Proposal - Coil Gun Linear Accelerator

"But what is a Coil Gun Linear Accelerator?!", you may be asking. well... A Linear Accelerator works by creating a magnetic field, to move ferromagnetic objects( Things that can interact with magnetic fields ). This is done by running current through a coil, the coil produces a magnetic field and draws the ferromagnetic object towards it. However once the object is moving if it reaches halfway through the coil when the coil is still active the coil will begin to slow down the object, because the object is not magnetic it self it is simply drawn to where the magnetic field lines are the thickest; see image below.

For any given solenoid $$B = {\mu_0 {In\over L}}$$ Where $\mu_0$ is the magnetic permeability of the core of the solenoid. For our Linear Accelerator the $\mu_0$ of our coils will be approximated to that of a vacuum which is $$\mu_0 = { 4\pi\times 10^{-7}}$$

This means excatly as the object is halfway through the coil, the coil must instanly lose all of its power, to obtain maximum speed when the object leaves the Linear Accelerator. Since this is not possible, we will shutdown the coil just before the object is halfway through, testing will prove when the best time to turn of the coil is. The use of a limit switch will aid us in telling when to deactivate the coil.

Now that we know how to operate our Coil Gun Linear Accelerator, we can now calulate its efficiency, based on the mass of the object we want to accelerate, the distance of the end of the tube to the coil, and the time it takes for the object to pass another sensor( Two switches at the end of the Linear Accelerator ), we will be able to determine the acceleration of the object, the speed of the projectile, and therefore its kinetic energy. Based on the input of energy ( Energy provided to the coil ) divided by the kenetic energy of the object, will give us a percentage efficiency.