Electromagnetic Induction #2

Curved surface of a very long hollow cylinder of radius $R$ (much smaller than its length) is uniformly charged with surface charge density $\sigma$ . At the centre of this cylinder, a small insulating ring of radius $r$ ,mass $m$ and charge $q$ is coaxially placed.

The arrangement is in a gravity free space. If the cylinder is given an angular velocity $\omega_{0}$ about its axis, how much maximum angular velocity will the ring acquire and in which direction relative to angular velocity of the cylinder?

Answer comes in the form of $\omega_{max}=\frac{\alpha \mu_{0} \sigma Rq \omega_{0}}{m}$

Type your answer as $\alpha=?$

The problem is taken from my Physics Book.