>>11603411The field inside a coil by itself is strictly linear, but not when there's a bullet flying through it.
The inductance of a coil is linearly related to the relative permeability of the bullet (which is many orders of magnitude higher than air). So as the bullet enters the coil, inductance goes up and the magnetic field becomes stronger. So as the bullet flies into the coil (and as soon as it's completely surrounded by the coil), the magnetic field actually increases and puts /more/ force on the bullet. While this is happening, the ferromagnetic bullet becomes a magnet itself (pointing in the same direction as the coil).
But as you might remember from physics, Faraday's Law says that changing the magnetic flux through a loop results in EMF that creates an /opposing/ magnetic field that applies an opposite force to the magnet-bullet. This is what we avoid by turning off the coil when the bullet is right in the middle - so that the projectile gets to keep all of its momentum and avoids the opposite force that would be caused by back-EMF.
I actually found you some experimental data from JVE Journals of the force on a projectile going through a single coil with no switching. As you can see, there's an exponential increase in projectile force until a point, where it rapidly reverses and has a braking effect. Hope this helps.
