PPLATO | FLAP Glossary

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 x − y = 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: ε₀ε_rE²/2, in an electric field of magnitude E, where ε₀ is the permittivity of free space and ε_r is the relative permittivity of the medium in which the field is present. [PHYS 4.5]

is given by: B²/(2μ₀μ_r), in a magnetic field of magnitude B where μ₀ is the permeability of free space, and μ_r 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 ΔQ_rev 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 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 x–axis, 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 ΔQ/ΔT 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 x–coordinate of a particle’s position, and the uncertainty Δp_x 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 Δt ≥ h , 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, F_x, 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 F_x = −k_ss_x, where k_x 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 F_x^app = −F_x 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 P_triple 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 ϕ₂ − ϕ₁ = (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 ϕ₂ − ϕ₁ = 2nπ, 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 I_ind

is: the voltage V_ind = I_indR. [PHYS 4.4]

is described: in magnitude by Faraday’s law: V_ind = |dΦ/dt|, where dΦ/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 dΦ/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 V_ind 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 X_L = 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 = (υ_x, υ_y, υ_z) at time t. [MATH 4.1, PHYS 2.1, PHYS 2.2]

is represented: by the vector a = dυ/dt. That is, a_x = dυ_x/dt, a_y = dυ_y/dt, a_z = dυ_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 = |dθ/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, υ_x = dx/dt, υ_y = dy/dt, υ_z = 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 P_aV_a = P_bV_b. [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 (T_K) is related to its Celsius temperature scaleCelsius temperature (T_C) by the formula: T_K/K = T_C/(°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 × 10⁶ joule. [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: θ_i = θ_R. [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 I–V 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 = mυ, 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), υ_x(t) and a_x(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: F_x = −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 = l0^y. [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 = a^y. [MATH 1.5]

usually is written: as log_a(x). [MATH 1.5]

logarithm to base e

of: a number, x

is: the number, y which satisfies the equation, x = e^y. [MATH 1.5]

usually is written: as log_e(x), log_ex (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. log_e[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 = a^x. [MATH 1.5]

is indicated symbolically: by x = log_a(y), (so x = log_a(a^x)), 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, F_mag, 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_⊥

F_mag = |q|υ_⊥B(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 F_mag on a particle of charge q travelling with velocity υ at the point r through the relationship

F_mag = 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 = Nϕ. [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 F_mag 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 F_mag = I l × 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, m_l.

magnetic (spin) quantum number

See spin magnetic quantum number, m_s.

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 = (υ_x, υ_y, υ_z).

is: a scalar quantity that describes the ’size’ or ‘length’ of the vector υ = (υ_x, υ_y, υ_z). [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 A_r 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, ... x_n−2, x_n−1, x_n 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.

	sin(α + β) = sin(α)cos(β) + cos(α)sin(β)		$\sin(\alpha) + \sin(\beta) = 2\sin\left(\dfrac{\alpha+\beta}{2}\right)\cos\left(\dfrac{\alpha-\beta}{2}\right)$
	cos(α + β) = cos(α)cos(β) − sin(α)sin(β)
	sin(2α) = 2sin(α)cos(α)		$\sin(\alpha) - \sin(\beta) = 2\cos\left(\dfrac{\alpha+\beta}{2}\right)\sin\left(\dfrac{\alpha-\beta}{2}\right)$
	cos(2α) = cos²(α) − sin²(α)
	cos(2α) = 1 − 2sin²(α)		$\cos(\alpha) + \cos(\beta) = 2\cos\left(\dfrac{\alpha+\beta}{2}\right)\cos\left(\dfrac{\alpha-\beta}{2}\right)$
	cos(2α) = 2cos²(α) − 1
	$\cos^2(\alpha/2) = \frac12(1 + \cos(\alpha))$		$\cos(\alpha) - \cos(\beta) = -2\sin\left(\dfrac{\alpha+\beta}{2}\right)\sin\left(\dfrac{\alpha-\beta}{2}\right)$
	$\sin^2(\alpha/2) = \frac12(1 - \cos(\alpha))$