

of: electromagnetic radiation (usually emitted from a specified source)

is: the distribution of spectral brightness with respect to the wavelength or frequency of the radiation.

shows: the set of wavelengths at which the excited atoms or molecules in the source emit radiation. [PHYS 8.2]

may consist: of characteristic emission lines (in which case the spectrum is referred to as the emission line spectrum). [PHYS 8.2]

emission transition

in: the Bohr model for atomic hydrogen

occurs: when the electron moves from one bound state to another bound state of lower energy. [PHYS 8.2]

gives rise: to emitted electromagnetic radiation whose frequency is given by the Planck–Einstein formula. [PHYS 8.2]

is more generally: any transition between different quantum states that results in the emission of radiation.

emissivity

of: a surface

is: a constant ε ≤ 1, which is introduced into Planck’s function for the spectral brightness of a black body in order that it should more closely represent the spectrum of radiation coming from the surface. [PHYS 7.3]

is useful: only over a specified range of wavelengths. [PHYS 7.3]

empirical

means: based on experiment and/or observation.

emulsion

is: the thin layer on a photographic film which contains the light sensitive material used to record optical images in a camera. [PHYS 6.4]

energy

of: a body or system

is: a measure of its capacity to do work. [PHYS 2.4]

can exist: in several different forms. The energy that a body has because of its motion is called its kinetic energy (see also rotational_kinetic_energyrotational, translational_kinetic_energytranslational and vibrational kinetic energy); while energy arising from its position in relation to other bodies with which it is interacting or from its internal configuration is called its potential energy (see also electrical_potential_energyelectrical, gravitational_potential_energygravitational and strain potential energy). [PHYS 2.4, PHYS 2.5]

is sometimes named: to reflect the situation in which it arises, e.g. mechanical energy, acoustic energy, heat and mass energy.

remains: for an isolated system, constant in sum over all its different forms, according to the principle of conservation of energy (see also first law of thermodynamics). [PHYS 2.4, PHYS 2.5]

may be converted: from one form into another, subject to various limitations (see also second law of thermodynamics). [PHYS 2.4, PHYS 2.5]

is: a scalar quantity, with dimensions M L2 T−2. [PHYS 2.5]

has as its SI unit: the joule (J), where 1 J = 1 N m = 1 kg m2 s−2. [PHYS 2.4. PHYS 2.5]

See also equipartition_of_energy_theoremequipartition of energy and internal energy.

energy band

for: electrons (or other charged particles)

in: a solid

is: a set of narrowly separated energy levels that the electrons (or other charged particles) may occupy. (Note that the energy bands are a property of the solid as a whole, not of the individual atoms within the solid.) [PHYS 11.4]

is formed: from an energy level for the electrons in individual atoms, which becomes split and broadened by the influence of other nearby atoms in the solid. [PHYS 11.4]

is usually separated: from other bands, just as the individual electron energy level from which it is derived is separated from other energy levels (though it is also possible for different bands to overlap). [PHYS 11.4]

See also, band theory, conduction band and valence band.

energy density

is: stored energy per unit volume of a medium. [PHYS 4.5]

is given by: ε0εrE2/2, in an electric field of magnitude E, where ε0 is the permittivity of free space and εr is the relative permittivity of the medium in which the field is present. [PHYS 4.5]

is given by: B2/(2μ0μr), in a magnetic field of magnitude B where μ0 is the permeability of free space, and μr is the relative permeability of the medium in which the field is present. [PHYS 4.5]

energy level

of: a system

in: a bound system, for example, in an atom or nucleus

and, furthermore, in: a quantum state of the bound system

is: one of several energies which the particle can have, and which appear as energy eigenvalues of the time–independent Schrödinger equation. [PHYS 8.2, PHYS 10.3, PHYS 10.4]

is also: according to quantum mechanics, a discrete value of energy, so long as the particle is in a bound state. If the particle can occupy the level for only a very short length of time, the Heisenberg uncertainty principle implies a spread in the measured values of the level’s energy, but the energy level remains discrete. [PHYS 8.4, PHYS 10.2, PHYS 10.3]

conventionally is: negative; the configuration of zero potential energy being chosen so that the particle’s negative potential energy outweighs its positive kinetic energy. [PHYS 10.3]

always includes: non–zero kinetic energy, even at the lowest of energy levels: according to quantum mechanics, a particle confined can never be still (see zero point energy). [PHYS 8.4]

will be: degenerate if more than one quantum state of the system corresponds to the energy of the level.

energy level diagram

for: a particle in a bound system, such as an atom or nucleus

shows: all the (conventionally) negative energy levels corresponding to bound states of the system, extending from the ground level to the ionization level, each one characterized by the quantum numbers of the state (or states if the energy level is degenerate). [PHYS 8.2, PHYS 9.2]

also shows: above the ionization level, the continuum of (conventionally) positive energy levels corresponding to the unbound states, in which the particle is free from the rest of the system. [PHYS 8.2, PHYS 9.2]

enlarged

means: made larger – as for an image formed by a lens or a mirror, when the image is larger than the object. [PHYS 6.3]

entrance pupil

is: the image of the aperture stop of an optical system, formed by all the lenses which precede it. [PHYS 6.4]

entropy

of: a system

is: a function_of_statefunction of its state. [PHYS 7.4]

requires for its full definition: a state of fixed entropy to be arbitrarily chosen, since only differences in entropy are physically meaningful.

changes: in going from a state a to a state b when a and b are linked by a reversible isothermal process involving heat transfer ΔQrev at temperature T by the amount $\Delta S = \dfrac{\Delta Q_{\rm rev}}{T}$. [PHYS 7.4]

more generally differs: between two states a and b which are linked by an arbitrary reversible process, by the amount $\displaystyle \Delta S = S_b - S_a = \int_a^b\dfrac{dQ}{T}$ where the integral is evaluated over the reversible process. (This remains true even if the state is changed from a to b by some other process.) [PHYS 7.4]

is exemplified: by the entropy of n moles of ideal gas at temperature T and occupying volume V:

$S = \dfrac{3nR}{2}\log_{\rm e}\left(\dfrac{T}{T_0}\right) + nR\log_{\rm e}\left(\dfrac{V}{V_0}\right) + S_0$

where R is the molar gas constant and S0 is the entropy assigned to a state with temperature T0 and volume V0. [PHYS 7.4]

provides: a measure of the extent to which energy transferred in the process is not available to do useful work. [PHYS 7.4]

in effect is: a measure of disorder. [PHYS 7.4]

has as its SI unit: J K−1. [PHYS 7.4]

See also second law of thermodynamics and principle of entropy increase.

envelope

of: a wave group

is: a curve or surface serving to characterize the group by moving with the group speed, and modulating the amplitudes of the individual waves that make up the group, as they move through the group at their individual phase speeds.

environment

is: that part of the Universe which does not constitute the system being studied. [PHYS 7.3, PHYS 7.4]

equality

is: a mathematical statement expressing the fact that one number (or algebraic expression) is equal to another. [MATH 1.1]

uses: the symbol: =. [MATH 1.2]

equating real and imaginary parts

is: a procedure which allows an equation involving complex numbers to be rewritten as two equations involving only real numbers. The procedure consists of equating the real parts of the expressions on either side of the equality, and then equating the imaginary parts. [MATH 3.1]

equation

is: an equality between two algebraic expressions. [MATH 1.1]

See also solution and identity.

equation of a circle

of: radius R

centred: on the origin

is: x2 + y2 = R2. [MATH 2.2]

See conic sections in the Maths For Science handbook.

equation of a line in three dimensions

in: a three–dimensional system of Cartesian coordinates

is: $\dfrac{x-a}{l}=\dfrac{y-b}{m}=\dfrac{z-c}{n}$ where (a, b, c) are the coordinates of a point on the line, and the constants l, m, n determine the direction of the line. [MATH 2.2]

equation of a plane

in: a three–dimensional system of Cartesian coordinates

is: ax + by + cz = d, where a, b, c and d are constants. [MATH 2.2]

equation of a straight line

in: standard form

is: y = mx + c where m is the gradient (or slope) of the straight line and c is the intercept on the y–axis. [MATH 2.2, MATH 1.3, PHYS 1.3]

also can be written: in the form ax + by + c = 0. [MATH 2.2]

equation of motion

is: an equation that expresses (explicitly or implicitly) the position of a moving object as a function of time. Such equations often take the form of differential equations and are usually obtained from Newton’s second law of motion. [MATH 6.1]

equation of state

for: any substance

is: an equation (usually an approximation) which relates the mass m or number of moles n of a fixed quantity of the substance to its volume V, pressure P, and temperature T (and/or any other relevant thermodynamic coordinates). [PHYS 7.2]

is exemplified: by the equation of state of an ideal gas, PV = nRT. [PHYS 7.2]

equation of state of an ideal gas

is: the equation PV = nRT, which relates the number n of moles, the volume V, the pressure P and the temperature T of a sample of ideal gas, where R = 8.314 J K−1 mol−1 is the molar gas constant. [PHYS 7.2, PHYS 7.3, PHYS 7.4]

is also known: as the ideal gas law, and may be written in a variety of ways. A particularly common form is PV = NkT, where N is the number of molecules in the sample and k = 1·380 × 10−23 J K−1 is Boltzmann’s constant. [PHYS 7.2, PHYS 7.3, PHYS 7.4]

equiangular

describes: a polygon when all of its interior angles are equal. [MATH 2.1]

equidistant

describes: two points which are at the same distance from a third. [MATH 2.1]

equilateral

describes: a polygon whose sides are all of the same length. (Used especially in the case of an equilateral triangle.) [MATH 2.1]

equilateral polygon

is: a polygon whose sides are of equal length. [MATH 2.1]

equilateral triangle

is: a triangle with three equal sides, and hence with three equal angles each of 60° (or, equivalently, of π/3 radians). [MATH 1.6, MATH 2.1]

equilibrium

is: the condition of a system in which its state of motion remains unchanged, i.e. the total linear momentum P and total angular momentum L are constant vectors. [PHYS 5.1, PHYS 7.3]

See also mechanical equilibrium, translational equilibrium and rotational equilibrium.

equilibrium state

of: a system

is: any state of the system in which it is in equilibrium (stable_equilibriumstable, unstable_equilibriumunstable or neutral_equilibriumneutral), usually specified in terms of appropriate (thermodynamic) coordinates. [PHYS 7.3, PHYS 7.4]

is exemplified: by any set of values for n, P, V and T which satisfy the equation of state of an ideal gas. [PHYS 7.3, PHYS 7.4]

equilibrium surface

See PVT–surface.

equilibrium system

is: a system in an equilibrium state.

equipartition of energy theorem

is: a theorem of classical statistical mechanics which relates the average microscopic internal energy of a system $\langle E_{\rm int}\rangle$ to the temperature via the number of degrees of freedom present in the system.

states that: if there are f degrees of freedom, then the mean internal energy per molecule will be given by $\langle E_{\rm int}\rangle = fkT/2$, where T is the absolute temperature, and k is Boltzmann’s constant. [PHYS 7.5]

equipotential contour

of: a specified potential

is: a curve passing only through points at which the specified potential has the same (arbitrarily chosen) value. [PHYS 3.1]

has the property: that at any point it is at right angles to the field associated with the potential. [PHYS 3.1]

usually is drawn: so that the potential changes by a fixed amount between consecutive equipotential contours. This means that consecutive contours are close together where the field is strong. [PHYS 3.1]

often is abbreviated: to ‘equipotential’. [PHYS 3.1]

equipotential line

See equipotential contour.

equipotential surface

of: a specified potential

is: a surface passing only through points at which the specified potential has the same (arbitrarily chosen) value. [PHYS 3.1, PHYS 3.3]

has the property: that at any point it is perpendicular to the field associated with the potential. [PHYS 3.1, PHYS 3.3]

usually is drawn: so that the potential changes by a fixed amount between consecutive equipotential surfaces. This means that consecutive surfaces are close together where the field is strong. [PHYS 3.1, PHYS 3.3]

often is abbreviated: to ‘equipotential’. [PHYS 3.1]

equivalent circuit

is: a circuit which produces identical effects to a circuit which it has replaced. [PHYS 4.1]

can be used: as an aid to circuit analysis. [PHYS 4.1]

erect (image)

means: upright − as for an image formed by a lens or a mirror, when the image is the same way up as the object. [PHYS 6.2, PHYS 6.3]

Contrast with inverted image.

erecting prism

is: a prism used to invert an already inverted image in an optical system and so make it erect. [PHYS 6.4]

error (of observation)

See uncertainty.

error bar

consists: of lines drawn on both sides of a point on a graph, to indicate the size of the uncertaintyexperimental error on that point. Lines drawn parallel to the x–axis show the size of the uncertainty in the xcoordinate; lines drawn parallel to the y–axis show the size of the uncertainty in the ycoordinate. [PHYS 1.3]

error function

is: a function that arises in various contexts, including the analysis of gaussian_distributionnormally distributed (Gaussian) errors.

is defined: by $\displaystyle {\rm erf}(x) = \dfrac{2}{\sqrt{\pi}}\int_0^x\exp(-y^2/2)\,dy$. [MATH 5.5]

escape speed

is: the minimum speed which must be given to a projectile for it to completely escape from the gravitational force of the Earth. [PHYS 2.4, PHYS 3.2]

is given: by $\upsilon_{\rm es} = \sqrt{\dfrac{2GM_{\rm E}}{R_{\rm E}}}$

where ME is the mass of the Earth, RE its radius and G is Newton’s universal gravitational constant. [PHYS 2.4, PHYS 3.2]

essential constants

are: independent arbitrary constants which appear in the general solution of a differential equation. [MATH 6.1]

Euler’s formula

is: an important relationship between the exponential, sine_functionsine and cosine functions:

eiθ = cos(θ) + isin(θ), where i2 = −1. [MATH 3.2, PHYS 5.5]

evaporation

is: a process whereby liquid is converted into gas (or more properly vapour) at a temperature below the boiling point.

involves: the escape of those molecules with above average kinetic energy from the liquid and therefore results in the cooling of the liquid.

is balanced: in a closed vessel containing liquid and vapour in equilibrium, by condensation.

even (function)

is: a function f(x) such that f(−x) = f(x). [MATH 1.6, MATH 4.4, MATH 5.2, PHYS 11.2]

event

in: Einstein’s special theory of relativity

is: an idealized occurrence at a point in space and an instant of time, and may therefore be located in an appropriate frame of reference by means of four coordinates (x, y, z, t).

exchange particles

See elementary particles.

excitation

is: the process whereby the electron in an atom is given additional energy and so moves to a bound state of higher energy. The additional energy may be provided by incoming radiation, by heating or via collisions with other particles, such as electrons. [PHYS 8.2]

excited level

is: the energy level corresponding to each excited state for an electron in an atom. [PHYS 8.2]

equivalently is: an energy level other than the ground level. [PHYS 10.3]

excited state

of: an electron

in: an atom or some other bound system

is: any bound state, other than the ground state, for the electron. [PHYS 8.2, PHYS 8.3]

equivalently is: a state of the system in which the energy corresponds to an excited level. [PHYS 10.3]

excluded volume

is: the volume occupied by a gas but from which molecules are excluded by virtue of their individual volumes. [PHYS 7.5]

exit pupil

is: the image of the aperture stop in an optical system, formed by all the lenses which follow it. [PHYS 6.4]

expansion

is: the process of making something larger in size.

expand (an expression)

of: an expression that involves brackets

describes: the process of finding an equivalent expression with fewer brackets. [MATH 1.1]

experiment

A planned investigation of natural phenomena, usually involving equipment, under conditions that are to some extent determined by the investigator.

See also experimental data.

experimental data

consists: of observations, particularly numerical measurements, which have been obtained in an experiment. [PHYS 1.1]

exponent

is: a superscript following a number or expression that indicates repeated multiplication (if the exponent is a positive integer) or some related operation in other cases. [MATH 1.5]

See arithmetic and algebra in the Maths For Science handbook.

exponential change

describes: any process in which a quantity exhibits exponential growth or exponential decay. If q is such a quantity, then q = q0ekt where q0 is a constant, t is an independent variable (e.g. time) and k is a positive or negative constant according to whether q is growing or decaying. [MATH 1.5]

is exemplified: by the change in an investment when the interest is compounded continuously as can be seen from the equation $\displaystyle {\rm e}^{kt} = \lim_{m\to0}(1+m)^{kt/m}$. [MATH 1.5]

exponential decay

describes: an exponential change in which the changing quantity decreases with time. [MATH 1.5]

is exemplified: by the radioactive decay law N = N0eλt

exponential form (of a complex number)

represents: a complex number as z = reiθ where r and θ are real. r is known as the modulus_of_a_complex_numbermodulus of z and is usually written as |z|, while θ is known as the argument of z and usually is written as arg(z). Adding an integer multiple of 2π to θ leaves the value of reiθ unchanged, so the arguments of a given complex number has infinitely many possible values. The unique value that satisfies the restriction −π < θπ is called the principal value of the argument. [MATH 3.2, PHYS 5.5]

Compare and contrast with Cartesian form and polar form, and see complex numbers in the Maths For Science handbook for the relationship between them.

exponential function

is: the function exp(x) = ex. [MATH 1.5]

has the general feature: the bigger it is, the faster it grows (or shrinks). [MATH 1.5]

more specifically, has: the property of being its own derivative, which makes it especially useful for doing calculus with exponential functions and logarithmic_functionlogarithms. [MATH 1.5]

sometimes refers: to the function f(x) = ax, which is related to the function exp(x) = ex by:

ax = exp(xloge(a)) [MATH 1.5]

exponential growth

describes: an exponential change in which the changing quantity increases with time. [MATH 1.5]

exponential law

is: any equation relating two quantities, x and y, that may be written in the form y = kax, where k is any constant and a is any positive constant. (Often a = e). [MATH 1.5, PHYS 1.3]

exponential representation (of a complex number)

See exponential form (of a complex number).

exposure

is: a measure of the total light energy reaching a photographic film or emulsion. [PHYS 6.4]

determines: the imaging response of the film or emulsion. [PHYS 6.4]

exposure time

is: the time interval over which a photographic film or emulsion is exposed to light. [PHYS 6.4]

expression

is: a combination of numbers and algebraic symbols. [MATH 1.1]

may be: the sum of several terms, or may be a single number or symbol. [MATH 1.1]

extended body

is: a body for which the size and shape are important. [PHYS 2.8]

extended image

is: an image with a finite size in an optical system, being an image of an extended object.

is usually shown: on a ray diagram as a directed line segment drawn at right angles to the optical axis. [PHYS 6.3]

extended object

is: an object which has a finite size in an optical system, as opposed to being a point object. Any actual object is an extended object. [PHYS 6.2]

is usually shown: on a ray diagram as a directed line segment drawn at right angles to the optical axis. [PHYS 6.3]

extension

is: a quantity that describes the displacement of the mobile end of a spring or some other elastic body from its natural (unextended) position. [PHYS 2.4]

exterior angle

is: the angle between a side of a polygon and an adjacent side produced. [MATH 2.1]

external force

is: a force whose source lies outside the system being considered. [PHYS 2.5]

is given: by the rate of change of linear momentum of the system. [PHYS 2.5]

extrapolation

is: the process of using values of a dependent variable, measured over a finite range of the corresponding independent variable(s), to estimate the value of the dependent variable corresponding to a value of the independent variable(s) that falls outside the measured range. [PHYS 1.3]

is exemplified: by the extension of a graph beyond the range of values within which measurements have been made. [PHYS 1.3]

Contrast with interpolation.

eye lens

in: a compound eyepiece

is: the lens which is nearer to the eye. [PHYS 6.4]

also describes: the lens of the eye itself. [PHYS 6.4]

See lens (of the eye).

eyepiece (lens)

in: an optical instrument

is: the lens nearest to the eye. [PHYS 6.4]

if compound is: the combination of lenses nearest to the eye. [PHYS 6.4]

f–number

of: a lens

is: a quantity that indicates the ratio of the focal length to the diameter of the lens aperture. [PHYS 6.4]

controls: the light–gathering ability of a lens for a given focal length; the higher the f–number the smaller the aperture of the lens and the greater the depth of field. [PHYS 6.4]

is exemplified: by f/5.6 for a lens with a focal length 5.6 times greater than its aperture diameter. [PHYS 6.4]

often is called: f–stop. [PHYS 6.4]

factor

of: a product

is: any one of the numbers or expressions that are multiplied together to create the product. [MATH 1.1]

See operation.

factorial

of: a non–negative integer, n

is denoted: by n!

is defined: as n! = n(n − 1)(n − 2)(n − 3) ... (2)(1) for n ≥ 1 and as 0! = 1 for n = 0. [MATH 1.7]

factorization

of: an algebraic expression (which may include complex numbers)

is: the procedure by which the expression is converted into factorized form. [MATH 1.3, MATH 1.4, MATH 3.3]

can always be carried out: for a quadratic function or any other polynomial function. [MATH 1.3, MATH 1.4]

factorized form

of: a polynomial function (especially a quadratic function)

is: the form f(x) = a(xα)(xβ) ... (xζ), which makes clear the roots of the equation f(x) = 0, i.e. any values of x at which the graph of the function f(x) intersects the x–axis. [MATH 1.3, MATH 1.4]

See factorization.

