Problem 4.65

A loop (Fig. 4.23) is formed by two parallel conductors connected by a solenoid with inductance \(L\) and a conducting rod of mass \(m\) which can freely (without friction) slide over the conductors. The conductors are located in a horizontal plane in a uniform vertical magnetic field with induction \(B .\) The distance between the conductors is equal to \(l .\) At the moment \(t=0\) the rod is imparted an initial velocity \(v_{0}\) directed to the right. Find the law of its motion \(x(t)\) if the electric resistance of the loop is negligible.