Beating the physics of a railgun

[Anthony physics]

Ive recently been thinking of rail guns. When i first learned about this type of motor ( we use to call it the linear motor), i read that the projectile would eventually reach a top speed because of faraday's law creating a counter current. However, what if the magnetic field ( the one that is required for lorentz force to work) was created by an electromagnet that was wired in series with the actual rails. It seems that the "faraday induced voltage" could never get strong enough to cancel out the voltage of the battery powering the rails. I say this because the "faraday induced voltage" relies on the magnetic flux and should the voltages cancel out, the magnetic field would be canceled also. Since no mag field, their would no longer be any mag flux and the "faraday induced voltage would be zero" allowing the projectile to accelerate.

Ive tried to model the scenario with an equation of speed vs distance traveled of the projectile but i keep hitting a wall as the "faraday induced voltage" depends on the speed which depends on the current which depends on the "faraday induced voltage". Having the magnetic field also depend on the faraday induced voltage and complicates it even further.

Im sure I've gone wrong with my reasoning somewhere but regardless Has anyone tried to model this scenario or even model the speed vs distance graph of a railgun with constant mag field??

Thanks for any and all responses!

 

[A.T.]

their would no longer be any mag flux and the "faraday induced voltage would be zero" allowing the projectile to accelerate.

What would accelerate the projectile if there is no longer any magnetic field?

 

[Anthony physics]

I guess i missworded. The point was, there would never be a point when the current or the field would be zero because as they get smaller and smaller, the back voltage produced by faraday would also get smaller and smaller