Fahrenheit

describes: a temperature scale which is related to the Celsius scale by the equation TF/(°F) = 9TC/(5°C) + 32 where TF is a temperature in degrees Fahrenheit and TC is the corresponding temperature in degrees Celsius.

far point

is: the farthest point from which light entering the eye may be imaged on the retina. [PHYS 6.4]

is: for a normal eye, at infinity. [PHYS 6.4]

farad, F

is: the SI unit of capacitance. [PHYS 4.5]

is defined: as one coulomb per volt: 1 F = 1 C V−1. [PHYS 4.5]

See capacitor. [PHYS 4.5]

Faraday’s law

states: that the magnitude of the induced voltage in a circuit is numerically equal to the rate of change of the magnetic flux linkage in the circuit: Vind = |/dt|. [PHYS 4.4]

See also electromagnetic induction and Lenz’s law.

fast neutrons

are: neutrons produced directly in nuclear fission and having kinetic energy (typically 1 MeV or more) which is too high to initiate further nuclear fission in uranium, but may do so in plutonium.

Contrast with thermal neutrons.

fast reactor

is: a breeder reactor which uses fast neutrons to induce nuclear fission in plutonium. [PHYS 9.3]

Fermat’s principle

states: that if a light ray passes from one fixed point to another fixed point, then the time taken to traverse the actual path will, to a first approximation, be equal to the time taken for light rays to traverse adjacent paths. That is, the time taken to traverse the path will be stationary with respect to small variations in the path. [PHYS 6.2]

means, in mathematical terms: that if the journey time along conceivable rays from one fixed point to the other is T(x) where x is some suitable parameter, then the actual path (or paths) will be determined by finding the value (or values) of x for which dT/dx = 0. [PHYS 6.2]

means, in physical terms: that light travels along the path which is locally of least time. [PHYS 6.2]

permits deduction: of all the basic rules and principles of geometrical optics. [PHYS 6.2]

fermion

is: any particle which has an intrinsic spin angular momentum which is a half–integer multiple of h/(2π) where h is Planck’s constant.

ferrites

are: ceramic materials made from sintered oxides of iron and barium. [PHYS 4.2]

can be formed: into strong permanent magnets. [PHYS 4.2]

in granular form can be: bonded with plastics and used in record/erase tapes for information storage. [PHYS 4.2]

ferromagnetic

describes: a class of materials which are strongly attracted by a permanent magnet even when not permanently magnetized. [PHYS 4.2]

comprise: primarily the five chemical_elementelements iron (Fe), cobalt (Co), nickel (Ni), gadolinium (Gd) and dysprosium (Dy), together with some associated alloys. [PHYS 4.2]

fibre bundle

is: a collection of many hundreds or thousands of individual optical fibres, bound together within a single sheath. [PHYS 6.2]

field

throughout: a region of space

is: a physical quantity to which a definite value can be ascribed at each point in the region, at a particular time. [PHYS 3.1]

See scalar field and vector field.

field ion microscope

is: a microscope that uses the (quantum) wave–like properties of a beam of ions to achieve finer resolution than is possible with an optical or (in some aspects) even an electron microscope. [PHYS 7.1]

field lens

in: a compound eyepiece

is: a lens which increases the ability of the eye lens to accept incoming rays over a wide range of angles. [PHYS 6.4]

field lines

are: directed curves that provide a means of representing a vector field. [PHYS 3.1]

are drawn: so that at any point the tangent_to_a_curvetangent to the line represents the direction of the field at that point, and the spacing of the lines is related to the field strength. That is, where the lines are close together the field is strong and where they are further apart the field is weaker. [PHYS 3.1]

See also equipotential surface.

field stop

is: a stop or aperture which defines the maximum angle of acceptance of rays passing through the eye lens of a compound eyepiece. [PHYS 6.4]

filter circuit

is: a circuit designed to block (or pass) signals in specific frequency ranges. [PHYS 5.4]

final velocity

is: the velocity at the end of a period of time. [PHYS 2.1]

See uniform acceleration equations.

finite series

is: a series with a limited (finite) number of terms. [MATH 1.7]

Contrast with infinite series.

first derivative test

is: a test to determine the location and nature of local extrema of a given function f(x).

involves: (a) finding the points at which f′(x) = 0, (b) investigating the behaviour of the sign of f′(x) in the neighbourhood of these points. If f′(a) = 0 and f′(x) changes from positive to negative at x = a then there is a local maximum at a. If f′(a) = 0 and f′(x) changes from negative to positive at a then there is a local minimum at a. If f′(a) = 0, but f′(x) does not change sign at x = a then further investigation is required. [MATH 4.4]

See stationary points and graph sketching in the Maths For Science handbook.

first focal point

in: the paraxial approximation

is: for a convex lens, the point F1 on the optical axis, from which rays are refracted by the lens to emerge parallel to the axis. [PHYS 6.3]

is: for a concave lens, the point F1 on the optical axis, from which rays which have been refracted parallel to the axis by the lens, appear to emanate. [PHYS 6.3]

is also called: first focus or object focus.

See focal length.

first focus

See first focal point.

first ionization energy

of: an atom

is: the energy required to remove the least tightly bound electron from the atom in its ground state. [PHYS 8.4]

first law of thermodynamics

states: that if a system undergoes a change from one equilibrium state to another, the difference between the heat Q supplied to the system and the work W done by the system will depend only on the initial and final equilibrium states and not on the process by which the change is brought about. [PHYS 7.3, PHYS 7.4, PHYS 7.5]

justifies: the introduction of a function of state known as the internal energy U which changes by an amount ΔU = QW in the process. [PHYS 7.3, PHYS 7.4, PHYS 7.5]

represents: the conservation of energy, but also has an additional implication. Because Q and W are not functions of state, their respective contributions to U cannot be disentangled, and it does not generally make sense to speak of the ‘heat content’ of a system. [PHYS 7.3, PHYS 7.4, PHYS 7.5]

first–order differential equation

is: a differential equation in which no derivative of the dependent variable of order_of_a_differential_equationorder higher than first order_of_a_differential_equationorder appears. [PHYS 5.4]

has: a general solution which always involves the introduction of an arbitrary constant. This constant can only be determined in any particular situation by imposing an appropriate boundary condition. [PHYS 5.4]

usually is assumed: to be of the degree_of_a_differential_equationfirst degree and may be written in the general form

$a(x)\dfrac{dy}{dx} + b(x)y = f(x)$. [MATH 6.2]

first term (of an arithmetic progression)

See arithmetic progression.

fissile

means: capable of undergoing nuclear fission. [PHYS 9.3]

fission

See nuclear fission.

fixed point

See calibration point.

flint glass

is: a glass of relatively high refractive index and thus high dispersive power. [PHYS 6.4]

fluid

is: a material which is not a solid and which is incapable of sustaining tensile stress, uni–axial compressive stress or shear stresses in equilibrium but can only sustain uniform stress or volume stress (i.e. pressure). [PHYS 7.6]

more simply, is: any substance which can flow. This is usually taken to mean a liquid or a gas. [PHYS 7.2]

fluid resistance

TBD

flux

of: particles

if: there are N particles per unit length moving along the x–axis each with velocity υx

is: the net rate at which particles cross a fixed plane per unit time, i.e. F = x. [PHYS 11.1]

See also flux (in quantum mechanics).

flux (in quantum mechanics)

of: particles, in a stream of particles represented by the spatial wavefunction ψ(x) = Aexp(ikx), which is an eigenfunction of the momentum operator.

given that: the average number of particles per unit length is the constant |A|2, and their velocity is obtained from the momentum, $\upsilon_x = p_x/m = \hbar k/m$

is: the net number crossing a fixed plane per unit time, i.e. $F =\lvert\,A\,\rvert^2 \hbar k/m$. [PHYS 11.1]

flux linkage

through: a coil of N turns

is given by: Φ = where ϕ is the magnetic flux through a single turn.

flux of a vector field

across: a surface S

is defined: to be the surface integral $\int_S{\boldsymbol V}\,{\boldsymbol\cdot}\,d{\boldsymbol S}$ where V represents the vector field, and dS is an element of area which is directed along an (abstractly chosen) outward pointing normal to the surface S. [MATH 2.6]

fluxmeter

is: a moving–coil galvanometer, designed with a damping force but no restoring force, so that a current pulse produces a non–returning deflection whose size is proportional to the total charge passed. [PHYS 4.4]

is used: to measure magnetic fields in conjunction with a search coil. [PHYS 4.4]

focal length

of: a lens or mirror

is: for parallel incident light, the distance (the image focal length) from the lens to its image focus; or the distance (the object focal length) from the lens to its object focus; or the distance from the mirror to the focus of the mirror. For a thin lens, the image focal length and object focal length are the same. [PHYS 6.3]

is: within the Cartesian sign convention a positive quantity for a convex lens or a concave mirror, and a negative quantity for a concave lens or a convex mirror. [PHYS 6.3]

focal point

in: the paraxial approximation

refers: for a lens to the object focus on the optical axis, from which rays are refracted by the lens to emerge parallel to the optical axis; also to the image focus on the optical axis, to which parallel rays converge after refraction by the lens. [PHYS 6.3]

is: for a concave mirror the point (called the focus) on the optical axis, to which rays parallel to the optical axis converge after reflection at the mirror. [PHYS 6.3]

is: for a convex mirror the point (called the focus) on the optical axis, from which rays parallel to the optical axis appear to diverge after reflection at the mirror. [PHYS 6.3]

See first focal point, second focal point, focal length.

focus (of a conic section)

See conic section.

focus (of a lens)

See focal point.

focus (of a mirror)

See focal point.

force

in: Newtonian mechanics

describes: the amount of ‘push’ or ‘pull’ exerted on a particle which, if unopposed, causes it to depart from the uniform motion predicted by Newton’s first law of motion. [PHYS 2.3]

therefore is: that which causes (or tends to cause) acceleration. [MATH 5.1]

is: a vector quantity, so it has both direction and magnitude_of_a_vector_or_vector_quantitymagnitude. [MATH 2.4, PHYS 2.3]

is quantified: by means of Newton’s second law of motion, which tells us that the acceleration a of a particle is proportional to the resultant force F that acts on it, and inversely proportional to its mass m. Thus, in terms of vectors,

F = ma

or in terms of (scalar) components,

Fx = max, Fy = may, Fz = maz [PHYS 2.3]

has as its SI unit: the newton (N). [MATH 2.4]

force constant

in: simple harmonic motion

is: the magnitude of the restoring force per unit extension. [PHYS 5.2]

force laws

are: rules that allow the prediction of the forces acting in any given situation. [PHYS 2.3]

include: Newton’s law of gravitation, the law of terrestrial gravitation, the laws of friction, Hooke’s law, Coulomb’s law and the Lorentz force law. [PHYS 2.3]

forced convection

See convection.

forced oscillations

See driven oscillator.

forced oscillator

See driven oscillator.

forced vibration

is: vibration which occurs when a system is supplied with energy periodically in order to keep it oscillating. [PHYS 5.2]

See driven oscillator.

forces of adhesion

are: attractive intermolecular forces acting across a boundary or interface between two materials and tending to cause their surfaces to stick together. [PHYS 7.6]

forces of cohesion

are: attractive intermolecular forces acting within a material and tending to hold the material together. [PHYS 7.6]

Fourier’s law

states: that the rate at which heat is transferred along a uniform bar of cross–sectional area A by conduction is proportional to the temperature gradient along the bar:

$\dfrac{dQ}{dt} = -\kappa A\dfrac{dT}{dl}$

where κ is the thermal conductivity coefficient, a characteristic of the material of the bar. (The minus sign indicates that the direction of heatheat flow is from high temperature to low temperature.) [PHYS 7.3]

fraction

is: the ratio of two integers or algebraic expressions. [MATH 1.1]

fractional error

is: a dimensionless expression for the error (i.e. uncertainty) in a quantity, obtained by dividing the absolute error by the quantity itself. [PHYS 1.1, PHYS 1.2]

See also percentage error.

fracture

is: the process of breaking. [PHYS 7.6]

frame of reference

is: a three–dimensional physical setting, such as a laboratory, which provides the assumed context in which events takes place. [PHYS 2.7]

is normally: fixed with respect to a specific observer. [PHYS 2.3]

is represented: by a coordinate system, that allows a unique position to be assigned to each event, and a system of suitably synchronized clocks (or some equivalent system) that enables a unique time to be assigned to each event. [PHYS 2.3]

Fraunhofer diffraction

is: diffraction in which a plane wavefront (i.e. parallel light) is incident on an aperture and the resulting diffraction pattern is observed also as plane wavefronts. [PHYS 6.1]

therefore: its observation involves either large distances or lenses. [PHYS 6.1]

free convection

See convection.

free fall

is: the motion of an object (generally close to the surface of the Earth or other large body) solely under the influence of gravitational force. [PHYS 3.2]

free particle

is: a particle moving freely without any force acting on it and therefore with no changes in its energy. [PHYS 10.2]

free space

is synonymous: with vacuum.

freezing point

of: a substance

is: the temperature at which the solid and liquid phases of the substance can coexist in equilibrium at a specified pressure (usually, but not necessarily, standard atmospheric pressure).

is synonymous: with melting point.

frequency

is: the number of cycles of a periodic motion occurring per second, at any fixed position. [MATH 6.4, PHYS 5.1, PHYS 5.5, PHYS 5.6, PHYS 5.7, PHYS 6.1]

therefore is equal: to the reciprocal of the period of the motion: f = 1/T. [MATH 6.4, PHYS 5.7, PHYS 5.1]

has as its SI unit: the hertz (Hz), where 1 Hz = 1 s−1. [PHYS 5.4]

frequency–stabilized laser

is: a laser whose frequency is stabilized by some process and so constitutes an oscillator of exceedingly high Q–factor with a very narrow resonance_absorption_bandwidthresonance bandwidth, and hence potential application as a time or frequency standard. [PHYS 5.3]

Fresnel lens

is: a flat lens, usually of large aperture and made from plastic, whose thickness (and hence weight) is reduced by a series of concentric steps in the curved surface. [PHYS 6.4]

is used: where a large-aperture inexpensive lens is required, e.g. in an overhead projector or in the back window of a bus. [PHYS 6.4]

friction

is: the phenomenon whereby a force (called a frictional force) acts on a body when it is in contact with another body (or with a viscous medium) and when there is relative_velocityrelative motion, or a tendency for relative_velocityrelative motion, between those bodies (or between the body and the medium). [PHYS 2.3, PHYS 5.2]

frictional force

is: a force that arises from friction. [PHYS 5.2]

acts in a direction: that opposes the actual or potential relative_velocityrelative motion that gives rise to it. [PHYS 5.2]

is, when there is actual relative motion: sliding friction, the magnitude_of_a_vector_or_vector_quantitymagnitude of which is given by μslideR, where R is the magnitude_of_a_vector_or_vector_quantitymagnitude of the reaction force on the body concerned, and μslide is a constant known as the coefficient of sliding friction. [PHYS 2.3, PHYS 5.2]

is, when there is only potential relative motion: static friction, the maximum magnitude_of_a_vector_or_vector_quantitymagnitude of which is given by μstaticR, where R is the magnitude of the reaction force on the body concerned, and μstatic is a constant known as the coefficient of static friction. [PHYS 2.3, PHYS 5.2]

fulcrum

of: a turning motion

is: the line about which the motion takes place, sometimes called the axis of rotation. [PHYS 2.7]

function

consists: of two sets and a rule, such that to each element_of_a_setelement of the first set (the domain) is associated a single element_of_a_setelement of the second set (the codomain). If the domain consists of the values of a variable x and the codomain consists of the values of a variable y then x is called the independent variable and y, the dependent variable and we write y = f(x). In such circumstances it is usual to say that f is a function of x and that y is its value. (Note that this definition excludes the possibility of defining a function that is multi–valued.) [MATH 1.3, MATH 5.2]

function of a function

See composite function.

function of a function rule

is: a rule for differentiating composite functions (i.e. functions of functions)

states: that if y is a function of u so that y = f(u) and u is a function of x so that y = g(x), then

$\dfrac{dy}{dx} = \dfrac{dy}{du}\times\dfrac{du}{dx} = f'(x)\times g'(x)$ [MATH 4.3]

See the chain rule in the Maths For Science handbook.

function of state

is: any property of a system that is entirely determined at any time by the state of the system at that time. In particular, it does not depend on the processes which brought the system to that state. [PHYS 7.3, PHYS 7.4]

is exemplified: by the internal energy U of a fixed quantity of ideal gas, which is determined by the temperature of the gas at any time (provided the gas is in equilibrium). Thus, changes in internal energy are determined by changes in temperature (one of the thermodynamic coordinates that specify the state) irrespective of the processes that bring them about. [PHYS 7.3, PHYS 7.4]

is NOT exemplified: by the heat Q supplied to a fixed quantity of ideal gas. The heat required to bring about a particular change of state will generally depend on the exact process involved, not just the initial and final states. [PHYS 7.3, PHYS 7.4]

function of two variables

is: a function whose domain consists of ordered pairs of values such as (x, y) where x and y are independent variables. [MATH 6.4]

fundamental

on: a string of finite length l

is: that standing wave of the string which has the greatest possible wavelength (and hence the lowest possible frequency, known as the fundamental frequency). [PHYS 5.6, PHYS 5.7]

is exemplified: for a string fixed at both ends with linear mass density μ and under a tension FT by the standing wave of wavelength 2l which has (fundamental) frequency

$\dfrac{1}{2l}\sqrt{\dfrac{F_{\rm T}}{\mu}}$

may be more generally applied: to other oscillatory systems that exhibit standing waves.

