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 $\mathbf{B}(t)$