Problem 4.66

A coil of inductance \(L\) connects the upper ends of two vertical copper bars separated by a distance \(l\). A horizontal conducting connector of mass \(m\) starts falling with zero initial velocity along the bars without losing contact with them. The whole system is located in a uniform magnetic field with induction \(B\) perpendicular to the plane of the bars. Find the law of motion \(x(t)\) of the connector.