See harmonics.

fundamental constant

See universal constant.

fundamental force

is: any of the four known forms of interaction (gravitational_interactiongravitational, electromagnetic_interactionelectromagnetic, strong_interactionstrong, and weak_interactionweak) between elementary particles. These interactions (particularly the gravitational_interactiongravitational and electromagnetic interactions, which have unlimited ranges) are the ultimate cause of all the other ‘forces’ of physics.

fundamental frequency

See fundamental.

fundamental interaction

is: any of the four known modes (gravitational_interactiongravitational, electromagnetic_interactionelectromagnetic, strong_interactionstrong, and weak_interactionweak) by which elementary particles interact.

fundamental particle

is: a synonym for elementary particle.

is sometimes used more specifically: to mean those particles that are currently thought to be truly ‘elementary’, thereby including quarks, leptons, and exchange particles but excluding composite particles such as the proton and the neutron.

fundamental theorem of algebra

states: that any polynomial of degree n with complex number coefficients has, counting repeated roots an appropriate number of times, exactly n complex root_of_an_equationroots. [MATH 1.4, MATH 3.1]

fundamental theorem of calculus

relates: definite and indefinite integrals of a given function and thereby simplifies the evaluation of a definite integral, provided that an indefinite integral of its integrand can be found. [MATH 5.1, MATH 5.2]

states: that if F(x) is any indefinite integral of f(x) so that $\dfrac{dF}{dx} = f(x)$, then

$\displaystyle \int_a^b f(x)\,dx = \left[F(x)\right]_a^b = F(b) - F(a)$. [MATH 5.1, MATH 5.2]

fusion

can refer: to melting − the phase transition in which a solid becomes a liquid, upon absorption of the requisite amount of latent heat. [PHYS 7.4]

also can refer: to nuclear fusion. [PHYS 9.3]

fusion curve

is: the curve on the PT projection of the PVT–surface, which separates the solid phase from the liquid phase. [PHYS 7.4]

gamma–decay, γ–decay

is: a form of radioactive decay in which a nucleus emits a γ–ray (i.e. a photon with high energy, typically hundreds of keV, and possibly much higher). [PHYS 9.2]

gamma–radiation, γ–radiation

is: a form of electromagnetic radiation emitted in radioactive decay and characterized by wavelengths shorter than those of X–rays (i.e. less than or approximately equal to 0.4 nm). [PHYS 9.2]

galvanometer

See moving–coil galvanometer.

gas phase

is: a fluid phase of matter characterized by the lack of a definite volume or shape other than that imposed by a container. [PHYS 7.1]

at the microscopic level, can be described: as a system in which the thermal kinetic energy is much greater than the intermolecular bonding energies. [PHYS 7.1]

Gauss’ law

states: that for an electric field E, in a vacuum, the flux of E out of a closed surface S (as given by the surface integral of E over S with a suitably chosen outward pointing normal at each point on S) is equal to the total charge enclosed by S divided by the permittivity of free space, so

$\displaystyle \int_S {\boldsymbol E}\,{\boldsymbol\cdot}\,d{\boldsymbol S} = \dfrac{1}{\varepsilon_0}\times\left\{\text{the total charge} \atop \text{within surface }\right\}$ [MATH 2.6]

Gaussian distribution

is: a smooth curve (or the function describing such a curve) with the property that in a wide range of practical situations it represents the shape taken by the histogram of a large number of measurements of some quantity as the measurement intervals are made smaller and smaller. [PHYS 1.2]

is also known: as a normal distribution. Measurements with histograms that approach Gaussian distributions are said to be normally distributed. [PHYS 1.2]

mathematically can be described: by an equation of the form $y = \dfrac{1}{\sigma\sqrt{2\pi}}\exp\left[-(x-\langle x\rangle)/(2\sigma^2)\right]$, where $\langle x\rangle$ is the mean of the distribution and σ is the standard deviation of the distribution. (The mean and the standard deviation of a set of normally distributed measurements provide estimates of these two quantities.) [PHYS 1.2]

Gaussian integral

is: an integral of the form

$\displaystyle \int_0^\infty x^{2n}\exp(-ax^2)\,dx\quad\text{or}\quad\int_{-\infty}^\infty x^{2n}\exp(-ax^2)\,dx$

where n is a positive integer or zero, and a is a positive constant.

See further integration in the Maths For Science handbook for details of the evaluation of Gaussian integrals. [MATH 5.5]

general solution

of: a linear differential equation of order n

is: a solution that involves n essential constants. [MATH 6.1, PHYS 5.5]

generator

of: a geometrical surface (e.g. a cone)

is: a straight line which when moved in a prescribed way sweeps out the geometric surface. [MATH 2.3]

generic PVT–surface

is: the PVT–surface of a ‘typical’ substance. [PHYS 7.4]

is used: to illustrate general statements about features and properties of PVT- surfaces. [PHYS 7.4]

geometric figure

is: any shape (involving points, lines, curves, etc.) of interest to those studying geometry. [MATH 2.1]

geometric progression

is: a series of the form:

$\displaystyle \sum_{k=1}^n ar^{k-1} = a + ar + ar^2 + \dots + ar^{n-1}$

The constant, r is known as the common ratio. [MATH 1.7]

geometric series

See geometric progression.

geometric series for complex numbers

where: z is a complex variable

is: a series of the form a + az + az2 + ... +azn, the sum of which is equal to (1 − zn+1)/(1 − z) if z ≠ 1. [MATH 3.3]

geometric vector

is: a directed line segment that may be used to represent a vector quantity. [MATH 2.5]

geometrical optics

is: the branch of optics which is based on the ray approximation to the wave model of light. [PHYS 6.1, PHYS 6.2]

assumes: that light follows paths called rays which obey the principle of reversibility and the principle of rectilinear propagation, and which satisfy the law of reflection and the law of refraction. [PHYS 6.1, PHYS 6.2]

geometry

is: that branch of mathematics which is concerned with the properties of space and of figures in space. [MATH 2.1]

geostationary

describes: Earth satellites which orbit in such a way that they are permanently located above a particular point on the Earth’s surface. Such satellites must travel with the same angular velocity as the Earth itself, and the satellite orbit must be directly above the equator. [PHYS 2.6]

also describes: the orbit for such Earth satellites. [PHYS 2.6]

geosynchronous

is often used synonymously: with geostationary.

is sometimes used more generally: to indicate an Earth satellite in an orbit with a 24 hour period that might be inclined at an angle to the equator. (Such a satellite would cross the same point on the equator at the same time each day, but would not be permanently located above that particular point.)

global maximum

of: a function

on: an interval

is: the greatest value of the function on that interval. [MATH 4.4]

also known as: absolute maximum.

See stationary points and graph sketching in the Maths For Science handbook.

global minimum

of: a function

on: an interval

is: the least value of the function on that interval. [MATH 4.4]

also known as: absolute minimum.

See stationary points and graph sketching in the Maths For Science handbook.

graded–index fibre

is: an optical fibre in which the refractive index gradually decreases from the axis of the fibre and in which continuous refraction is used to confine light rays within the fibre and away from the surface of the fibre. [PHYS 6.2]

gradient

of: a straight line (or the corresponding linear function)

is: a measure of the rate at which one quantity changes with another quantity. As a graph with given scales on the Cartesian axes, the gradient controls the angle between the line and the horizontal.

is often used synonymously with: the slope of the straight line.

is given: for a straight line drawn as a graph on conventional Cartesian axes, with x horizontal and y vertical, by the ratio of a difference in y values to the corresponding difference in x values between any two points on the straight line,

i.e. $\text{gradient} = \dfrac{y_2-y_1}{x_2-x_1} = \dfrac{\Delta y}{\Delta x} = \dfrac{\text{rise}}{\text{run}}$ [MATH 1.3, MATH 2.2, PHYS 1.3]

may be easily found: from the gradient–intercept form of the equation of a straight line, y = mx + c, where it is represented by the constant m.

may be used more generally: at a point on a curve, to refer to the gradient of the straight line that is a tangent_to_a_curvetangent to the curve at the point. is equal, in this more general sense; to the derivative of the function that describes the curve, evaluated at the point in question i.e. the gradient of y = f(x), at x = a is f′(a). [MATH 4.2]

gradient–intercept form

of: the equation of a straight line

is: y = mx + c where m is the gradient (i.e. slope) of the straight line and c is the intercept of the straight line with the y–axis. [MATH 2.2, MATH 3.1]

gram, g

is: an SI unit of mass, a submultiple of one of the seven base units.

is defined by: 1 g = 10−3 kg.

graph

is: the representation of an equation or function in geometric form, normally using Cartesian coordinates. In the case of a function f(x) the graph is usually that of the equation y = f(x). [MATH 1.3, MATH 5.2, PHYS 1.3]

graph sketching

is: the process of constructing a ‘rough’ graph of a function, which shows the salient features of the function without requiring detailed plotting. [MATH 4.4]

grating relation

for: a diffraction grating with slits separated by a distance d illuminated by normally incident light of wavelength λ

relates: the angles θn, at which nth order maxima in the diffraction pattern will be found, to n, λ and d. [PHYS 6.1, PHYS 8.2]

states: that = dsinθn. [PHYS 6.1, PHYS 8.2]

grating spacing

is: the distance between the slits in a diffraction grating. [PHYS 6.1]

gravitational constant

See Newton’s universal gravitational constant.

gravitational energy

See gravitational potential energy.

gravitational field

throughout: a region of space

is: a vector field which gives rise to a gravitational force on a test mass placed at any point in the region. [PHYS 3.1]

is defined: at any point specified by a position vector r, as the gravitational force per unit mass that would act on a test mass placed at that point. So, generally,

${\boldsymbol g}({\boldsymbol r}) = \dfrac{{\boldsymbol F}(\text{on }m\text{ at }{\boldsymbol r})}{m}$

where is the test mass. [PHYS 3.1, PHYS 3.2]

is related: to the gravitational potential by the requirement that it points in the direction of most rapid decrease of the potential, and has a magnitude given at every point by the magnitude of the rate of change of the potential (e.g. in the radial direction from an isolated point mass, so that gr = −dVgrav/dr). It therefore always points in a direction at right angles to lines or surfaces of equal potential, and from high potential towards low potential. [PHYS 3.1, PHYS 3.2]

has as its SI unit: the newton per kilogram (N kg−1). [PHYS 3.1, PHYS 3.2]

gravitational field strength

at: any point

is: the magnitude_of_a_vector_or_vector_quantitymagnitude of gravitational field at that point. [PHYS 3.1]

therefore is also: the magnitude_of_a_vector_or_vector_quantitymagnitude of the acceleration of a unit point mass in free fall due to gravity at that point. [PHYS 3.2]

See also surface gravity.

gravitational force

is: in Newtonian mechanics, an attractive force that acts between particles having mass. [PHYS 3.1]

is described: by the universal law of gravitation, which says that the gravitational force on a particle of mass m2 due to a particle of mass m1 a distance r away is

${\boldsymbol F}_{\rm grav} = {\boldsymbol F}_{21} = -\dfrac{Gm_1m_2}{r^2}\hat{\boldsymbol r}$

where G is Newton’s universal gravitational constant and r^ is a unit vector pointing from m1 to m2. [PHYS 3.1]

arises: from the gravitational interaction, one of the fundamental interactions in nature. [PHYS 3.1, PHYS 9.2]

See also surface gravity.

gravitational interaction

is: the fundamental interaction that gives rise to gravitational force. [PHYS 9.2]

comprises: together with the electromagnetic_interactionelectromagnetic, weak_interactionweak and strong_interactionstrong interactions, the four known fundamental interactions of nature. [PHYS 9.2]

gravitational mass

is: the mass of a body as determined by the gravitational force that it experiences or exerts. (See Newton’s law of gravitation.) [PHYS 2.3]

Contrast with inertial mass.

gravitational potential

at: a point in space where there is a gravitational field

is: the gravitational potential energy per unit mass due to the gravitational field at that point. [PHYS 3.1, PHYS 3.2]

has as its SI unit: the joule per kilogram (J kg−1).

gravitational potential energy

is: the potential energy that a body has by virtue of its position in a gravitational field. [PHYS 2.4]

requires for its full definition: a position of zero gravitational potential energy to be arbitrarily chosen, since only differences in gravitational potential energy are physically meaningful.

changes: in going from point A to point B, by an amount equal to the negative of the work done by the gravitational field when the body is moved from A to B. [PHYS 3.2]

is exemplified: by the gravitational potential energy of a particle of mass m2 in the gravitational field of a particle of mass m1 when the distance between the two particles is r. Subject to the conventional choice that Egrav = 0 when r → ∞, this is given by

$E_{\rm grav} = -\dfrac{Gm_1m_2}{r}$

where G is Newton’s universal gravitational constant. [PHYS 2.4, PHYS 3.1, PHYS 3.2, PHYS 5.2]

is related: to the gravitational potential Vgrav in a region by Egrav = mVgrav, so when a mass m moves through a gravitational potential difference ΔVgrav, the change in gravitational potential energy ΔEgrav is given by ΔEgrav = mΔVgrav. [PHYS 3.1, PHYS 3.2, PHYS 4.1]

often is abbreviated: to gravitational energy. [PHYS 3.1, PHYS 3.2]

has as its SI unit: the joule (J).

gravity

is: the phenomenon that gives rise to gravitational effects such as the gravitational force on an object.

gray, Gy

is: the SI unit of absorbed dose of ionizing radiation.

is defined: by 1 Gy = 1 J kg−1. [PHYS 9.3]

See also sievert.

grazing incidence

is: a situation in which the angle of incidence at a surface is very close to 90°. [PHYS 6.2]

ground level

of: an atom

is: the energy level corresponding to the ground state of an electron in an atom. [PHYS 8.2]

more generally is: the energy level corresponding to the minimum energy for a system. [PHYS 10.3]

ground state

of an atom, is: the state of the atom in which all the electrons occupy the lowest possible energy levels. [PHYS 8.2, PHYS 8.3, PHYS 8.4]

generally, is: a condition or state for a system in which its energy has the minimum value. [PHYS 10.3]

group

of: chemical elements

is: a set of chemical elements, commonly placed in a vertical column in a periodic table because of similarities in chemical properties. [PHYS 8.4]

group speed

of: wave groups composed of superpositions of waves with a variety of frequencies

in: dispersive media (i.e. when waves of different frequencies propagate at different speeds)

is: the speed at which the envelope of the wave group propagates. [PHYS 5.6]

generally will differ: from the phase speed of any of the individual waves which contribute to the formation of the wave group. [PHYS 5.6]

gyroscope

is: a spinning wheel, mounted on very low friction bearings called gymbals, which exert no torque and so allow the axis of rotation to maintain its direction through conservation of angular momentum, even if the support on which the gyroscope and gymbals are mounted, alters its orientation. [PHYS 2.8]

therefore can be used: as a navigational device on ships, aeroplanes, and spacecraft. [PHYS 2.8]

half–angle formulae

are: a class of trigonometric identities. [MATH 1.6]

See trigonometric functions in the Maths For Science handbook.

half–argument identities

are: a class of hyperbolic function identities. [MATH 4.6]

See hyperbolic functions in the Maths For Science handbook.

half–life

of: radioactive nuclei in a prepared sample

is: the time taken for half the nuclei in the sample to decay. [MATH 1.5, PHYS 9.1, PHYS 9.2]

hence is: the time taken for the activity to halve. [PHYS 9.2]

is: a property of radionuclides, unaffected by the physical or chemical environment. [PHYS 9.2]

half–power points

on: the power absorption curve of an oscillator

are: the frequencies on either side of the resonance, at which the power absorption has half its peak value. [PHYS 5.3]

Hall effect

is: the creation of a potential difference, the Hall voltage, when a current- carrying specimen is placed in a magnetic field having a components_of_a_vectorcomponent at right angles to the current. [PHYS 4.3]

Hall probe

is: a device to measure magnetic fields using the Hall effect. [PHYS 4.3]

usually contains: a semiconductor wafer and a sensitive voltmeter. [PHYS 4.3]

Hall voltage

is: the transverse potential difference created by the Hall effect. [PHYS 4.3]

arises: when a current–carrying specimen is placed in a transverse magnetic field. [PHYS 4.3]

is: transverse to the directions of both the magnetic field and the current. [PHYS 4.3]

arises from: the Lorentz force on the current–carrying charged particles. [PHYS 4.3]

halogens

are: the chemical elements fluorine, chlorine, bromine, iodine and astatine. [PHYS 8.4]

occupy: Group VII of the periodic table. [PHYS 8.4]

are named after: the Greek words hals (sea–salt) and gennao (I produce) because three of the element_chemicalelements (chlorine, bromine and iodine) can be prepared from this source. [PHYS 8.4]

Hamiltonian operator

in: quantum mechanics

is: the differential operator which corresponds to the total energy of a system. [PHYS 10.4, PHYS 11.3]

has: the time–independent Schrödinger equation as an eigenvalue equation. [PHYS 10.4, PHYS 11.3]

is represented: for a particle of mass m moving in one dimension, parallel to the xaxis, with a potential energy function U(x), by

$\hat{\rm H} = \dfrac{-\hbar^2}{2m}\dfrac{d^2}{dx^2} + U(x)$ [PHYS 10.4]

harmonic oscillator

is: an oscillator undergoing simple harmonic motion (SHM). [PHYS 5.3]

harmonically driven linearly damped harmonic oscillator

is: a harmonic oscillator with a damping force which is a linear function of the velocity of the oscillator (i.e. of the first derivative of the displacement of the oscillator), and which is driven by an external driving force of a simple sinusoidal form. [PHYS 5.3, PHYS 5.5]

harmonics

for: standing waves on a string

are: the sequence of allowed frequencies. The first in the series is the fundamental. Those other than the fundamental are sometimes referred to as overtones. [PHYS 5.6, PHYS 5.7]

heat

is defined: as energy transferred as a direct result of temperature difference. [PHYS 5.2, PHYS 7.2, PHYS 7.4, PHYS 7.5]

therefore is seen: as energy undergoing a particular process rather than as a particular ‘form’ of energy. [PHYS 5.2, PHYS 7.2, PHYS 7.4, PHYS 7.5]

contributes: along with work, to changes in the internal energy of a system, though it is impossible to say how much of the internal energy was provided as heat and how much as work unless the entire history of the system is known. [PHYS 5.2, PHYS 7.2, PHYS 7.4, PHYS 7.5]

may be transferred: from place to place by conduction, convection or radiation. [PHYS 7.3]

is also used to refer, somewhat improperly: to the internal kinetic energy of a body arising from the random microscopic motion of the atoms and molecules that it contains. [PHYS 7.3]

heat capacity

of: a system with uniform temperature

is: the ratio ΔQT of the heat transferred to a single-phase system, to the corresponding change in temperature of the system. [PHYS 7.4]

strictly should be defined: as the limit of this quantity as ΔT becomes vanishingly small, since the value of the ratio will depend on the state of the system. [PHYS 7.4]

therefore also depends: on the constraints applied during heating; see principal specific heats. [PHYS 7.4]

has as its SI unit: J K−1. [PHYS 7.4]

See also molar specific heat and specific heat. [PHYS 7.4]

heat energy

is: an archaic term which casts heat as a ‘form’ of energy, that is still sometimes used to refer to part or all of the internal energy of a system.

is exemplified: by the statement that when one body collides inelastically with another, part of the kinetic energy is transformed into heat energy which results in a rise in temperature of the colliding bodies. [PHYS 5.2]

See heat.

heat engine

is: a device (such as a steam engine) where the supply and removal of heat (generally in a closed cycle) results in the device doing work. [PHYS 7.4]

heavy damping

of: a damped harmonic oscillator

is: a condition in which the oscillator will not complete any oscillations before coming to rest, but having a higher level of damping than in critical damping. [PHYS 5.2, PHYS 5.5]

is often used as synonymous: with overdamping.

See critical damping and light damping.

