question_answer 39)

    A magnetic field covers a large region where a wire AB slides smoothly over two parallel conductors separated by a distance d, Fig. 4(EP).11. 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 , what is the current in the circuit? What is the force needed to keep the wire moving at constant velocity?

Answer:

                    In Fig. 4(EP). 11, we have shown a wire AB of length  = d, resistance R moving with a velocity along positive direction of X-axis over two parallel wires OX and CD at y = 0 and y = d respectively. The magnetic field covering the region is At t = 0, AB is at  = 0 and velocity = At t = t, AB is at = t Motional emf in AB = Its direction, as per Fleming's right hand rule is along negative y-axis. e.m.f. due to change in magnetic field = It is also along negative y-axis.  total e.m.f. induced = Current induced, The direction of current is clockwise, i.e., along ABOC (absorbing negative sign).  Force needed along  ; F = F = F =