Sol. The changing magnetic field induces an electric field in the ring. Let us imagine the ring divided into small sections each of length Δ s and denote the tangential component of the induced electric field by E t (in the general case E t can vary from point to point). The charge on a small section of the ring is

Δ Q = Q ,

where r is the radius of the ring. The force exerted on it is

Δ F t = Δ Q E t

and the resultant torque is

Δτ = r Δ F t .

The total torque experienced by the ring is thus

τ = = Q E t = .

Identifying the expression Σ E t Δ s as the induced electromotive force along the ring, which is directly proportional to the rate of change in the magnetic flux, we have

= – = – π r 2 .

As a result of the torque, the ring, which has a moment of inertia I = mr 2 , starts to spin with angular acceleration α . During a time interval Δ t its angular velocity changes by

Δω = αΔ t = Δ t = Δ t = – Δ B.