Top Speed of a Railgun: Lorentz Force

[Anthony physics]

Ive asked this question before but i wrote it in a very confusing manner so ill do it again but in more qualitative terms:

The "classical railgun" i first learned about (mag field is produced by a permanent magnet) has a top speed because as the slug accelerates, the time derivative of mag flux increases continuously until induced voltage = voltage of battery.

However what about when the mag field is produced by the current running through the rails themselves? ( like the us navy railgun) It seems that there would never be a top speed because as current tends toward 0, so does mag flux and therefore the voltage created by faraday's law would never quite reach the battery voltage and acceleration will continue to exist. Is this true??

Note: for the purpose of this question please assume the only force involved is the lorentz force, do not include friction.

Thank you

 

[Simon Bridge]

Have you tried writing the equations that govern the force and so the motion?

Some notes:
...what happens when the slug moves at the same speed as the charge carriers in the wire that make up the current?
... for simplified formulae, see for example: https://en.wikipedia.org/wiki/Railgun#Mathematical_formula