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.