Physics problem

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Can anyone figure this one out?:

since F=Bil
F=ma
and
v= u +at
you know when t = 0, v = 0 therefore u=0
so F= bil=ma
a = Bil/m
since v = u+at (u=0)
v = Bilt/m

Hi Gilb,

thanks for that! I hadn't thought of it that way! There's more to the story though: because the movement of the rod (to the left) increases the area confined within the loop, the magnetic flux through it increases (flux = B times Area), and thus a displacement current is induced in the loop that counteracts the cause of its induction (Lenz's Law), i.e. a clockwise current, effectively a reduction of i. One might conclude, then, that v is simply zero at all times, but that doesn't make sense either, because then the flux doesn't change, no displacement current is induced, and there's nothing to counteract the v you calculated. In other words, if v is zero it can't be zero... So where's the "equilibrium point"?
The value of the displacement current is considered to be "epsilon naught" (8.854 x 10^-12) times the rate of change of the magnetic flux through the loop (d(flux)/dt).

I'm not in EE so I don't know the equations right away. It looks like a simplified rail gun. I remember trying to figure out the velocity once and it had a lot of variables.

In a rail gun you have to have a lot of amperage to get the power to move a piece of metal. (Most rail gun have around 1% efficiency. As a result you have to have a high initial velocity before the projectile hits the conducting rails, or it will weld itself into one piece of metal. If a rail gun were built then the initial velocity wouldn't be zero anyway.

I remember reading a few years ago about the field pushing against itself, and also about the electrons pushing themselves and moving it instead of the field moving it....confusing.....

I've heard of a Lorentz force being used. It might be similar to Lenz's Law, not sure though...

A Google search for "rail gun equation/formula" or similar will probably get equations you need.

Gilb was right! And gets the award for masterfully decyphering confusing NT language... It turns out the phrase "G supplies a constant current i" means that G keeps i constant at all times, i.e. it compensates for any effects of induction. This makes the situation exactly as described by Gilb, F = iLB = ma.