A conducting wire of length l , positioned perpendicular to a magnetic field B , travels with a velocity v . Determine the potential difference that is established across the ends of the wire.

Step-by-step solution

The magnetic force on a charge q moving with velocity v in a magnetic field B is given by F = q( v B ) . For a free electron, the charge is q = -e . The wire moves with velocity v perpendicular to the uniform magnetic field B . The average thermal velocity of free electrons is zero, so their average net velocity is the velocity of the wire, v . Since v is perpendicular to B , the magnitude of the average magnetic force is: F = e v B (90^ ) = e v B