Heisenberg uncertainty principle

imposes: a fundamental limitation on the combined precision with which certain pairs of observables can be simultaneously determined. [PHYS 10.2, PHYS 10.3, PHYS 11.1]

can be regarded: as a consequence of the wave nature of matter. [PHYS 10.2, PHYS 10.3]

is exemplified: for the uncertainty Δx in the xcoordinate of a particle’s position, and the uncertainty Δpx in the corresponding momentum component, by the relationship: $\Delta x\Delta p_x \ge \dfrac{h}{4\pi}$, where h is Planck’s constant. [PHYS 10.2, PHYS 10.3]

is also exemplified: by the relationship ΔE Δth , between the uncertainties in a measurement of energy and the time taken to make the measurement. [PHYS 10.2, PHYS 10.3, PHYS 11.1]

has nothing to do: with the methods employed to make the measurements. [PHYS 10.2, PHYS 10.3, PHYS 11.1]

helical

in: geometry

means: pertaining to a helix. [MATH 2.1]

helix

is: a curve drawn around a cylinder, with successive turns displaced in the axial direction. [PHYS 4.2]

henry, H

is: the SI unit of inductance.

is defined: by 1 H = 1 V s A−1, so a closed circuit will have an inductance of 1 H when the current in it varies at a rate of 1 A s−1 to produce an induced voltage of 1 V. [PHYS 4.4, PHYS 4.5]

is, for practical purposes: a medium sized unit. Widely used inductances vary from a few microhenry to hundreds of henry. [PHYS 4.5, PHYS 5.4]

See also coefficient of mutual inductance and coefficient of self inductance.

hertz, Hz

is: the SI unit of frequency.

is defined: by 1 Hz = 1 s−1, so a frequency of 1 Hz is equivalent to one cycle per second. [PHYS 5.1]

hidden variable theory

is: any theory that makes use of variables which, if their values were known, would permit more precise predictions of the outcomes of experimental measurements than those of conventional quantum theory. [PHYS 10.2]

implies: that quantum theory is an incomplete theory, and that the ‘fuzziness’ of its predictions is a reflection of our limited understanding and not a feature of the Universe itself. [PHYS 10.2]

is opposed: to the conventional Copenhagen interpretation of quantum physics. [PHYS 10.2]

high–pass filter

is: a filter circuit that passes high frequency signals with relatively undiminished amplitude, but blocks low frequency signals. [PHYS 5.4]

Contrast with low–pass filter.

higher derivatives

of: a function y = f(x) with first derivative $\dfrac{dy}{dx} = f'(x)$

are: the derivatives $\dfrac{d^n}{dx^n} = f^n(x)$ where n ≥ 2. [MATH 4.3]

histogram

is: a graphical representation of a set of measurements. [PHYS 1.2]

consists of: a number of rectangles, the areas of which are proportional to the number of measurements falling within a given interval, represented by the width of the rectangles. [PHYS 1.2]

hole

is: a vacancy in the one of the normally filled energy bands in a solid. [PHYS 11.4]

behaves: like a positive charge carrier and thereby contributes to the electrical conductivity of the solid. [PHYS 11.4]

hole conduction

is: electrical conduction due to mobile holes, such as may occur in a p–type semiconductor. [PHYS 4.3]

homogeneous differential equation

is: a differential equation in which every term involves the same single variable or one of its derivatives. [PHYS 5.3, PHYS 5.5]

homopolar generator

is: a device that generates a steady d.c. voltage by spinning a conduction_of_electricityconducting disc in a magnetic field. [PHYS 4.4]

Hooke’s law

states: that for sufficiently small stress, the strain in a material is directly proportional to the stress causing it. [PHYS 7.6]

therefore requires: that the restoring force, Fx, exerted by a spring that obeys Hooke’s law is proportional to the extension or compression, x, of the spring from its unstretched length, so that Fx = −kssx, where kx is the spring constant. [PHYS 2.3, PHYS 2.4, PHYS 5.1, PHYS 5.2]

sometimes is expressed: in terms of the applied force Fxapp = −Fx which is required to maintain a given extension. [PHYS 2.3, PHYS 2.4, PHYS 5.1, PHYS 5.2]

leads: to the definition of a range of elastic moduli such as Young’s modulus, shear modulus and bulk modulus. [PHYS 7.6]

horizontal asymptote

is: an asymptote which is horizontal and which therefore has zero gradient. [MATH 4.4]

horizontal point of inflection

is: a point of inflection at which the first derivative is zero.

horsepower, hp

is: a non-SI unit of power.

is defined: by 1 hp = 7.457 × 102 W. [PHYS 2.4]

Hund’s rule

for: a subshell of an atom in its ground state.

is: an empirical rule requiring that the number of unpaired electrons in the subshell has its maximum value. [PHYS 8.3]

Huygens’ principle

states: that each point on a wavefront may treated as a source of secondary wavelets, or waves, that expand radially from their source with the same speed as the original wave. [PHYS 6.1]

hydrogen bond

is: a weak bond which may occur in hydrogen–containing materials, resulting from the ’sharing’ of a hydrogen atom between two other atoms. [PHYS 7.1]

typically has: an bonding energy of less than 0.5 eV

is important: in many organic molecules and solids. [PHYS 7.1] [PHYS 7.1]

hydrostatic pressure

is: the pressure (which is the same in all directions) developed internally in a body of fluid due to the weight of the elements of fluid above. [PHYS 7.6]

hyperbola

is: a conic section that may be described by an equation of the form

$\dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1$ where $b=a\sqrt{e^2-1}$ with e > 1,

though it often arises in the form of a rectangular hyperbola for which y = k/x. [MATH 1.3, MATH 2.3, PHYS 1.3, PHYS 3.2]

See conic sections in the Maths For Science handbook for further details.

hyperbolic functions

are: the functions sinh, cosh, tanh and (usually) the related reciprocal functions sech, cosech and coth. [MATH 4.6]

take their name: from the fact that

x = acosh(t)

y = bsinh(t)

are parametric equations for a hyperbola. [MATH 4.6]

See hyperbolic functions in the Maths For Science handbook for further details.

hyperbolic function identities

are: identities relating the hyperbolic functions, such as cosh2(x) − sinh2(x) = 1. [MATH 4.6]

See hyperbolic functions in the Maths For Science handbook for a detailed listing.

hypermytropia (long sight)

is: the condition in which eyes are unable to focus on objects as close as the standard near point (taken to be at 25 cm). [PHYS 6.4]

occurs: when the lens of the eye has too long a focal length, even when fully accommodated. [PHYS 6.4]

usually is corrected: by using an auxiliary converging lens. [PHYS 6.4]

Contrast with myopia.

hypotenuse

of: a right–angled triangle

is: the side opposite the right angle. [MATH 1.6, MATH 2.1]

is also: the longest side of such a triangle. [MATH 1.6, MATH 2.1]

i

symbolizes: the algebraic quantity satisfying the rule i2 = −1; the basis of imaginary numbers. [MATH 3.1]

ideal elastic string

See ideal string.

ideal gas

is: a gas that obeys the ideal gas equation of state, PV = nRT, where P is the pressure of the gas, V is its volume, n is the amount of gas (expressed in moles), R is the molar gas constant and T is the absolute temperature. [PHYS 7.2, PHYS 7.3, PHYS 7.4, PHYS 7.5]

exists: only as an idealized entity, but is well approximated by a real gas at sufficiently low density. [PHYS 7.2, PHYS 7.3, PHYS 7.4, PHYS 7.5]

ideal gas absolute temperature scale

is: a temperature scale based on measurements made with real gases using a constant–volume gas thermometer, and extrapolated to the limit of zero pressure in which the gas may be considered to be an ideal gas. [PHYS 7.2]

is defined: by the thermometric relation

$\displaystyle T = \lim_{P_{\rm triple}\to0}\left(\dfrac{P}{P_{\rm triple}}\right) \times 273.16\,{\rm K}$

where P is the pressure of a fixed volume of gas at temperature T, and Ptriple is the pressure of the same sample of gas, occupying the same volume, at the triple–point temperature of H2O which is defined to be 273.16 K. [PHYS 7.2]

ideal gas equation of state

is: a relationship between pressure P, volume V and temperature T, which is obeyed by an ideal gas. [PHYS 7.2, PHYS 7.5]

sometimes is referred to: as the ideal gas law. [PHYS 7.2, PHYS 7.5]

is written: as

PV = nRT or PV = NkT

where n is the number of moles of gas, R is the molar gas constant, and T is the absolute temperature. Equivalently, N is the number of molecules in the system and k is Boltzmann’s constant. [PHYS 7.2, PHYS 7.5]

ideal gas law

See ideal gas equation of state.

ideal spring

is: an elastic body which may be compressed or extended by an external force and in which Hooke’s law is obeyed. [PHYS 2.3]

ideal string

is: an elastic string which always obeys Hooke’s law when it is stretched, irrespective of the amount of stretching. [PHYS 2.3]

ideal transformer

is: a transformer with 100% flux linkage between the primary and secondary coils and with 100% transfer of electrical power between the two coils, with no dissipation of power. [PHYS 4.4]

ideal voltage generator

is: a voltage generator with zero output resistance (i.e. zero internal resistance). [PHYS 4.1]

is symbolized: by an open circle with a labelled arrow alongside to indicate the magnitude and polarity of the voltage. [PHYS 4.1]

identity

is: an equation relating two expressions that is true for all meaningful values of the variables involved in those expressions. [MATH 1.6]

is exemplified: by (x + 1)2 = x2 + 2x + 1. [MATH 1.6]

sometimes is indicated: by using the symbol ≡ in place of the more usual =. [MATH 1.6]

ill–conditioned

describes: a system of equations for which small changes in the coefficients cause large changes in the solutions. [MATH 2.2]

image

is: a representation of an object. [PHYS 6.2, PHYS 6.3]

is produced: by reflection at a mirror surface, or refraction at an interface between transparent media or at a combination of interfaces such as a lens or some other optical system. [PHYS 6.2, PHYS 6.3]

arises: when light rays leaving a point on the object are brought back together (real image) or appear to be brought back together (virtual image) to a common point. [PHYS 6.2, PHYS 6.3]

can be seen: either as a point image or an extended image. [PHYS 6.2, PHYS 6.3]

image distance

is: the distance υ, measured along the optical axis, between an image and a lens or mirror. [PHYS 6.3]

might more appropriately be termed: the image position, since (according to the Cartesian sign convention) it may be a positive or negative quantity, depending on the side of the origin on which it lies. [PHYS 6.3]

See also thin lens equation and spherical mirror equation. [PHYS 6.3]

image focus

See second focal point.

imaginary axis

is: the axis in a complex plane (or Argand diagram) along which the imaginary part of a complex number is represented. [MATH 3.1]

imaginary number

is: a complex number of the form iy where y is a real number and i2 = −1. [MATH 1.4, MATH 3.1]

therefore is: a complex number in which the real part is zero. [MATH 1.4, MATH 3.1]

imaginary part

of: a complex number, z = x + iy (where x and y are real numbers)

is: the term y. [MATH 1.4, MATH 3.1, PHYS 5.5]

often is denoted: by Im(z). [MATH 1.4, MATH 3.1, PHYS 5.5]

impedance (electrical)

of: a single electrical component or a two terminal network, in which an alternating current of peak value I0 flows in response to an externally supplied alternating voltage of peak value V0

is: the quantity Z = V0/I0. [PHYS 5.4, PHYS 5.5]

is analogous: to the resistance of a d.c. circuit component. [PHYS 5.4, PHYS 5.5]

is given: by $Z = \sqrt{R^2+X^2}$ where R is the resistance and X is the reactance of the component or network. [PHYS 5.4]

has as its SI unit: the ohm (Ω). [PHYS 5.4, PHYS 5.5]

generally depends: on the angular frequency of the supply (since X depends on that frequency).

is at a minimum: for a series LCR circuit at the circuit’s natural frequency. [MATH 6.3, PHYS 5.3, PHYS 5.4]

is at a maximum: for a parallel LCR circuit at the circuit’s natural frequency. [MATH 6.3, PHYS 5.3, PHYS 5.4]

See complex impedance, mechanical impedance.

impedance matching

is: a method of linking two circuits which have different impedances to ensure the maximum transfer of power between them. [PHYS 4.4]

may be achieved: using the primary and secondary coils of a transformer. [PHYS 4.4]

implicit differentiation

is: a form of differentiation using the chain rule. [MATH 4.3]

is used: for differentiating implicit functions which are defined by an equation that relates the dependent variable (y) and the independent variable (x) but where neither variable is the subject of the equation. [MATH 4.3]

is done: by differentiating both sides of the equation, which yields, in general, an expression in y and x for dy/dx. [MATH 4.3]

is exemplified: by implicit differentiation of x2 + y2 = a2 with respect to x, which yields 2x + 2y(dy/dx) = 0, so that (dy/dx) = −x/y. [MATH 4.3]

implicit function

is: a function defined by an equation that relates the dependent variable (y) and the independent variable (x) but where neither variable is the subject of the equation. [MATH 4.3, MATH 6.1]

is exemplified: by the function y(x) defined by y + siny = 3x. [MATH 4.3, MATH 6.1]

improper integral

is: a definite integral in which:

(a) one or both of the limits of integration is an infinite quantity (positive or negative), or

(b) the integrand becomes infinite at some point or points in the range of integration, or

(c) both of the above apply. [MATH 5.2]

may be evaluated: as limits of appropriate proper integrals. [MATH 5.2]

impulse

is: the product of the force acting and the time over which it acts, (i.e. impulse = FΔt for a constant force).

is: a vector quantity

has as its SI unit: the N s (i.e. newton second).

is equal: to the change in momentum which follows from the impulse, i.e. Δp = FΔt. [PHYS 2.5]

impurity conduction

is: electrical conduction due to impurities that contribute electrons or holes to a material (particularly a semiconductor). [PHYS 11.4]

in anti–phase

describes: the phase relationship between two specified oscillations such as A = A0sin(ωt + ϕ1) and B = B0sin(ωt + ϕ2) that have the same angular frequency ω and which respectively involve phase constants ϕ1 and ϕ2 that differ by an odd integer multiple of π so that ϕ2ϕ1 = (2n + 1)π, where n is any integer. The maxima of one oscillation then coincide with the minima of the other. [PHYS 5.1, PHYS 5.7, PHYS 6.1]

may also be applied: to waves at a common point (or possibly at separate points) by comparing the oscillations caused by the waves at the relevant point(s).

See phase relationship, in phase and out of phase.

in phase

describes: the phase relationship between two specified oscillations such as A = A0sin(ωt + ϕ1) and B = B0sin(ωt + ϕ2) that have the same angular frequency ω and which respectively involve phase constants ϕ1 and ϕ2 that differ by an integer multiple of 2π so that ϕ2ϕ1 = 2, where n is any integer. The maxima of one oscillation then coincide with the maxima of the other, as do all other stages of the oscillation. [PHYS 5.1, PHYS 5.4, PHYS 5.6, PHYS 5.7, PHYS 6.1]

may also be applied: to waves at a common point (or possibly at separate points) by comparing the oscillations caused by the waves at the relevant point(s).

See phase relationship, in anti–phase and out of phase.

incident ray

is: an incoming ray which falls on (is incident on) some surface or interface. [PHYS 6.1, PHYS 6.2]

incoherent

describes: two waves sufficiently unrelated that knowing the phase of one at some particular time and position does not enable the phase of the other to be predicted at some other position (if spatially incoherent) or time (if temporally incoherent). Usually the phase difference between incoherent waves varies rapidly and randomly. [PHYS 6.1]

may also be applied: in its temporal sense, to two oscillations. [PHYS 5.3]

incompressible

describes: a sample of (idealized) material (usually a liquid or a solid) that cannot be compressed (i.e. which does not change its volume in response to applied forces). [PHYS 7.2]

inconsistent

describes: a set of equations that cannot all be true simultaneously. [MATH 1.4]

increasing function

is: a function f(x) for which f(a) < f(b) for all a < b

always exists: over an interval, if its derivative f′(x) is positive at all points of the interval. [MATH 4.4]

indefinite integral

of: a function f(x)

is denoted: $\displaystyle \int f(x)\,dx$ where f(x) is called the integrand, and the symbol dx is the element of integration which shows the integration variable, x with respect to which the integration is to be performed. [MATH 5.1, MATH 5.2]

is: any function F(x) such that $\dfrac{dF}{dx} = f(x)$. [MATH 5.1, MATH 5.2]

is not: unique, since if F1(x) is an indefinite integral of f(x), then so is F2(x) = F1(x) + C, where C is an arbitrary constant. For this reason, if F(x) is a particular indefinite integral of f(x), it is customary to write

$\displaystyle \int f(x)\,dx + C$

where C represents an arbitrary additive constant, called the constant of integration. [MATH 5.1, MATH 5.2]

is also called: inverse derivative or anti–derivative or primitive of f(x).

indefinite integration

is: the procedure whereby indefinite integrals are analysed and determined. [MATH 5.2]

independent

describes: a set of simultaneous linear equations with the property that none of the equations can be expressed as a sum of multiples of the other equations. [MATH 1.4]

independent arbitrary constants

in: the solution to a differential equation

are: two or more arbitrary constants which cannot be replaced by a single arbitrary constant. [MATH 6.1]

See essential constants.

independent errors

are: errors such that the size of one does not influence the size of the other. [PHYS 1.2]

independent oscillators

are: oscillators for which the displacement of one does not affect the restoring force acting on the other. [PHYS 5.1]

independent variable

in: an experiment (or a calculation)

is: the quantity whose value is set by the experimenter (or by the person doing the calculation). [PHYS 1.3]

controls: the value of any dependent variables to which it is connected by a set of experimental observations (or by a mathematical function). [MATH 1.3]

on graphs is plotted: conventionally along the horizontal axis. [PHYS 1.3]

index

is: a synonym for power (mathematical) or exponent. [MATH 1.1]

as a term is sometimes used: in preference to power because of the possibility of confusing power (mathematical) with power (physical). [MATH 1.1]

induced current

is: a current produced by electromagnetic induction in a complete circuit. [PHYS 4.4]

is exemplified: by the current that flows around a closed loop of wire, placed with its plane perpendicular to a uniform magnetic field, when either the magnitude of the field is changed, or when the area of the loop is altered.

induced fission

is: a process in which an atomic nucleus is induced by an external agency to undergo nuclear fission. [PHYS 9.3]

is exemplified: by the fission of 23592U when induced by the absorption of a thermal neutron. [PHYS 9.3]

induced magnetisation

See magnetic induction.

induced voltage

in: a complete circuit of resistance R carrying an induced current Iind

is: the voltage Vind = IindR. [PHYS 4.4]

is described: in magnitude by Faraday’s law: Vind = |/dt|, where /dt is the rate of change of the flux linkage Φ through the relevant closed circuit. [PHYS 4.4]

is described: in polarity by Lenz’s law, which says that the induced voltage will act to oppose the change that caused it. (For this reason it is sometimes said to be a back voltage or back e.m.f.) [PHYS 4.4]

may be determined in more general situations: e.g. between the ends of a electrical_conductorconductor moving through a magnetic field, so that it cuts magnetic flux at the rate /dt, by applying Faraday’s law and Lenz’s law, or by using the Lorentz force law. [PHYS 4.4]

inductance

is: the property of a coil which causes an induced voltage to arise across the coil when the current in the coil is changing (self inductance), or when the current in a nearby coil is changing (mutual inductance).

is also: an abbreviation for the coefficient of self inductance, L that quantifies the self inductance of a coil by means of the relation

$V_{\rm ind} = L\left\lvert\,\dfrac{dI}{dt}\,\right\rvert$

where Vind is the magnitude of the induced voltage, and |dI/dt| is the magnitude of the rate of change of the current in the coil. [PHYS 4.4, PHYS 4.5, PHYS 5.4] The polarity of the voltage is such as to oppose the change in the current (Lenz’s law): it is a back e.m.f. The back e.m.f. generated by an inductance L is −LdI/dt, so the voltage drop across such an inductance is LdI/dt.

has as its SI unit: the henry (H). [PHYS 5.4, PHYS 5.5]

induction (electromagnetic)

is: the phenomenon that gives rise to an induced voltage in a electrical_conductorconductor due to the presence of a changing magnetic field, or because of relative_velocityrelative motion between the electrical_conductorconductor and a magnetic field.

induction (electrostatic)

See electrostatic induction.

induction (mathematical)

is: a technique of proving a theorem by showing that if a result is true for some value of a parameter, such as n, then it is also true for n + 1. Completion of the proof then consists of showing explicitly (and usually trivially) that the result is indeed true for the smallest allowable value of n.

inductive reactance

of: an inductor with inductance L when passing alternating current of angular frequency ω

is: the ratio of the peak voltage to the peak current, V0/I0. [PHYS 5.4, PHYS 5.5]

is given: by XL = ωL. [PHYS 5.4, PHYS 5.5]

See complex inductive reactance, impedance, reactance.

inductive time constant

is: the time for the induced voltage, magnetic flux or current in an inductive circuit to decay exponentially by a factor e. [PHYS 4.5]

is given: for a circuit with resistance R and self inductance L by τ = L/R. [PHYS 4.5]

inductor

is: a coil designed to have a large inductance so as to produce a large induced voltage when the current in it changes. [PHYS 4.4, PHYS 4.5]

typically is: a solenoid with many closely–wound turns around a magnetic material (e.g. an iron core). [PHYS 4.5]

in a circuit is: a circuit component of fixed inductance and, ideally, negligible resistance. [PHYS 5.4, PHYS 5.5]

inelastic collision

is: a collision during which some or all of the kinetic energy is converted into other forms of energy. [PHYS 2.4, PHYS 2.5]

inequality

is: a mathematical statement expressing the fact that one number (or algebraic expression) is less than, or greater than, another. [MATH 1.1]

may be combined with: the equality to express "greater than or equal to", or, "less than or equal to".

uses: one or more of the symbols: > (greater than), ≥ (greater than or equal to), < (less than), or ≤ (less than or equal to), or their variants. The symbols ≫ and ≪ are used to express "much greater than" and "much less than", respectively. [MATH 1.2]

inert gases

See noble gases.

inertia

of: a body

is: the tendency of the body to continue in a state of uniform motion. [PHYS 2.3]

is measured: by the inertial mass of the body, according to Newton’s second law. [PHYS 2.3]

inertial confinement

is: confinement of a plasma by virtue of the inertia of the material in the plasma - so that it stays together for a sufficient time for nuclear fusion to begin within it. [PHYS 9.3]

requires: that the plasma be created within a very short time scale. This is done through irradiation by an intense pulsed laser beam or beambeam of particles. [PHYS 9.3]

inertial frame of reference

is: a frame of reference in which Newton’s first law holds; that is, one which is not itself accelerating, and in which objects do not accelerate unless a resultant force (i.e. a net force) acts on them. [PHYS 2.3]

inertial mass

of: a body

is: the mass of the body as determined by its acceleration in response to a known applied force. (See Newton’s second law of motion) [PHYS 2.3]

Contrast with gravitational mass.

infinite potential well

is: a potential well with infinitely high potential energy at the edges and thus capable of confining any particle, however high its (finite) energy. [PHYS 10.4]

infinite series

is: a series with an unlimited number of terms. [MATH 1.7]

infinitesimal

is: a quantity that is much smaller than others under consideration, and which can be considered to vanish in an appropriate limit.

infinitesimal calculus

See calculus.

infinity

is: a concept used to represent a far larger number or quantity than any other under consideration. [MATH 1.3, MATH 1.7]

is also: used in the term “projecting to infinity” to indicate extending the varying quantity to a very distant point or time. [MATH 2.3]

is denoted: by the infinity symbol, ∞

infinity symbol, ∞

is: a symbol used to represent a far larger number or quantity than any other under consideration. [MATH 1.3, MATH 1.7]

infrared (radiation)

is: a type of electromagnetic radiation characterized by wavelengths in the range between those of visible light and microwaves (i.e. approximately 700 nm to 1 mm).

