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.