Problem 3.311

A thin non-conducting ring of mass \(m\) carrying a charge \(q\) can freely rotate about its axis. At the initial moment the ring was at rest and no magnetic field was present. Then a practically uniform magnetic field was switched on, which was perpendicular to the plane of the ring and increased with time according to a certain law \(\mathbf{B}(t)\) Find the angular velocity \(\omega\) of the ring as a function of the induction \(\mathbf{B}(t)\)