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 motional electromotive force (EMF) induced in a straight conducting wire of length l moving with velocity v perpendicular to a uniform magnetic field B is given by: E = ( v B ) l Since the velocity v , magnetic field B , and the length of the wire l are mutually perpendicular, the magnitude of the induced EMF is: E = vBl This induced EMF is equal to the potential difference established across the ends of the wire. Therefore, the potential difference is lBv .