A rectangular metal frame of negligible resistance is placed on a smooth, horizontal table. One of its longer sides is replaced by a straight, conducting rod PQ of length l and resistance r. The other three sides form rigid rails and are connected to an external resistor R (with R≫r). The entire arrangement lies in a uniform magnetic field of magnitude B directed normally into the table. The rod PQ is pulled outward along the rails with a constant speed v so that the area of the rectangle increases.
parts:
(i) Determine the direction of the induced current in the complete circuit.
(ii) Show that the magnitude of the current through the resistor R is R+rBlv.
(iii) Prove that the mechanical power supplied to keep the rod moving at constant speed equals the electrical power dissipated as heat in the resistors.