Using battery current to generate magn force

[hy23]

Homework Statement

A circuit is formed by an aluminum bar that can slide along two (parallel) metal rails which are joined by a battery. There is a magnetic field which passes through the circuit. The battery also has an internal resistance of r. Everything else has ~no resistance. When the circuit is closed, battery sends current around the circuit.

Show that the aluminum bar reaches a terminal velocity.

Homework Equations

$$\epsilon$$=Blv
$$\epsilon$$=emf
v=velocity
l=length of aluminum bar
B=magnetic field

The Attempt at a Solution

At first inspection it seems like the answer is straightforward...v=$$\epsilon$$/Bl
but I doubt it's that easy and after thinking about it I'm very confused.

So this is what made me confused: the battery sends a current through the aluminum bar, and the magnetic field then exerts a magnetic force on the aluminum bar, making it slide along the rails, but then this increases the magnetic flux through the circuit, so then a current opposing the battery current must be induced...but then wouldn't the currents cancel out and no movement occur?

Also in a short circuit, is the terminal voltage 0?
Since $$\epsilon$$-IR=V
and I=$$\epsilon$$/R

 

[AvroArrow]

so V=0? I'm sorry, this may be a bit of a mess and I hope it makes sense. Any help is appreciated, thank you.