How to get the coilgun (Gauss Gun) electomagnetic field strength...

[speakreveal]

So in a coilgun, I need to know how long the electromagnetic field has to be to propel a .336kg mass at 500m/s^2 (a force of 168N) in each coil
find the horizontal component of the electric field
There are five coils, each one 1m apart.

What's the formula to achieve the necessary em field strength to propel the ferromagnetic projectile?