Figure 6.20 shows a metal rod PQ resting on the smooth rails AB and positioned between the poles of a permanent magnet. The rails, the rod, and the magnetic field are in three mutual perpendicular directions. A galvanometer G connects the rails through a switch K. Length of the rod = 15 cm, *B *= 0.50 T, resistance of the closed loop containing the rod = 9.0 mΩ. Assume the field to be uniform.

**(a) **Suppose K is open and the rod is moved with a speed of 12 cm s^{−1} in the direction shown. Give the polarity and magnitude of the induced emf.

**(b) **Is there an excess charge built up at the ends of the rods when

K is open? What if K is closed?

**(c) **With K open and the rod moving uniformly, there is *no net force *on the electrons in the rod PQ even though they do experience magnetic force due to the motion of the rod. Explain.

**(d) **What is the retarding force on the rod when K is closed?

**(e) **How much power is required (by an external agent) to keep the rod moving at the same speed (=12 cm s^{−1}) when K is closed? How much power is required when K is open?

**(f) **How much power is dissipated as heat in the closed circuit?

What is the source of this power?

**(g) **What is the induced emf in the moving rod if the magnetic field is parallel to the rails instead of being perpendicular?