See electromagnetic spectrum.

inhomogeneous differential equation

is: a differential equation which is not a homogeneous differential equation. [MATH 6.3]

is exemplified by: $a\dfrac{d^2y}{dx^2}+b\dfrac{dy}{dx}+cy=d$

since at least one of the terms (the one on the right) is not proportional to y nor to any one of its derivatives.

initial conditions

are: the n conditions given with a differential equation of order n which specify the value of the dependent variable and of its derivatives up to order (n − 1) at a particular value of the independent variable. [MATH 6.1]

are sufficient: to determine the n essential constants which appear in the general solution to the differential equation. [MATH 6.1]

describe: the initial state of a physical system at some initial time (usually t = 0) if the differential equation describes the behaviour of the system. [PHYS 5.4, PHYS 5.5]

initial phase

is synonymous: with phase constant. [MATH 6.3, PHYS 5.5]

initial state

of: a system

is: the state of the system at the beginning of a process.

initial velocity

is: the velocity of a body or particle at the start of a period of time. [PHYS 2.1]

See uniform acceleration equations.

inner shell

of: an atom

is: an (electron) shell of lower energy (i.e. higher binding energy) than most of the other shells in the atom. (According to Bohr’s model of the atom, electrons with such energies would be in orbits of relatively small radius.)

insoluble

describes: an equation (or system of simultaneous equations) which has no solution. [MATH 1.4]

more loosely, also describes: an equation (or system of simultaneous equations) for which no formula or procedure for solving it is known. [MATH 1.4]

instantaneous a.c. power

dissipated between: two points that differ in voltage by V(t) and between which a current I(t) flows

is given by: P = V(t)I(t). [PHYS 5.4]

instantaneous acceleration

of: a particle (relative to a specific frame of reference)

at: a given time t

is: a vector quantity that specifies the rate of change of the particle’s velocity υ = (υx, υy, υz) at time t. [MATH 4.1, PHYS 2.1, PHYS 2.2]

is represented: by the vector a = dυ/dt. That is, ax = x/dt, ay = y/dt, az = z/dt. [MATH 4.1, PHYS 2.1, PHYS 2.2]

has as its SI unit: m s−2. [MATH 4.1]

can be determined: as the limiting value of average acceleration, calculated over shorter and shorter time intervals. [MATH 4.1, PHYS 2.1, PHYS 2.2]

also can be determined: as the gradient of a velocity–time graph at time t. [MATH 4.1, PHYS 2.1, PHYS 2.2]

usually is known: simply as acceleration. [MATH 4.1, PHYS 2.1, PHYS 2.2]

instantaneous angular speed

is: the modulus of the instantaneous rate of change of angular position with time, i.e. ω = |/dt|. [PHYS 2.6]

is also: the magnitude_of_a_vector_or_vector_quantitymagnitude of the angular velocity.

instantaneous speed

is: the magnitude_of_a_vector_or_vector_quantitymagnitude of the instantaneous velocity. [MATH 4.1]

instantaneous velocity

of: a particle (relative to a specific frame of reference)

at: a given time t

is: a vector quantity that specifies how fast a body is moving and its direction of motion. [MATH 2.4]

is more specifically: the rate of change of the particle’s position r = (x, y, z) at time t [MATH 4.1, MATH 5.1, PHYS 2.1, PHYS 2.2]

is represented: by the vector υ = dr/dt. That is, υx = dx/dt, υy = dy/dt, υz = dz/dt. [MATH 4.1, MATH 5.1, PHYS 2.1, PHYS 2.2]

has as its SI unit: m s−1. [MATH 4.1]

can be determined: as the limiting value of average velocity, calculated over shorter and shorter time intervals. [MATH 4.1, PHYS 2.1, PHYS 2.2]

also can be determined: as the gradient of a position–time graph at time t. [MATH 4.1, PHYS 2.1, PHYS 2.2]

usually is known: simply as velocity. [MATH 4.1, PHYS 2.1, PHYS 2.2]

has: as its magnitude, the speed of the particle. [MATH 2.4, PHYS 2.1, PHYS 2.2]

See relative velocity.

insulator (electrical)

See electrical insulator.

insulator (thermal)

is: a material with a low coefficient of thermal conductivity, typically less than 1.0 W m−1 K−1.

integer

is: a positive or negative whole number, or zero i.e. an element_of_a_setelement of the set {... −2, −1, 0, 1, 2, 3, ...}. [MATH 1.2]

integral

is: a term used to refer to a definite integral or an indefinite integral. [MATH 5.1, PHYS 2.4]

integral sign

is: the distorted ’s’ symbol used (together with an element of integration) to indicate the operation of integration. [MATH 5.1, MATH 5.2]

integrand

is: the function to be integrated in a integral. [MATH 5.1, MATH 5.2]

integrating factor

is: a function by which each term of a linear first–order differential equation is multiplied, in order that the equation may be solved by direct integration. [MATH 6.2]

integration

is: the process of analysing and evaluating an integral. [MATH 5.1, MATH 5.2, PHYS 2.4]

See definite integral and/or indefinite integral for further details, or see integration in the Maths For Science handbook.

integration by parts

is: a technique of integration applicable to (some) functions that may be written as products of functions, based on the formula

$\int f(x)g(x)\,dx = F(x)g(x) - {\displaystyle\int}F(x)\dfrac{dg}{dx}\,dx$ [MATH 5.3]

See techniques of integration in the Maths For Science handbook.

integration by substitution

is: a technique of integration based on the replacement of the original integration variable by a new integration variable that is a function of the original variable.

See techniques of integration in the Maths For Science handbook.

integration element

See definite integral or indefinite integral.

integration variable

is: the variable over which the integration is performed.

See also definite integral or indefinite integral.

intensity

of: a wave or beam

is: the amount of energy transported by the wave or beam per unit time per unit area perpendicular to the direction of propagation. [PHYS 6.1]

intensity level

of: a sound of intensity I (measured in W m−2)

is given by:

$\beta = 10 \times \log_{10}\left(\dfrac{I}{I_0}\right)$ decibel

where I0 = 1 × 10−12 W m−2. [PHYS 5.7]

has as its SI unit: the decibel, represented by the symbol dB. Audible, non–painful sounds usually have intensity levels in the range 0 to 120 dB. [PHYS 5.7]

interaction (fundamental)

describes: the action of fundamental forces between particles. [PHYS 9.1]

is classified: in four kinds: gravitational_interactiongravitational, electromagnetic_interactionelectromagnetic, strong_interactionstrong (nuclear) and weak_interactionweak (nuclear), although it is now known that the weak_interactionweak and electromagnetic_interactionelectromagnetic interactions are linked. [PHYS 9.1]

interatomic or intermolecular forces

are: the forces that act among atoms or molecules. [PHYS 7.1, PHYS 7.5]

normally are important: in the liquid phase or solid phase. [PHYS 7.1, PHYS 7.5]

result: essentially from a combination of electrostatic forces and quantum mechanical exchange effects. [PHYS 7.1, PHYS 7.5]

intercept

of: a straight line

is: the constant c in the equation of a straight line, y = mx + c. [PHYS 1.3]

therefore is: the value of y when x = 0, i.e. the point at which the straight line crosses the y–axis. [MATH 2.2, MATH 3.1, PHYS 1.3]

more generally refers: to the common point of two straight lines that intersect. [MATH 2.1]

intercept form

of: the equation of a straight line

is: $\dfrac xa + \dfrac yb = 1$

where the straight line meets the x–axis at a and the y–axis at b. [MATH 1.3]

interface

between: one optical medium and another

is: a boundary surface at which a ray may undergo reflection or refraction. [PHYS 6.2]

is more generally: a surface separating two different materials.

interference

between: coherent waves in a region of space

is: the phenomenon that allows the waves to combine to result in a wave whose properties at any point are determined by the properties of the various contributing waves. (The procedure for combining the individual waves in simple (linear) cases is specified by the superposition principle.) [PHYS 5.6]

over the whole region produces: an interference pattern. [PHYS 6.1]

See constructive and destructive interference.

interference filter

when illuminated: from a specific direction

uses: the phenomenon of interference to prevent all but a narrow range of wavelengths from passing through. [PHYS 6.1]

typically consists: of a thin transparent coating on a glass base (in which case the interference is between beams successively reflected from the back and front surfaces of the coating), or of a thin cavity between two glass plates (in which case the interference is between beams successively reflected from the front and back surfaces of the cavity). [PHYS 6.1]

works: by accumulated destructive interference between all wavelengths which are not close to twice the path length between the two reflective surfaces. [PHYS 6.1]

interference fringes

are: patterns of bright and dark fringes produced by the interference of two or more coherent light beams. [PHYS 6.1]

can be observed: on a screen or directly. [PHYS 6.1]

are exemplified: by the two–slit interference pattern in Young’s experiment. [PHYS 6.1]

interference pattern

is: the observed pattern of varying intensity that results from the interference of coherent waves (usually beams, often beams of light) over a region of space. [PHYS 6.1]

See diffraction pattern.

interior angle

is: the angle between two adjacent sides of a geometric figure, which is enclosed within the boundary of the figure. [MATH 1.6]

is exemplified: by the three interior angles of any triangle, whose sum always is 180°. [MATH 1.6]

intermolecular forces

See interatomic or intermolecular forces.

internal energy

of: a system

is: the energy arising from the kinetic energy of the systemsystem’s constituents and the potential energy of their mutual interaction. [PHYS 7.3, PHYS 7.4, PHYS 7.5]

does not include: any contribution from the motion or position of the system as a whole. [PHYS 7.3]

changes: only as a result of heat transferred to the system or work done by (or on) the system, according to the first law of thermodynamics. Thus ΔU = ΔQ − ΔW. [PHYS 7.3, PHYS 7.4]

is: a function of state of the system. [PHYS 7.3, PHYS 7.4]

internal force

is: a force which occurs within a system. [PHYS 2.5]

occurs: between a pair of interacting bodies. [PHYS 2.5]

is always: one of a pair of action–reaction forces associated with the pair of interacting bodies. [PHYS 2.5]

internal resistance

is: the intrinsic resistance of a voltage generator. [PHYS 4.1]

is also called: output resistance. [PHYS 4.1]

is responsible: for the decrease in terminal potential difference of a non-ideal voltage generator when the current through it increases. [PHYS 4.1]

International Practical Temperature Scale 1990

is: an internationally agreed set of devices and procedures for the measurement of temperature. [PHYS 7.2]

is: at the time of writing (August 1995), the latest in an evolving sequence of internationally agreed practical temperature scales. [PHYS 7.2]

embodies: the best advice for those who need to calibrate and/or use thermometry which is practical but which is also as close to the Kelvin temperature scale as modern instrumentation will allow. [PHYS 7.2]

interpolation

is: the process of using values of a dependent variable, measured at a finite set of values of the corresponding independent variable(s), to estimate the value of the dependent variable corresponding to a value of the independent variable(s) that falls between those at which measurements were made. [PHYS 1.3]

Contrast with extrapolation.

intersect

is: what two curves (including straight lines) do if they have a point in common. [MATH 2.1]

is also: what two surfaces do if they have a curve in common.

interval

is: an unbroken range of real numbers which may be regarded as a segment of the number line. [MATH 4.4]

usually is specified: using inequality symbols, i.e. by statements such as −2 < x ≤ 4 or 1.2 ≤x ≤ 3. [MATH 4.4]

may or may not include: the endpoints which are used to define it. [MATH 4.4]

intrinsic angular momentum

See spin angular momentum.

intrinsic conduction

is: electrical conduction arising from charged particles present in a pure material (especially a semiconductor). [PHYS 11.4]

Contrast with impurity conduction.

invariant

under: a specified process or transformation

describes: a quantity that is left unchanged by the specified process or transformation. [PHYS 2.5]

is exemplified by: the numbers 0 and 1 which are invariant under the process of squaring numbers, or the centre of a sphere which is invariant under the process of rotating the sphere about an axis through its centre. [PHYS 2.5]

inverse derivative

is: the result of inverse differentiation. [MATH 5.1]

See indefinite integral.

inverse differentiation

of: a function f(x)

is: the process of finding another function F(x) called the inverse derivative or indefinite integral of f(x). [MATH 5.1, MATH 5.2]

usually is called: indefinite integration. [MATH 5.1, MATH 5.2]

is also known as: anti–differentiation.

inverse function

of: f(x)

is: the function that reverses the action of f(x). If f is the given function and g is its inverse, then g(f(x)) = x for all x in the domain of f. [MATH 1.3]

usually is denoted: by f−1 [MATH 1.3]

should not be confused: with a reciprocal. Note that a special notation is adopted when dealing with the inverses of the exponential, logarithmic, trigonometric functions and hyperbolic functions. [MATH 1.3]

inverse hyperbolic functions

are: the inverse functions of the basic hyperbolic functions and the reciprocal hyperbolic functions.

comprise: arcsinh(x), arccosh(x), arctanh(x), arccosech(x), arcsech(x) and arccoth(x). [MATH 4.6]

See hyperbolic functions in the Maths For Science handbook for further details.

inverse power

is: a term used to refer to a negative power (i.e. index) or powers appearing in the denominator of a mathematical expression. Thus Newton’s law of gravitation (an inverse square law) may be referred to as an inverse power law. [MATH 1.1]

inverse reciprocal trigonometric functions

are: the inverses of the reciprocal trigonometric functions. [MATH 1.6]

comprise: the functions arcsec(x), arccosec(x), arccot(x). [MATH 1.6]

See inverse trigonometric functions and trigonometric functions in the Maths For Science handbook.

inverse square law

states: that a quantity decreases as the square of some relevant distance. PHYS 3.1, PHYS 3.3]

is exemplified: by Newton’s law of gravitation and Coulomb’s law:

${\boldsymbol F}_{\rm grav} = -\dfrac{Gm_1m_2}{r^2}\hat{\boldsymbol r}$

${\boldsymbol F}_{\rm el} = -\dfrac{q_1q_2}{4\pi\varepsilon_0r^2}\hat{\boldsymbol r}$ [PHYS 2.4, PHYS 3.1, PHYS 3.3]

See also inverse square law of illumination.

inverse square law of illumination

is: a law relating the intensity of electromagnetic radiation, or other wave, radiation_generalradiating from a point source to the inverse square of the distance from that source. [PHYS 5.7, PHYS 6.1]

is a consequence: of geometry and the conservation of energy. [PHYS 6.1]

is exemplified: by the intensity of a propagating spherical wave, such as a sound wave or a light wave. [PHYS 5.7, PHYS 6.1]

inverse trigonometric functions

are: the inverses of the standard trigonometric functions and (usually) the inverses of the related reciprocal trigonometric functions. [MATH 1.6]

comprise: arcsin(x), arccos(x), arctan(x) and arcsec(x), arccosec(x), arccot(x). [MATH 1.6]

See trigonometric functions in the Maths For Science handbook for further details.

inversely proportional

describes: the relationship between two variables, x and y, if their product xy remains constant as x and y are varied. [MATH 1.1]

is symbolized: x ∝ 1/y. [MATH 1.1]

Contrast with directly proportional.

inversion rule

states: that if y = g(x) is a function of x which possesses an inverse function x = h(y) then

$\dfrac{dg}{dx} = \dfrac{1}{dh/dy}$ [MATH 4.3, MATH 5.3, MATH 6.2]

less formally, states: that dy/dx = 1/(dx/dy). [MATH 4.3, MATH 5.3, MATH 6.2]

inverted

means: upside down - as for an image formed by a lens or a mirror, when the image is the other way up as compared with the object. [PHYS 6.3]

ion

is: formed from an atom or molecule that has become electrically charged by ionization, usually through having lost or gained one or more electrons.

can be symbolized: by means of an appropriate chemical symbol together with a superscript indicating the sign of the ion’s charge and its magnitude in units of e (e.g. Na+, Cl or He2+). [PHYS 8.1, PHYS 8.2]

has properties: that are usually quite different from the atom or molecule.

ionic bonding

is: a type of chemical bonding in which appropriate chemical substances are regarded as collections of ions. The principal force between the ions is the attraction between their opposite charges. [PHYS 8.4]

ionization

is: the process in which an atom is stripped of one or more of its electrons.

ionization energy

of: an atom (in a specified state, usually the ground state)

is: the minimum energy required to just remove the most weakly bound electron from the atom, and thereby to create a singly charged ion. [PHYS 8.2, PHYS 8.3, PHYS 8.4]

is also called: the first ionization energy of the atom. [PHYS 8.2, PHYS 8.3, PHYS 8.4]

is synonymous: with ionization potential. [PHYS 8.2]

ionization level

for: an electron

in: an atom

is: the energy level that marks the boundary between the negative energy levels of the bound states of the atom and the positive energies of the unbound states in the continuum. [PHYS 8.2, PHYS 8.3]

therefore is: the energy below which the electron must remain bound in the atom, and above which the electron becomes free from the atom. [PHYS 8.2, PHYS 8.3]

thus is taken: as the energy zero. [PHYS 8.2, PHYS 8.3]

ionization potential

is synonymous: with ionization energy. [PHYS 8.2]

ionized

describes: an atom or molecule which has become an ion. [PHYS 8.2, PHYS 11.3]

ionizing radiation

is: radiation_generalradiation (particles or photons) that can produce ionization in matter. [PHYS 9.2, PHYS 9.3]

therefore is: radiation which is sufficiently energetic to supply the necessary ionization energy and which is capable of interacting with electrons. [PHYS 9.2, PHYS 9.3]

is exemplified: by X–rays, α–particles, β–particles, γ–radiation and neutrons. [PHYS 9.2, PHYS 9.3]

iris

of: the eye

is: the coloured tissue in front of the lens and whose variable aperture, the pupil, controls the amount of light entering the eye. [PHYS 6.4]

iris diaphragm

is: a mechanical system of overlapping metal leaves which can form an aperture of variable size for a lens. [PHYS 6.4]

irradiation

is: the process of exposing something to radiation_generalradiation

irrational number

is: a real number which cannot be expressed as a fraction (for example, e, π or, $\sqrt{2}$). [MATH 1.2, MATH 3.1]

irreversible process

is: a process in which it is not possible to return the system undergoing the process and its environment to their original states after the process has taken place. [PHYS 7.4]

increases: the entropy of the Universe (system + environment), according to the principle of entropy increase. [PHYS 7.4]

isobaric

describes: a process that takes place at constant pressure. [PHYS 7.4]

isochoric

describes: a process that takes place at constant volume. [PHYS 7.4]

isolated system

is: a system which does not interact with its environment.

has: different shades of meaning for different kinds of system.

is exemplified: by a mechanical system that is not acted upon by any external forces and which neither gains or loses energy. For such a system, the only forces acting are internal forces, and the total energy and the total momentum are conserved. [PHYS 2.4, PHYS 2.5]

isosceles triangle

is: a triangle with two sides of equal length, and hence with two equal interior angles. [MATH 1.6]

isotherm

is: a curve on a PVT–surface (or some similar surface), or on one of its projections, passing only through points that represent states of the same temperature. [PHYS 7.4]

isothermal condition

for: a fixed quantity of ideal gas

is: a condition that characterises an isothermal process in the sense that all the states involved in the process must satisfy the condition. (Though it is not the case that all states satisfying the condition must be involved in the process.) [PHYS 7.4]

may be written: in the form PV = constant, where the value of the constant is characteristic of the process. [PHYS 7.3, PHYS 7.4]

may also be written: in the form PaVa = PbVb. [PHYS 7.3, PHYS 7.4]

isothermal phase transition

is: a phase transition that occurs without any change of temperature. (Temperature changes during a phase transition such as melting can be brought about by changing the pressure or other external conditions during the transition.)

isothermal process

is: a process that occurs at constant temperature, so that ΔT = 0. [PHYS 7.3]

is characterized: for an ideal gas by the isothermal condition PV = constant, where P is the pressure, V is the volume, and the constant is determined by the initial state of the gas. [PHYS 7.3]

isotopes

of: a given chemical element

have: the same number of protons in their nuclei as all other isotopes of that element_chemicalelement, but different numbers of neutrons. [PHYS 9.1]

therefore have: the same atomic number but different mass numbers. [PHYS 8.1]

sometimes are referred to loosely: as nuclides. [PHYS 9.1, PHYS 9.2]

iteration

is: a numerical procedure which uses a formula (called an iteration formula) to obtain a succession of approximations (usually) to the root of an equation. [MATH 1.4]

iteration formula

See iteration.

iterative methods

See iteration.

