Difficult inductance + torque rolling rail problem

[oreosama]

Homework Statement

Homework Equations

[tex]F = I\vec{l} \times \vec{B}[/tex]
[tex]\varepsilon = BLv[/tex]

The Attempt at a Solution

Every direction i go seems real wrong


[tex]F = I\vec{l} \times \vec{B}[/tex]

[tex]F = \frac{\varepsilon \vec{l} \times \vec{B}}{R}[/tex]
[tex]F = \frac{\varepsilon LB}{R}[/tex]
[tex]ma = \frac{VLB}{R}[/tex]
[tex]v = \frac{VLB}{mR}t[/tex]


while the math seems to all be good here, this implies like every answer after is going to be infinity which seems plain wrong.. I assume I should havea current from the battery versus a current induced and thus have two forces. but things get messy and I can never get a v just in terms of t when I mess with it in this direction. thanks for any help

 

[haruspex]

I assume I should havea current from the battery versus a current induced and thus have two forces.

Not quite. The motion of the cylinder through the field will induce a "back emf". I'm no expert in this area, but my guess is that the cylinder will cease to accelerate when the back emf equals and cancels the applied emf.