Dynamic Current Density
In order to keep things as simple as possible we're going to begin
by looking at the dynamic current density of an air cored coil. This analysis
will only use the self induced voltage of the coil and will not consider the induced
voltage generated by the projectile.
The first thing we need to do is establish how we are going to
rate a coils dynamic current density. One way to do this is to look at the largest
possible dJ/dt at turn on. We will make use of the inductance
equation which gives us the inductance in terms of the coil dimensions and
number of turns.