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 uniform magnetic field was switched on, which was perpendicular to the plane of the ring and increased with time according to a certain law: `(dB)/(dt) = k`.
Find the angular velocity `omega` of the ring as a function of `k`.

Explanation

To find the angular velocity \( \omega \) of the non-conducting ring as a function of \( k \), we can follow these steps:

### Step 1: Understand the situation
Initially, the ring is at rest, and a uniform magnetic field \( B \) is switched on, which is perpendicular to the plane of the ring. The magnetic field increases with time at a rate of \( \frac{dB}{dt} = k \).

### Step 2: Determine the induced electric field
According to Faraday's law of electromagnetic induction, the induced electromotive force (emf) \( \mathcal{E} \) in the ring due to the changing magnetic field is given by:
\[
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