I–V characteristic

for: any circuit component

of: an electrical circuit

is: a graph of current, I against voltage, V.

See linear component. [PHYS 4.1]

Josephson junction

is: a device in which a thin electrically insulating film is sandwiched between two pieces of superconductor. The existence of quantum tunnelling allows this device to exhibit highly non-classical behaviour that is exploited in more complicated devices such as SQUIDS. [PHYS 11.1]

joule, J

is: the (derived) SI unit of energy and work.

is defined: by 1 J = 1 N m = 1 kg m2 s−2.

represents: the energy transferred when the point of application of a constant force of magnitude_of_a_vector_or_vector_quantitymagnitude one newton is displaced by one metre in the direction of the force. [PHYS 2.4, PHYS 2.5]

Joule heating

is: heating produced by an electric current in a resistanceresistive circuit component.

is explained microscopically: in a metal, as the result of collisions between electrons and lattice ions. [PHYS 4.1]

kelvin, K

is: the SI unit of temperature, one of the seven base units.

is defined: as 1/273.16 of the triple–point temperature of H2O on the thermodynamic Kelvin temperature scale.

is equal: to a degree Celsius (°C), though due to differences in the zero points of the Celsius temperature scaleCelsius and thermodynamic Kelvin temperature scalethermodynamic Kelvin temperature scales, the absolute temperature of an object in kelvin (TK) is related to its Celsius temperature scaleCelsius temperature (TC) by the formula: TK/K = TC/(°C) + 273.15 [PHYS 7.2]

is never referred to: as degrees kelvin or °K but only as kelvin or K.

Kelvin temperature scale

See thermodynamic Kelvin temperature scale.

Kepler’s laws of planetary motion

describe (approximately): the basic features of planetary motion. [PHYS 2.8, PHYS 3.2]

state: that

1 The orbits of planets in the solar system are ellipses with the Sun at one focus.

2 The radial line from the Sun to a planet sweeps out equal areas in equal intervals of time.

3 The square of the orbital period is proportional to the cube of the semi–major axis of the ellipse. [PHYS 2.8, PHYS 3.2]

were deduced empirically: by Johannes Kepler (1571–1630). [PHYS 3.2]

were later explained: by Isaac Newton (1642–1727), using Newton’s laws of motion and Newton’s law of gravitation. [PHYS 3.2]

kilogram, kg

is: the SI unit of mass, one of the seven base units. [PHYS 1.1, PHYS 2.3]

is defined: by the international prototype kilogram, which is kept at the International Bureau of Weights and Measures at Sevres in France, and takes the form of a cylinder made from a platinum–iridium alloy. Replicas are kept in other standards laboratories.

kilowatthour, kWh

is: a non-SI unit of energy.

is defined: by 1 kWh = 1 kW × 1 h = 3.6 × 106 J i.e. 3.6 × 106joule. [PHYS 4.1]

commonly is used: by electricity supply companies for billing customers and referred to in that context as the ‘unit’ of electrical energy.

kinematics

is: the branch of mechanics concerned with motion and its description, but not its causes. [MATH 5.1, PHYS 2.3]

Compare with dynamics.

kinetic energy

is: the energy which an object possesses by virtue of its motion. An object of mass m moving with speed υ has a translational kinetic energy $E_{\rm tran} = \frac12m\upsilon^2$. [PHYS 2.4]

is classified: in three types: translational kinetic energy, vibrational kinetic energy and rotational kinetic energy. [PHYS 2.4]

kinetic theory

is: a theory which attempts to explain the bulk thermodynamic and transport properties of systems in terms of the interactions of atoms or molecules (often treated as hard spheres in rapid unhindered motion apart from collisions and encounters with the walls of a containing vessel, and usually subject to Newton’s laws of motion), and generally assuming that the energy and momentum is randomly distributed among the particles in the system. [PHYS 7.5]

kinetic theory of ideal gases

is: kinetic theory specifically applied to the model system of the ideal gas, leading to the equation

$PV = \frac13Nm\langle\upsilon^2\rangle = \frac23N\langle E_{\rm kin}\rangle$

where $\langle\upsilon^2\rangle$ is the mean of the squares of the molecular speeds and $\langle E_{kin}\rangle$ is the average translational kinetic energy per molecule. The gas has pressure P volume V and contains N molecules, each of mass m. [PHYS 7.3, PHYS 7.5]

Kirchhoff’s laws

for: the an electric current in a circuit.

See Kirchhoff’s current law and Kirchhoff’s voltage law.

Kirchhoff’s current law

states: that the algebraic sum of the currents at a node is zero, or equivalently that the total current flowing into each node is equal to the total current flowing out of the node. [PHYS 4.1]

Kirchhoff’s voltage law

states: that the algebraic sum of the voltages across all electrical components in a closed loop or mesh is zero, or equivalently, the sum of the voltage increases is matched by the sum of the voltage decreases. [PHYS 4.1]

lag

See phase lag.

lanthanides

are: the 14 closely similar chemical elements from La to Yb (atomic numbers from 57-70) inclusive. [PHYS 8.4]

span: a region of the periodic table in which the 4f subshell of atoms in their ground state is being progressively filled. [PHYS 8.4]

Laplace’s equation

is: a linear, homogeneous, second–order differential equationsecond–order, partial differential equation of the form

$\dfrac{\partial U}{\partial x^2}+\dfrac{\partial U}{\partial y^2}+\dfrac{\partial U}{\partial z^2} = 0$ [MATH 6.4]

laser

is: a light source of high coherence that produces a nearly parallel beam, often of high intensity. [PHYS 6.1]

is named: for Light Amplification by Stimulated Emission of Radiation. [PHYS 6.1]

laser action

is: the process by which stimulated emission produces amplification of light within the cavity of a laser. [PHYS 5.3]

latent heat

is: the heat absorbed or emitted by a sample during an isothermal phase transition. [PHYS 7.4]

See also specific latent heat, molar latent heat.

lateral magnification

in: an optical system

is: the ratio of the size of an extended image to the size of the corresponding extended object, when measured normal to the optical axis. [PHYS 6.3]

for a lens is called: lens transverse magnification. [PHYS 6.3]

lattice

is: a regular array of points in space that underlies the specification of crystal structure in terms of a given arrangement of one or more atoms reproduced at every point of the lattice. [PHYS 11.4]

is less rigorously: a regular array of points within a (crystalline) solid about which atoms or ions may be considered to oscillate. [PHYS 4.1]

lawlaws

is: a relationship, usually expressed mathematically, between variables.

is often determined: by experiment or observation.

See law of physics.

law of inertia

See Newton’s first law of motion.

law of physics

is: a relationship between physical variables that is believed to be valid under a wide range of circumstances and is (ideally) well supported by experimental evidence.

law of reflection

for: a ray of light

from: a surface

states: that

(i) the reflected ray, the incident ray and the normal to the surface all lie in one plane, and

(ii) the angle of reflection is always equal to the angle of incidence: θi = θR. [PHYS 6.1, PHYS 6.2]

law of refraction

of: a ray of light

from: one medium into another

states: that

(i) the incident ray, the refracted ray and the normal to the boundary all lie in one plane, and

(ii) the angle of incidence θ1 and the angle of refraction θ2 are related by Snell’s law:

$\dfrac{\sin\theta_1}{\sin\theta_2} = \dfrac{\mu_2}{\mu_1} = \text{constant}$

where μ1 and μ2 are the refractive indices of the two media, respectively. (The refractive indices usually depend on the frequency of the light, giving rise to dispersion.) [PHYS 6.1, PHYS 6.2]

law of static moments

states: that a body is in rotational equilibrium if the clockwise moments balance the counter clockwise moments in every plane. [PHYS 2.7]

law of terrestrial gravitation

states: that close to the Earth’s surface, any body of mass m experiences a gravitational force that acts vertically downwards and has magnitude_of_a_vector_or_vector_quantitymagnitude mg, where g is the magnitude of the acceleration due to gravity (approximately 9.81 N m s−2). [PHYS 2.3]

law of universal gravitation

was first formulated: by Isaac Newton (1642–1727). [PHYS 2.3, PHYS 3.1]

states: that every particle of matter in the Universe attracts every other particle with a force that is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them. [PHYS 2.3, PHYS 3.1]

can be expressed: for two masses m1 and m2 separated by a distance r as

${\boldsymbol F}_{\rm grav} = -{\boldsymbol F}_{21} = \dfrac{-Gm_1m_2}{r^2}\hat{\boldsymbol r}$

as the force on m2 due to m1

where G is Newton’s universal gravitational constant and r^ is a unit vector pointing from m1 to m2. [PHYS 2.3, PHYS 3.1, PHYS 3.2]

also known as: universal law of gravitation.

laws of thermodynamics

of: thermodynamic systems

define: how the fundamental physical quantities (temperature, energy, and entropy) behave under various circumstances.

are:

zeroth law of thermodynamics

first law of thermodynamics

second law of thermodynamics

Lawson criterion

for: ‘break even’ conditions in a plasma fusion reactor, so that fusion energy output is just equal to the energy expended to produce this output

requires: that the product of the number density of nuclei in the plasma and the confinement time be greater than a given value. This value depends on the reaction concerned and the temperature. [PHYS 9.3]

LCR circuit

is: an electrical circuit containing an inductance L, a capacitance C and a resistance R.

lead

See phase lead.

lead–acid accumulator

is: a storage cell made from two lead electrodes with a sulphuric acid electrolyte, ‘charged’ by passing a direct current through it.

is also: a battery of such storage cells. [PHYS 4.5]

is used: to make car batteries. [PHYS 4.5] [PHYS 4.5]

least distance of distinct vision

is: the distance from the eye to the closest point at which objects can be clearly focused (i.e. the near point). [PHYS 6.4]

varies: with age but is commonly taken to be 25 cm. [PHYS 6.4]

Leclanché dry cell

is: an electric storage cell consisting of a carbon electrode surrounded by a moist electrolytic paste enclosed in a zinc case which forms the cell’s other terminal. [PHYS 4.5]

is used widely: as a portable power source, e.g. in torches and portable radios, but is increasingly being replaced by the broadly similar alkaline cell. [PHYS 4.5]

left–handed (Cartesian) coordinate system

is: a three–dimensional Cartesian coordinate system (consisting of three mutually perpendicular coordinate axes which meet at a point called the origin), in which an observer located at the origin and looking along the z–axis in the direction of increasing z finds that a left–handed screw motion through 90° (i.e. a 90° anticlockwise rotation) is needed to bring the x–axis into the position previously occupied by the y–axis. [PHYS 6.2]

Contrast with right–handed coordinate system, which is more commonly used.

length

is: one of the fundamental dimensional quantities of mechanics (along with mass and time).

is used: to describe the distance from one end of an object or interval to the other end.

has as its SI unit: the metre (m), one of the seven base units.

lens

is: a piece of glass or other transparent material shaped so that its surfaces curve inwards or outwards. Usually the surfaces are spherical in shape. [PHYS 6.3]

is used: generally to make parallel light converge to form an image, or to form parallel light from light diverging from an object. [PHYS 6.3]

lens (of the eye)

is: the flexible lens of the eye. [PHYS 6.4]

has: a focal length which can be varied by change of the shape of the lens, through contraction of the ciliary muscles. [PHYS 6.4]

lens maker’s equation

is: an equation which relates the focal length f of a lens to the radii of curvature, r1 and r2 of its surfaces and the refractive index μ of the material used:

$\dfrac1f = (\mu-1)\left(\dfrac{1}{r_1}-\dfrac{1}{r_2}\right)$ [PHYS 6.3]

lens transverse magnification

is: the lateral magnification of a lens. [PHYS 6.3]

therefore is: the ratio of image height to object height measured in the direction perpendicular to the optical axis of the lens. [PHYS 6.3]

Lenz’s law

states: that the polarity of any induced voltage or the direction of any induced current is such as to oppose the change causing it. (This law is a consequence of the law of conservation of energy.) [PHYS 4.4]

lever arm

of: a force causing, or tending to cause, rotation about a fulcrum

is: the perpendicular distance between the line of action of the force and the fulcrum. [PHYS 4.3]

lepton

See elementary particle.

Lewis structure

is: a diagram, named after the American chemist Gilbert Lewis (1875–1946), which shows how the outer electrons of the atoms in a chemical compound are shared in order to create electron pair bonds, in accordance with the theory of covalent bonding. [PHYS 8.4]

light

is: a form of electromagnetic radiation, visible to the human eye, and characterized by wavelengths in the approximate range 400 nm to 700 nm.

See electromagnetic spectrum.

light damping

of: a damped oscillator

is: the condition in which the oscillator will complete many oscillations (with gradually decreasing amplitude) before coming to rest. [PHYS 5.2, PHYS 5.5]

is often used as synonymous: with underdamping.

See damped mechanical oscillator and/or damped electrical oscillator for further details.

Contrast with critical damping and heavy damping.

light ray

is: a directed line (i.e. a line with an arrow on it) drawn to represent the passage (or potential passage) of light. [PHYS 6.1, PHYS 6.2]

usually is drawn: at right angles to the wavefront. [PHYS 6.1, PHYS 6.2]

has direction: which indicates the direction of energy flow. [PHYS 6.1, PHYS 6.2]

normally is restricted: to situations in which diffraction effects are negligible. [PHYS 6.1, PHYS 6.2]

light wave

is: an electromagnetic wave with a wavelength in the approximate range 400 nm to 700 nm that can be used to model certain aspects of the behaviour of light.

limit

of: the function f(x)

as: x approaches a

if: f(x) can be made as close as we wish to L by making x sufficiently close to a

is: L. [MATH 4.1, MATH 4.2, PHYS 2.1]

is indicated: by writing $\displaystyle \lim_{x\to a}\left(f(x)\right) = L$. [MATH 1.5]

is exemplified: $\displaystyle \lim_{x\to\infty}\left(\dfrac1x\right) = 0$. [MATH 1.5]

limit of a sequence

See convergent sequence.

limits of integration

refers: to the upper limit of integration and lower limit of integration. [MATH 5.1]

See definite integral.

line

is: an abbreviation for straight line.

line integral

from: point A to point B

along: a curve C in three (or possibly two) dimensions

of: a vector quantity F(x, y, z) that depends on position and is defined at all points on C

is given: by

$\displaystyle \int_A^B {\boldsymbol F}\,{\boldsymbol\cdot}\,d{\boldsymbol s} = \lim_{\Delta{\boldsymbol s}\to0} \sum {\boldsymbol F}\,{\boldsymbol\cdot}\,\Delta{\boldsymbol s}$

where: Δs is a small displacement along C, and the sum is over a sequence of small displacements that lead from A to B along C. Note that in this definition F Δs represents a scalar product. [PHYS 2.4]

line of action (of a vector)

of: a vector (particularly, though not necessarily, a force)

is: a construction line of indefinite length running through the vector. [PHYS 2.7]

is useful: for calculating moments and in analysing problems. [PHYS 2.7]

line segment

is: a finite part of a straight line.

line source

is: a source of light whose height is generally much greater than its width. Ideally the width should be less than the wavelength of the light and the height much greater than the wavelength of the light. [PHYS 6.1]

line spectrum

of: electromagnetic radiation (usually from a specified source)

describes: the emission spectrum or the absorption spectrum when these involve radiation of definite characteristic wavelengths. [PHYS 8.2]

is more specifically called: the emission line spectrum or the absorption line spectrum. [PHYS 8.2]

linear

describes: a linear function or its corresponding straight line graph. [PHYS 1.3]

linear combination

of: two quantities or expressions y1 and y2 (often two solutions to a differential equation)

is: a quantity or expression of the form ay1 + by2, where a and b are constants. [MATH 5.2, PHYS 5.6]

linear component

of: an electric circuit

is: a circuit component in which the current I is directly proportional to the applied voltage V, giving rise to an IV characteristic that is a straight line through the origin. [PHYS 4.1]

linear differential equation

in: a dependent variable y

is: a differential equation in which every term that contains y at all contains no power_mathematicalpowers of y and its derivatives other than the first, no functions of y and its derivatives, and no products of y and its derivatives among themselves. [MATH 6.1, PHYS 5.5]

therefore is: of first degree. [MATH 6.1]

is exemplified: by

$a(x)\dfrac{d^ny}{dx^n}+b(x)\dfrac{d^{n-1}y}{dx^{n-1}}+\ldots+q\dfrac{dy}{dx}+r(x)y = f(x)$

(This is linear in y, but is also inhomogeneous unless f (x) = 0)

has the property: if homogeneous, that a linear combination of solutions is also a solution.

linear differential equation with constant coefficients

is: a linear differential equation in which the coefficients of y and its derivatives are constants rather than functions of x. [MATH 6.2, MATH 6.3]

linear energy density

in: a one–dimensional system

is: the energy per unit length. If ΔE is the energy associated with a short length Δl, centred on a point with position coordinate x at time t, then the linear energy density at point x at time t is

$\displaystyle D_E(x,t) = \lim_{\Delta l\to0}\left(\dfrac{\Delta E}{\Delta l}\right)$. [PHYS 5.6]

has as its SI unit: the joule per metre (J m−1), though this is identical to the newton (N). [PHYS 5.6]

linear equation

in: a variable x

is: an equation that may be written in the form ax + b = 0, where a and b are independent of x. [MATH 1.4]

therefore is: a polynomial equation in x of degree 1. [MATH 1.4]

linear form

is: an expression which involves only the first power of the independent variable.

is exemplified: by 3x + 2(x − 1) but not by 3/(x − 1).

linear function

is: a function of the form f(x) = ax + b, (the right–hand side is a linear form). [MATH 1.4, PHYS 1.3]

therefore is: a function whose graph is a straight line. [MATH 1.3]

linear homogeneous differential equation

is: a linear differential equation of the form

$a(x)\dfrac{d^ny}{dx^n}+b(x)\dfrac{d^{n-1}y}{dx^{n-1}}+\ldots+q\dfrac{dy}{dx}+r(x)y = 0$ [MATH 6.3]

contains: no non–zero term that does not involve the dependent variable y or one of its derivatives. [MATH 6.3]

in particular contains: no constant term. [MATH 6.3]

has the property: that a linear combination of its solutions is also a solution.

linear inhomogeneous differential equation

is: a linear differential equation that is not homogeneous_differential_equationhomogeneous. [MATH 6.3]

linear mass density

of: a uniform body (particularly a body of uniform cross–sectional area, such as a string) of mass M and length L

is: the mass per unit length of the body, M/L

is defined more generally: at a point with position coordinate x in a (possibly non-uniform) body by

$\displaystyle \rho(x) = \lim_{\Delta l\to0}\left(\dfrac{\Delta m}{\Delta l}\right)$

where Δm is the mass of a small element of the body, of length Δl centred on the point specified by x.

linear momentum

of: a body

is given: by p = , where m is the mass of the body and υ is the velocity of the centre of mass of the body. [PHYS 2.5]

is equal: for a system of particles or bodies, to the vector sum of the individual momenta. [PHYS 2.5]

is fully specified: by giving both its magnitude_of_a_vector_or_vector_quantitymagnitude and its direction. [PHYS 2.5]

is conserved: for a system of interacting objects which are not subjected to external forces. The bodies collide and exchange momentum with each other, but the total momentum is constant. [PHYS 2.5]

at high speeds must be replaced by: relativistic momentum. [PHYS 2.5]

linear motion

of: an object

is: motion of the object along a straight line.

