A magnetic field covers a large region where a wire AB slides smoothly over two parallel conductors separated by a distance d (Fig. 6.10). The wires are in the x-y plane. The wire AB (of length d) has resistance R and the parallel wires have negligible resistance. If AB is moving with velocity v, what is the current in the circuit. What is the force needed to keep the wire moving at constant velocity?

Question

A magnetic field

covers a large region where a wire AB slides smoothly over two parallel conductors separated by a distance d (Fig. 6.10). The wires are in the x-y plane. The wire AB (of length d) has resistance R and the parallel wires have negligible resistance. If AB is moving with velocity v, what is the current in the circuit. What is the force needed to keep the wire moving at constant velocity?

Philoid · Accepted Answer

Given: - length of the wire AB = d

resistance = R

Velocity = V

moving along the positive direction of x-axis over two parallel wires OX and CD at y=0 and y =d

magnetic field covering the region is

at t=0, AB is at x=0

velocity =

motional EMF in AB =

hence current induced

∴ force needed along is F = BIl