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 unifrom magnetic field was switched on, which was perpendicular to the planeof the ring and increased with time according to a certain law `B (t)`, Find the angluar velocity `omega` of the ring as a function of the induction `B(t)`.

Explanation

Going to the rotating frame with an instantaneous anglular velocity `vec(omega) (t)`. In this frame, a Corilis force, `2 m vec(v) xx vec(omega) (t)`
acts which must be balanced by the magnetic force, `e vec(v) xx vec(B) (t)`
Thus, `vec(omega) (t) = (e)/(2m) vec(B) (t)`
(It is assumed that `vec(omega)` is small and varies slowly, so `omega^(2)` and `omega` can be neglected.)