can be represented: if the straight line is taken to be the x–axis of a Cartesian coordinate system, in terms of the positioninstantaneous position, instantaneous velocity and instantaneous acceleration of the object: x(t), υx(t) and ax(t). [MATH 4.1, MATH 5.1, PHYS 2.1]

linear relationship

between: two variables (x and y say)

can be represented: by a linear function or a linear (i.e. straight line) graph. [PHYS 1.3]

is exemplified: by y = mx + c where m and c are constants.

linear restoring force

is: a force, directed towards a fixed point, that is directly_proportionallinearly proportional to the displacement from that point and in the opposite direction to that displacement. [PHYS 5.1]

in one dimension may be written: Fx = −kx, where x is the displacement from the fixed point. A particle moving under the influence of such a force (and no other) will execute simple harmonic motion about the fixed point. [PHYS 5.1]

linear second–order differential equation

is: a differential equation in which every term is linear in a single variable or one of its derivatives, and where the highest derivative appearing is the second derivative. [PHYS 5.3]

is exemplified: by the equation of the linearly damped harmonic oscillator.

linear system

is: an equilibrium system in which the response of the system (e.g. the restoring force) is linearly dependent on displacement from equilibrium. [PHYS 5.1]

linearity

of: an equation (such as the wave equation, the time–dependent Schrödinger equation, or a general linear homogeneous differential equation)

is: a property whereby if y1 and y2 are both solutions, then so is any linear combination of the form ay1 + by2, where a and b are constants. [PHYS 5.6]

linearization

is: the procedure whereby a non-linear relationship between two or more variables (x and y say) is represented by a linear relationship between two or more other variables (u and υ say) which are expressed in terms of the original variables. In appropriate circumstance, this process may allow the constants involved in the original non-linear relationship to be determined from an analysis based on the corresponding linear relationship. [PHYS 1.3]

also can describe: the procedure whereby a non-linear relationship between variables is approximated by a linear relationship between the same variables. [MATH 6.1, PHYS 1.3]

linearly damped harmonic oscillator

is: a harmonic oscillator with a damping force which depends linearly on the velocity of the oscillator, or on the first derivative of the displacement of the oscillator. [PHYS 5.3]

is exemplified: by a damped mechanical oscillator with the equation of motion

$m\dfrac{d^2x}{dt^2} = -kx -b\dfrac{dx}{dt}$

linearly independent

describes: a set (e.g. a set of functions) in which no element can be expressed as a linear combination of other element_of_a_setelements of the set.

linearly polarized

describes: an electromagnetic wave whose electric field oscillates in the same plane at all points. [PHYS 6.1]

also known as: plane polarized.

liquid phase

is: the state of fluid matter characterized by a definite volume but no definite shape. [PHYS 7.1]

Lissajous figures

are: figures which result when two simple harmonic motions, which may differ in amplitude, frequency or phase, are added in perpendicular directions. [PHYS 5.1]

normally are viewed: on an oscilloscope. [PHYS 5.1]

litre, l

is: a non-SI unit of volume.

is defined: by 1 l = 10−3m3 (i.e. 10−3 metre cubed).

is often represented as: L (or sometimes as ℓ) to avoid confusion with the digit 1, especially in medicine.

load resistor

is: a resistor that is treated as ‘external’ to the circuit that supplies it with current. [PHYS 4.1]

loading curve

is: a graph of stress against strain for a material.

local action

is: the destruction or permanent change of an electrode in a storage cell as a result of chemical reactions. [PHYS 4.5]

local extrema

is: a collective term for local maxima and local minima. [MATH 4.4]

local maximum

is: a point (a, f(a)) on the graph of a function f(x) for which f(x) ≤ f(a) for all points x close to a. At such a point, df/dx = 0 and f(x) is said to be stationary.

always exists: if df/dx = 0 and d2f/dx2 < 0. This is a sufficient condition. [MATH 4.4, PHYS 6.2]

See stationary points and graph sketching in the Maths For Science handbook.

local minimum

is: a point (a, f(a)) on the graph of a function f(x) for which f(x) ≥ f(a) for all points x close to a. At such a point, df/dx = 0 and f(x) is said to be stationary.

always exists: if df/dx = 0 and d2f/dx2 > 0. This is a sufficient condition. [MATH 4.4, PHYS 6.2]

See stationary points and graph sketching in the Maths For Science handbook.

localized particle

is: a particle whose position is known, at least within prescribed limits. [PHYS 10.2]

locus

is: a collection of points specified by some conditions. [MATH 2.1]

logarithm to base 10

of: a number, x is: the number, y which satisfies the equation, x = l0y. [MATH 1.5]

usually is written: as log10(x) or log10x. [MATH 1.5]

sometimes is called: the common logarithm. (This does not imply that it is more common than the natural logarithm in physics!) [MATH 1.5]

logarithm to base a

of: a number, x

is: the number, y which satisfies the equation, x = ay. [MATH 1.5]

usually is written: as loga(x). [MATH 1.5]

logarithm to base e

of: a number, x

is: the number, y which satisfies the equation, x = ey. [MATH 1.5]

usually is written: as loge(x), logex (or sometimes lnx). [MATH 1.5]

is known: as the natural logarithm. [MATH 1.5]

less commonly is called: the Napierian logarithm or the hyperbolic logarithm. [MATH 1.5]

logarithmic decrement

in: damped_mechanical_oscillatordamped harmonic motion

is: the natural logarithm of the ratio of two successive displacement maxima, i.e. loge[A(t + T)/A(t)], where T is the period of the oscillation. [PHYS 5.2]

is equal approximately: to πγ/ω0, where γ is the damping constant and ω0 is the natural frequency of the oscillation. [PHYS 5.2]

See damped mechanical oscillator.

logarithmic function

is: a general term used to refer to any function that is the inverse of a function of the form y = ax. [MATH 1.5]

is indicated symbolically: by x = loga(y), (so x = loga(ax)), where the positive constant a is said to be the base of the logarithmic function. [MATH 1.5]

long sight

See hypermytropia.

longitudinal wave

is: a wave in which the disturbances that constitute the wave involve displacements along the direction of propagation of the wave. [PHYS 5.6]

is exemplified: by a sound wave.

Contrast with transverse wave.

Lorentz force law

is: the general equation for the electromagnetic force, or Lorentz force, F on a particle of charge q in an electric field E and/or magnetic field B. [PHYS 4.3]

is given: by ${\boldsymbol F} = q[{\boldsymbol E} + {\boldsymbol\upsilon}\,{\boldsymbol\times}\,{\boldsymbol B}]$. [PHYS 4.3]

Lorentz force

on: a charged particle

in: an electric field and/or a magnetic field

is found: by adding the separate forces that would be produced by each field acting independently, as described by the Lorentz force law. [MATH 2.7, PHYS 4.3]

is also called: the electromagnetic force. [MATH 2.7, PHYS 4.3]

low–pass filter

is: a filter circuit that passes low-frequency signals with relatively undiminished amplitude, but blocks high-frequency signals. [PHYS 5.4]

Contrast with high–pass filter.

lower limit (of integration)

See definite integral.

lower limit (of summation)

See summation symbol.

Lyman series

See series (spectroscopic).

Mach number

for: the speed of an object through a fluid

is: the ratio of the speed of the object to the local speed of sound. [PHYS 5.7]

macroscopic

describes: size scales sufficiently large that no account need be taken of the behaviour of individual atoms or molecules. [PHYS 7.2, PHYS 7.5]

magnet

is: a body which exhibits magnetism. [PHYS 4.2]

may: be either a permanent magnet or an electromagnet.

magnetic

is: the property of being attracted by a magnet.

magnetic confinement

of: a plasma

is achieved: by means of a magnetic field which produces an electromagnetic force on the plasma to prevent it from making contact with the vessel walls. [PHYS 9.3]

See plasma confinement.

magnetic dipole

is: a pair of equal strength magnetic north and south poles, as found in a bar magnet. [PHYS 4.2]

more generally is: any source of a magnetic field of the same configuration as that produced by a short bar magnet. [PHYS 4.2]

is exemplified: by a single loop of wire enclosing an area A and carrying a current I.

magnetic dipole moment

of: a magnetic dipole

is: a vector quantity μ that determines the torque acting on the magnetic dipole when it is placed in a given magnetic field (the torque depends on the orientation of the magnetic dipole). [PHYS 4.3]

is defined: as having a magnitude_of_a_vector_or_vector_quantitymagnitude given by the ratio of the maximum torque magnitude to the magnitude_of_a_vector_or_vector_quantitymagnitude of the magnetic field: μ = Γ/B. (In vector form the torque is written as Γ = μ × B) [PHYS 4.3]

is exemplified: for a magnetic dipole consisting of a single loop of wire of area A carrying a current I, by μ = IA. If the loop has N turns, all in the same plane and each of area A then μ = NIA. [PHYS 4.3]

magnetic field

throughout: a region of space

is: a vector field which gives rise to a magnetic force on moving charged particles at each point in the region, provided they are not travelling parallel to the magnetic field at the point in question. [PHYS 3.1]

is defined: at any point specified by a position vector r, as the vector quantity B(r) whose direction is identical to that in which the north pole of a vanishingly small compass needle, free to rotate in three dimensions, would point, and whose magnitude B(r), is obtained from the magnitude, Fmag, of the magnetic force that acts - by virtue of the Lorentz force law - on a particle of charge q as it moves through the point r in a direction at right angles to the magnetic field with a speed υ

Fmag = |q|υB(r)

So   $B({\boldsymbol r}) = \dfrac{F_{\rm mag}(\text{on }q\text{ as it moves through }{\boldsymbol r})}{\left\lvert\,q\,\right\rvert\upsilon_\perp}$ [PHYS 4.2]

may be more simply defined: as the vector field B(r) that determines the magnetic force Fmag on a particle of charge q travelling with velocity υ at the point r through the relationship

Fmag = qυ × B(r). [PHYS 4.3]

has as its SI unit: the tesla (T), where 1 T = 1 N s C−1 m−1. [PHYS 4.2]

also may be denoted: B(x, y, z), since r = (x, y, z). [PHYS 4.2]

magnetic field lines

are: a means of representing a magnetic field using directed curves (i.e. curves with arrows on them). [PHYS 4.2]

are drawn: so that at any point the magnetic field is tangential to the line and points in the direction indicated by the direction of the field line. [PHYS 4.2]

therefore are directed: away from north magnetic poles and towards south magnetic poles. (This direction is that in which the north pole of a freely suspended compass needle would point - which means of course that the north geographical pole of the Earth is actually a south magnetic pole!) [PHYS 4.2]

have spacing: which is related to the magnitude of the magnetic field, i.e. where the lines are close together the field is strong and where they are further apart the field is weaker. [PHYS 4.2]

magnetic field strength

at: any point

is: the magnitude of the magnetic field at that point. [PHYS 4.3]

magnetic flux

loosely is: the ‘amount of magnetic field’ enclosed by a circuit. [PHYS 4.4]

more precisely is: for a loop of area A whose axis makes an angle θ with a uniform magnetic field B, the quantity ϕ = BAcosθ. [PHYS 4.4]

has as its SI unit: the weber (Wb), where 1 Wb = 1 T m2. [PHYS 4.4]

magnetic flux density

is: the magnetic_field_strengthstrength of a magnetic field, expressed in terms of the magnetic flux per unit area when the area is at 90° to the field direction. [PHYS 4.4]

has as its SI unit: Wb m−2. (1 Wb m−2 = 1 T). [PHYS 4.4]

magnetic flux linkage

for: a circuit of N turns, each enclosing a magnetic flux ϕ

is: Φ = . [PHYS 4.4]

has as its SI unit: the weber (Wb). [PHYS 4.4]

conventionally is expressed also: in units of Wb turns. [PHYS 4.4]

magnetic force

is: the force Fmag produced by a magnetic field on a moving charged particle, or on a stream of charged particles constituting an electric current. [PHYS 4.3]

is quantified: for a particle with charge q and velocity υ in a magnetic field B by F = qυ × B. [PHYS 4.3]

is quantified: for a wire of length l carrying a current I in a uniform magnetic field B by Fmag = Il × B, where l is a vector of length l in the direction of the conventional current. [PHYS 4.3]

magnetic induction

is: the creation of temporary magnetic properties in a material through the presence of an external magnetic field. [PHYS 4.2]

magnetic monopole

is: a (hypothetical) isolated north or south magnetic pole. [PHYS 4.2]

magnetic pole

is: one of the two centres within a magnetic dipole at which the lines of magnetic field appear to originate or terminate. [PHYS 4.2]

is classified: in two types: north magnetic poles and south magnetic poles. The forces between poles are such that like poles repel and unlike poles attract. [PHYS 4.2]

magnetic (orbital) quantum number

See orbital magnetic quantum number, ml.

magnetic (spin) quantum number

See spin magnetic quantum number, ms.

magnetically coupled

describes: a situation in which one circuit is influenced electrically by electrical changes in a nearby circuit through the mechanism of electromagnetic induction and mutual induction. [PHYS 4.4]

magnetically hard

describes: materials, such as steel, which retain much of their induced magnetism when the magnetizing magnetic field is removed. [PHYS 4.2]

See magnetic induction and permanent magnetism. [PHYS 4.2]

magnetically soft

describes: materials, such as soft iron, which retain very little of their induced magnetization when the magnetizing magnetic field is removed. [PHYS 4.2]

See magnetic induction. [PHYS 4.2]

magnetism

is: the mutual attraction or mutual repulsion of two bodies that produce magnetic fields. [PHYS 4.2]

magnetron

is: an electronic device which generates microwaves using the resonance of electromagnetic waves confined in a cavity. [PHYS 5.3]

magnifying power

is: the ratio of the angles subtended at an observerobserver’s eye by an optical image and by the object from which it is derived, when that object is placed at the near point. [PHYS 6.4]

magnitude

See modulus.

magnitude (of a complex quantity)

See modulus (of a complex number).

magnitude (of a real quantity)

See modulus (of a real number).

magnitude (of a vector or vector quantity)

for: a vector (or vector quantity) υ = (υx, υy, υz).

is: a scalar quantity that describes the ’size’ or ‘length’ of the vector υ = (υx, υy, υz). [MATH 2.4, MATH 2.5, PHYS 2.1, PHYS 2.2, PHYS 2.7]

is always: positive. [MATH 2.4, MATH 2.5, PHYS 2.1, PHYS 2.2, PHYS 2.7] [MATH 2.4, MATH 2.5, PHYS 2.1, PHYS 2.2, PHYS 2.7]

is denoted: by |υ| or simply by υ. [MATH 2.4, MATH 2.5, PHYS 2.1, PHYS 2.2, PHYS 2.7]

is defined: by $\left\lvert\,\upsilon\,\right\rvert = \left(\upsilon_x^2+\upsilon_y^2+\upsilon_z^2\right)^{1/2}$

magnitude of the acceleration due to gravity

in: the absence of any other influences

is: the magnitude_of_a_vector_or_vector_quantitymagnitude of the acceleration due to gravity of a falling body close to the Earth’s surface.

is also: the magnitude_of_a_vector_or_vector_quantitymagnitude of the gravitational field close to he Earth’s surface.

is denoted: by g. [PHYS 2.2]

varies: from place to place across the Earth’s surface, but generally is within ±0.028 m s−2 of 9.805 m s−2. [PHYS 3.2]

magnitude of the area under a graph

refers: to the sum of the (positive) areas of the various distinct regions contained between a given graph and a given axis between given limits. [MATH 5.4]

Compare with area under a graph, which is the corresponding sum of (signed) areas.

main group elements

See typical elements.

mains voltage

is: the voltage supplied by standard power sockets connected to the national (mains) electricity supply. [PHYS 5.4]

major arc

is: the larger of the two arcarcs of a circle joining two points on the circumference that are not at opposite ends of a diameter. [MATH 2.1]

major axis

is: the longest diameter of an ellipse.

major segment

is: the region bounded by the major arc of a circle and the chord that joins its end points. [MATH 2.1]

many universe interpretation

in: quantum physics

suggests: that all possible paths for all particles are actually followed. In our Universe, when we detect a particle which has, for example, passed through a slit, we only see the end result of one path, but all the other paths have led to different results in an infinity of other universes. [PHYS 10.2]

is opposed: to the Copenhagen interpretation of quantum physics. [PHYS 10.2]

mass

is: one of the fundamental dimensional quantities of mechanics (along with length and time).

is: a property that determines both the acceleration an object will experience in response to an applied force (according to Newton’s second law) and the magnitude_of_a_vector_or_vector_quantitymagnitude of the gravitational force it will experience in response to a given gravitational field. These ways of interpreting mass are (at present) believed to be equivalent. [MATH 5.1, PHYS 1.1]

has as its SI unit: the kilogram (kg), one of the seven base units. [PHYS 1.1, PHYS 2.3]

should not be confused: with weight. [PHYS 2.3]

is also: an abbreviation used to indicate a particle or body of non–zero mass.

mass defect

is: the difference between the total mass of the free protons and neutrons of which a nucleus is made and the (smaller) mass of the nucleus itself. [PHYS 9.1]

is attributed: to the mass energy equivalence of the binding energy when the protons and neutrons are bound together. [PHYS 9.1]

mass energy

of: an object

is: the energy the object has by virtue of its mass, as described by Einstein’s mass–energy equation: E = mc2. [PHYS 2.4, PHYS 9.1]

mass number

of: an atom

is: the total number of protons and neutrons (i.e. the total number of nucleons) in the nucleus of the atom. [PHYS 8.1, PHYS 9.1]

usually is denoted: by the symbol A. [PHYS 8.1, PHYS 9.1]

is: for all known isotopes the closest whole number to the relative atomic mass Ar of the isotope. [PHYS 8.1, PHYS 9.1]

mass spectrometer

is: a device that uses electric and magnetic fields to determine the masses of molecules and submolecular particles, including atoms, nuclei and (some) elementary particles. (Strictly speaking it is used to determine the mass of a related ion, rather than the electrically neutral particles themselves.) [PHYS 4.3, PHYS 8.1, PHYS 9.1]

is also used: to determine the relative abundances of various kinds of particles within a given sample.

occurs: in various types, using different arrangements of fields.

mass spectrometry

is: the study of ionic masses using a mass spectrometer. [PHYS 4.3]

mass spectrum

is: the output from a mass spectrometer. [PHYS 8.1]

shows: the relative abundance of the various ions derived from a sample, as a function of their mass. [PHYS 8.1]

typically takes the form: of a graph in which ion current is plotted against charge–to–mass ratio (or possibly against relative atomic mass). [PHYS 8.1]

mathematical

means: pertaining to mathematics.

mathematical model

of: a physical situation or problem

is: an equation or a system of equations (possibly differential equations) that represent the situation or problem. [MATH 6.1]

mathematics

is: the study of number, order, shape, form and numerical data, including their representation by abstract symbols and the rules for manipulating those symbols.

matter

is: a general term for material substance irrespective of its specific form.

