Electromagnetism: Axle rolling on train rails

mardi 30 juillet 2013

Imagine a set of train tracks. Now there is one bridge (a resistor) connecting the two rails in one spot. On a different spot, there is rolling axle that acts as another bridge and it makes good electrical connection with the rails creating a full rectangular circuit. This axle rolls at a constant velocity. The only significant resistance in the circuit is from the resistor with resistance R. There is a uniform magnetic field, B, directed vertically downward and perpendicular to the horizontal rails. Assuming there is no friction on the rails, what horizontal force is necessary to keep the axle moving at a constant speed? Now I know the answer is F = B^2 * length of axle squared * velocity / resistance, but how do I find this? What force acts to slow down the axle in the first place since there is no friction? Thanks for the help.