Problem 3.302

A conducting rod $A B$ of mass $m$ slides without friction over two long conducting rails separated by a distance $l$ (Fig. 3.88). At the left end the rails are interconnected by a resistance $R .$ The system is located in a uniform magnetic field perpendicular to the plane of the loop. At the moment $t=0$ the rod $A B$ starts moving to the right with an initial velocity $v_{0} .$ Neglecting the resistances of the rails and the rod $A B,$ as well as the self-inductance, find: (a) the distance covered by the rod until it comes to a standstill; (b) the amount of heat generated in the resistance $R$ during this process.