Maxwell–Boltzmann energy distribution

is: a distribution function which describes the number of molecules in a gas that have energy in a small interval between E and E + ΔE, usually taken in the limit at ΔE tends to zero. [PHYS 7.5]

is given: by

$n(E)\Delta E = 2\pi N\left(\dfrac{1}{\pi kT}\right)^{3/2}E^{1/2}e^{-E/kT}\,\Delta E$

where k is Boltzmann’s constant, N is the total number of molecules in the gas and T is the absolute temperature of the gas. [PHYS 7.5]

Maxwell–Boltzmann speed distribution

is: a distribution function which describes the number of molecules in a gas that possess a speed in a small interval between υ and υ + Δυ, usually taken in the limit as Δυ tends to zero. [PHYS 7.5]

is given: by

$n(\upsilon)\Delta\upsilon = 4\pi N\left(\dfrac{m}{2\pi kT}\right)^{3/2}\upsilon^2e^{-m\upsilon^2/2kT}\,\Delta\upsilon$

where k is Boltzmann’s constant, m is the mass of a molecule, N is the total number of molecules in the gas and T is the absolute temperature of the gas. [PHYS 7.5]

Maxwell’s theory of electromagnetism

is: a classical theory of electromagnetic phenomena based on a set of partial differential equations that relate the electric and magnetic fields in a region to the charges and currents in and around that region, and to any non–uniformities or inconstancies in the fields within that region.

predicts: the existence of electromagnetic waves that travel through a vacuum with speed $c = 1{\large/}\sqrt{\varepsilon_0\mu_0\vphantom{\sup0}}$

mean (of values)

of: n values x1, x2, x3, x4, ... xn−2, xn−1, xn of a quantity x

is symbolized: by $\langle x\rangle$. [PHYS 1.1, PHYS 1.2]

is obtained: by adding all those quantities together and dividing the resulting sum by n. Thus

$\langle x\rangle = \dfrac{x_1+x_2+x_3+x_4+\ldots+x_{n-2}+x_{n-1}+x_n}{n}$ [PHYS 1.1, PHYS 1.2]

mean (of a distribution)

of: a normalized distribution f(x), i.e. a distribution for which $\displaystyle \int_a^b f(x)\,dx = 1$.

is: the integral $\displaystyle \int_a^b f(x)\,dx = 1$ where the upper_limit_of_integrationupper and lower_limit_of_integrationlower limits a and b depend on the range of possible values for the quantity x. [MATH 5.4]

mean collision frequency

of: a molecule in a gas

is: the average number of collisions per second made by a molecule in the gas. [PHYS 7.5]

therefore is: the reciprocal of the mean free time. [PHYS 7.5]

mean free path

of: a molecule in a gas

is: the average distance which the molecule will travel between collisions with other molecules. [PHYS 7.5]

therefore is: the product of the average speed and the mean free time. [PHYS 7.5]

mean free time

for: a molecule in a gas

is: the average time spent by the molecule between collisions with other molecules. [PHYS 7.5]

therefore is: the reciprocal of the mean collision frequency. [PHYS 7.5]

measure

means: (as a verb) to determine a quantitative value.

also means: (as a noun) a quantity that expresses in quantitative terms the extent to which a given quality is present.

See also measurement.

measurement

is: a process that determines the (usually) numerical value of a quantity.

is also: used to describe the numerical value itself.

more specifically is: in quantum mechanics, a process that entails the interaction of a system with a measuring device, the possible outcomes of which are restricted by the state of the system immediately prior to the measurement.

mechanical

means: pertaining to mechanics.

mechanics

is: the branch of physics concerned with the motion of bodies or systems with (effectively) a finite number of degrees of freedom and the response of such bodies to forces.

traditionally is: divided into the branches of statics, kinematics and dynamics.

mechanical energy

of: a physical system

is: the sum of the kinetic energy and the potential energy of the system. [PHYS 2.4]

mechanical equilibrium

is: the condition in which a system is in both translational equilibrium and rotational equilibrium. [PHYS 2.7]

mechanical impedance

of: a damped_mechanical_oscillatordriven damped mechanical oscillator in which a periodic driving force F0sin(Ωt) produces velocity oscillations described by υ0sin(Ωt − δ)

is: the quantity Zm = F0/υ0

is given: for a mass m oscillating on a spring of spring constant k and subject to a damping force of magnitude (where υ is the speed of the particle), by

$Z = \sqrt{b^2+\left(\dfrac{k}{\it\Omega}-{\it\Omega}m\right)^2}$

has as its SI unit: N s m−1.

Compare with impedance (electrical).

mechanical oscillator

is essentially: a mass on a spring, possibly subject to a damping force and a driving force.

See simple harmonic oscillator, damped mechanical oscillator, driven oscillator, as appropriate.

median

of: a triangle

is: a line drawn from one vertex of the triangle to the mid-point of the opposite side. [MATH 2.1]

medium

is: a material of interest

is exemplified by: an optical medium.

medium (for elastic waves)

is: a deformable material in which an equilibrium state can be identified and in which energy is required to bring about (at least some) deformations from the equilibrium state. [PHYS 5.6]

is exemplified: by an elastic solid, and by an open body of water in a uniform gravitational field. [PHYS 5.6]

medium (for light)

is: a transparent material through which light can travel. [PHYS 6.2]

includes: a vacuum as a special case, even though it does not consist of any ’substance’ in the normal sense. [PHYS 6.2]

melting point

of: a substance

is: the temperature at which the solid and liquid phases of the substance can coexist in equilibrium at a specified pressure (usually, but not necessarily, standard atmospheric pressure).

is synonymous: with freezing point.

meniscus

is: the curved surface of a liquid, usually when it is in contact with a solid surface. [PHYS 7.6]

mercury barometer

is: a device for measuring one pressure relative to another (commonly atmospheric pressure relative to a vacuum). [PHYS 7.2]

consists: of mercury contained in a U–tube. [PHYS 7.2]

works: when the two pressures are applied to the two sides. The difference is registered as a level difference. The pressure difference ΔP is related to the level difference h by the formula ΔP = ρgh, where ρ is the density of mercury and g the magnitude of the acceleration due to gravity. [PHYS 7.2]

mercury–in–glass thermometer

is: a glass capillary with a bulb containing mercury. Changes in temperature cause the glass and mercury to expand (or contract) by different amounts, and the result is that the meniscus moves to different positions in the capillary. [PHYS 7.2]

can be calibrated: by marking meniscus positions corresponding to fixed points such as the boiling and freezing points of water, and then interpolating between them. [PHYS 7.2]

mesh

within: a circuit

is: any continuous closed path. [PHYS 4.1]

is often called: a loop.

metal

is: a material that can be modelled as an array of positive ions immersed in a pool of free electrons. [PHYS 7.1]

therefore is: an excellent electrical conductor. [PHYS 7.1]

See metallic bond and metallic bonding.

metallic bond

is: a bond that does not involve the localization of any electron with a particular atom. [PHYS 11.4]

has: the bonding electrons effectively free to move throughout the lattice of a (crystalline) solid, so the electrons are shared by the crystal as a whole. [PHYS 11.4]

See metallic bonding.

metallic bonding

is: the type of chemical bonding that holds metals together. A simple model for a metal is an array of positive ions immersed in a sea of free electrons, and the bonding arises partly from electrostatic_forceelectrostatic attraction between the ions and the intervening electrons. [PHYS 7.1, PHYS 8.4]

therefore is: a type of chemical bonding in which an atom shares its bonding electron(s) with a very large number of other atoms. [PHYS 8.4]

See metallic bond.

method of least squares

is: a numerical method for determining the gradient and intercept of the straight line that best fits a given set of data points. [PHYS 1.3]

assumes: that the errors in the independent variable are negligible and that the error in each measurement is the same. [PHYS 1.3]

See statistics in the Maths For Science handbook for further details.

method of mixtures

is: a standard calorimetry procedure, in which heat from an object whose heat capacity is already known, is supplied to another object whose thermal properties are under investigation. Or vice versa. [PHYS 7.4]

method of undetermined coefficients

is: a method for finding a particular solution to some types of linear inhomogeneous differential equations. [MATH 6.3]

is based: on equating coefficients of like terms when a trial solution is substituted into the equation. [MATH 6.3]

metre, m

is: the SI unit of length, one of the seven base units. [PHYS 1.1]

is defined: as the distance light travels in a vacuum in 1/299 792 458 second. [PHYS 1.1]

microscope

is: an instrument for viewing nearby objects with high magnifying power. [PHYS 6.4]

microscopic

describes: size scales below visibility by the human eye and sufficiently small that the behaviour of molecules, or atoms may need to be considered. [PHYS 7.2, PHYS 7.5]

microstructure

of: a material, especially a solid,

is: the actual structure at the atomic level, which reflects the ideal state of the atom positions, modified by the presence of impurities and defects. [PHYS 7.6]

microwave radiation

is: a form of electromagnetic radiation characterized by wavelengths in the approximate range 1 mm to 0.03 m.

See electromagnetic spectrum.

millibar, mbar

is: a non-SI unit of pressure.

is defined: as one thousandth of a bar, where 103 mbar = 1 bar = 105 N m−2 = 105 Pa (= 1.013 25 atm). [PHYS 7.2]

Millikan’s oil drop experiments

are: a series of experiments first performed by Robert Millikan (1868–1953). [PHYS 3.3]

used: balanced gravitational and electrostatic forces on charged oil drops, to make the first accurate determinations of the charge on the electron, −e. [PHYS 3.3]

minimum deviation

of: a light ray

passing: through a prism

occurs: when the ray passes through the prism symmetrically. This is the arrangement which gives the maximum possible dispersion. [PHYS 6.3]

minor arc

is: the smaller of the two arcarcs of a circle joining two points on the circumference that are not at opposite ends of a diameter. [MATH 2.1]

minor axis

is: the shortest diameter of an ellipse.

minor segment

is: the region bounded by the minor arc of a circle and the chord that joins its end points. [MATH 2.1]

minute of arc, '

is: a unit of angular measure. [MATH 1.6]

is equal: to 1/60 of a degree. [MATH 1.6]

is abbreviated: arcmin. [MATH 1.6]

is exemplified: by 20′ = 20 arcmin = 1°/3.

See also second of arc. [MATH 1.6] [MATH 1.6]

mirage

is: an optical illusion arising from continuous refraction. [PHYS 6.2]

mirror

is: a surface at which reflection can take place. Its quality is determined in part by its reflectivity. [PHYS 6.2]

mirror transverse magnification

is: the ratio of image height to object height measured in the direction perpendicular to the optical axis of the mirror. [PHYS 6.3]

missing mass

See mass defect.

mixed partial derivative

are: partial derivatives of second or higher order that involve (partial) differentiation with respect to two or more independent variables. [MATH 6.4]

mixed symmetry

of: a function f(x)

is found: when the function is neither an even function nor an odd function. Such a function may be written as a sum of odd and even parts by writing it in the form

$f(x) = \frac12[f(x)+f(-x)]+\frac12[f(x)-f(-x)]$ [MATH 5.2]

mode

See modes of vibration.

model

is: an artificial construction invented to represent or to simulate the properties, the behaviour, or the relationships among individual parts of the real entity being studied. [PHYS 1.1]

often is: a mathematical model. [PHYS 1.1]

moderator

in: a nuclear fission reactor

is: a material whose function is to slow down fast neutrons to produce thermal neutrons and hence to maintain the nuclear chain reaction. [PHYS 9.3]

modes of vibration

of: a body

are: the different types of vibration (linear, torsional, pendulum–like, etc.) that the body can exhibit simultaneously. [PHYS 5.1]

See normal modes.

modulus (of a complex number)

of: the complex number z = x + iy.

is denoted: by |z|. [MATH 3.1, PHYS 5.5, PHYS 10.3]

is defined: by |z| = (x2 + y2)1/2. [MATH 3.1, PHYS 5.5, PHYS 10.3]

is always: positive. [MATH 3.1, PHYS 5.5, PHYS 10.3]

modulus (of a real number)

of: a real number x

is denoted: by |x|. [MATH 1.2, PHYS 2.7]

is defined: by |x| = (x2)1/2. [MATH 1.2, PHYS 2.7]

is always: positive. [MATH 1.2, PHYS 2.7]

is synonymous: with the absolute value or magnitude.

modulus notation

See: modulus.

modulus of elasticity

is: the ratio of stress to strain in an elastic material, within the region of validity of Hooke’s law where these are linearly related. [PHYS 7.6]

is exemplified: by bulk modulus, shear modulus, and Young’s modulus. [PHYS 5.7]

molar gas constant

is: the physical constant R that appears in the equation of state of an ideal gas; PV = nRT. [PHYS 7.2, PHYS 7.3, PHYS 7.4, PHYS 7.5]

has: the value R = 8.314 J K−1 mol−1 (to four significant figures). [PHYS 7.2, PHYS 7.3, PHYS 7.4, PHYS 7.5]

is related: to Boltzmann’s constant k and Avogadro’s constant NA by R = NAk.

is synonymous: with universal gas constant.

See also mole.

molar heat capacity

See molar specific heat.

molar latent heat

is: the amount of heat absorbed or emitted per mole of a substance during an isothermal phase transition. [PHYS 7.4]

has as its SI unit: J mol−1. [PHYS 7.4]

See also latent heat, specific latent heat.

molar mass

is: the mass per mole of a substance. [PHYS 7.2]

has as its SI unit: kg mol−1. [PHYS 7.2]

molar specific heat

is simply: the heat capacity per mole of a substance. [PHYS 7.4, PHYS 7.5]

should not be confused: with specific heat, which is heat capacity per kilogram of a substance. [PHYS 7.4, PHYS 7.5]

is quantified: as C = ΔQ/nΔT where n is the number of moles of the substance in the sample. (Strictly speaking the molar heat capacity should be defined as the limit of this ratio as ΔT becomes vanishingly small, since the heat capacity depends on the state of the sample.) [PHYS 7.4]

depends: on the constraints applied during heating: may be the molar specific heat CV at constant volume, or may be the molar specific heat CP at constant pressure. [PHYS 7.4]

has as its SI unit: J mol−1K−1. [PHYS 7.4]

sometimes is referred to: as molar specific heat capacity. [PHYS 7.4, PHYS 7.5]

Compare with specific heat, principal_molar_specific_heatsprincipal specific heats.

mole, mol

is: the SI unit of amount of substance, one of the seven base units. [PHYS 7.1, PHYS 7.2]

is defined: as the amount of a substance that contains the same number of elementary entities as the number of atoms in 12 g of the 12C isotope of carbon. (Measurements show that 12 g of the 12C contain (to four significant figures) 6.022 × 1023 atoms of 12C) The elementary entities may be atoms or molecules. For example, one mole of MgF2 contains 6.022 × 1023 magnesium atoms and 12.044 × 1023 fluorine atoms. [PHYS 7.1, PHYS 7.2]

facilitates: the evaluation of the molar mass of a substance, the numerical value of the molar mass in grams per mole being obtained by adding together the relative atomic masses of the atoms in the molecule. The relative atomic mass of magnesium is 24.3, and of fluorine is 19.0. Thus, one mole of MgF2 has a mass of [24.3 + (2 × 19.0)] g, or approximately 62.3 g. [PHYS 7.1, PHYS 7.2]

See Avogadro’s constant and Avogadro’s number.

molecular beam

is: a stream of directed molecules

is created: by allowing the molecules to escape from a container through a fine slit by molecular impacts on the slit space into a region beyond, where the pressure is lower. The pressure must be sufficiently low to avoid intermolecular collisions within the slit. Usually, the directionality of the beam is improved using a second slit placed behind the first. [PHYS 7.5]

molecule

is: the smallest freely existing part of a chemical element or chemical compound that retains the chemical identity of that chemical element or chemical compound. [PHYS 7.1, PHYS 8.1]

therefore is usually: a group of atoms bound together. For compounds composed of identical molecules, the type and relative number of each sort of atom present in each molecule is indicated by the chemical formula of that substance. For example, a molecule of water contains one atom of oxygen and two atoms of hydrogen, and is represented by H2O. [PHYS 7.1, PHYS 8.1]

exceptionally: some molecules consist of single atoms (e.g. noble gases).

moment

of: a vector υ about a point P

is: the vector product s × υ of the vector υ with a displacement vector s from the point P to any point on the line of action of the vector. [MATH 2.7]

moment of a force

for: a force F causing, or tending to cause, rotation about a point P

is: a measure of the turning effect of the force. [PHYS 2.7, PHYS 4.3]

is given: by r × F where r is a displacement vector from P to any point on the line of action of F. [MATH 2.7, PHYS 2.7]

is therefore: identical to the torque of F about P. [PHYS 2.7]

is mainly used: when dealing with coplanar forces, in which case the resultant moment of the forces about P may be obtained by adding the magnitude_of_a_vector_or_vector_quantitymagnitudes of the individual moments (found by multiplying the magnitude_of_a_vector_or_vector_quantitymagnitude of the force by the perpendicular distance between P and the line of action of the force) subject to the sign convention that those forces that promote anticlockwise rotation have positive moments while those that promote clockwise rotation have negative moments. [PHYS 2.7, PHYS 4.3]

moment of inertia

of: a body

is: a measure of its reluctance to be angular_accelerationrotationally accelerated. [PHYS 2.7, PHYS 2.8]

is calculated: from the distribution of mass in the body about the axis of rotation. [PHYS 2.7, PHYS 2.8]

may be defined: in terms of mass elements Δmi located at perpendicular distances ri from the axis of rotation by

$\displaystyle I = \sum_i r_i^2\Delta m_i$ [PHYS 2.7, PHYS 2.8]

may be defined: in terms of infinitesimal elements by

$I = \int r^2\,dm$

moment of momentum

is: a synonym for angular momentum.

momentum

See linear momentum and angular momentum

monatomic ideal gas

is: an ideal gas (and therefore obeying PV = nRT) in which the internal energy at any temperature T is given by U = 3NkT/2. [PHYS 7.4]

can be used: to model the behaviour of a real gas of single atoms (that have no effective rotational or vibrational degrees of freedom) at low density. [PHYS 7.4]

monochromatic

describes: light which may be modelled by electromagnetic waves of a single wavelength (or frequency) or by photons of a single energy. [PHYS 6.1, PHYS 6.3]

monolayer

is: a very thin layer of molecules, just one molecule thick. [PHYS 8.1]

most probable speed

of: gas molecules

corresponds: to the peak in the speed distribution function. [PHYS 7.5]

See Maxwell–Boltzmann speed distribution.

motion

is: continuous change of position.

motional induction

is: electromagnetic induction arising from the motion of an electrical conductor within (and relative to) a magnetic field. [PHYS 4.4]

moving–coil galvanometer

is: a generic term for ammeters and voltmeters that use the equilibrium orientation of a pivoted current carrying coil in a magnetic field (subject to some suitable restoring force or torque) to make electrical measurements. [PHYS 4.1]

multi–electron atom

is: an atom containing more than one orbital electron. [PHYS 8.3]

multi–valued function

is: an improper use of function, describing situations in which two or more values are associated with a single value of the argument. [MATH 1.3]

is exemplified: by $f(x) = \sqrt{x\vphantom{0}}$, which can take on two values of opposite signs unless (as is usual) the convention is adopted that $\sqrt{x\vphantom{0}}$ only represents the positive square root of x. [MATH 1.3]

multimeter

is: an instrument for measuring resistance, and voltages or currents (either d.c. or a.c.). [PHYS 4.1]

multiple roots

are: roots having the same value, but which must be counted separately for the purposes of the fundamental theorem of algebra. [MATH 4.4]

are exemplified: by the two roots of x2 − 2x + 1 = 0, both of which are equal to 1. [MATH 4.4]

multiplicity

of: a root α of a polynomial equation p(x) = 0

is: the number of times the factor (xα) occurs in the factorized form of p(x). [MATH 3.1]

mutual inductance

See coefficient of mutual inductance.

mutual induction

is: the production of an induced voltage in one coil or circuit due to the changing current in another coil or circuit. [PHYS 4.4]

See coefficient of mutual inductance.

myopia (short sight)

is: the condition in which eyes are unable to focus on objects as far away as the standard far point (taken to be at infinity). [PHYS 6.4]

occurs when: the lens of the eye has too short a focal length, even when unaccommodated. [PHYS 6.4]

usually is corrected: by an auxiliary diverging lens. [PHYS 6.4]

n–type semiconductor

is: a semiconductor in which the majority of mobile charge carriers are negatively charged (usually electrons). [PHYS 11.4]

n–dimensional

describes: an object or situation which requires the use of a coordinate system with n independent axes for its adequate description. [PHYS 2.1, PHYS 2.2]

natural angular frequency

is: the angular frequency that a harmonic oscillator would have if it were neither damped nor driven. [PHYS 5.4]

is exemplified: by a pure LCR circuit, in which the charge (and the current) have a natural angular frequency $\omega_0 = \sqrt{\dfrac{1}{LC}} = 1$. [PHYS 5.4]

natural exponential function

is: the function, ex. [MATH 1.5]

is so called: to distinguish it from the function, ax.

See exponential function. [MATH 1.5]

natural frequency

is: the frequency that a simple harmonic oscillator has if it is neither damped nor driven. [PHYS 5.2, PHYS 5.3, PHYS 5.4]

is exemplified: by an electrical oscillator, in which the charge (and the current) have a natural frequency $f_0 = \dfrac{1}{2\pi}\sqrt{\dfrac{1}{LC}}$. [PHYS 5.4]

is exemplif