A magnetic field B is confined to a region ra and points out of the paper (the z-axis), r=0 being the centre of the circular region. Charged ring (charge=Q) of radius b, b>a and mass m lies in the x-y plane with its centre at the origin. The ring is free to rotate and is at rest. The magnetic field is brought to zero in time t. Find the angular velocity ω of the ring after field vanishes.

Hint: The change in magnetic flux results in the rotation of the ring.
Since the magnetic field is brought to zero in time t, the magnetic flux linked with the ring also reduces from maximum to zero. This, in turn, induces an emf in-ring by the phenomenon of EMI. The induced emf causes the electric field E generation around the ring.
Step 1: Theinucedemf=electricfield(E)×(2πb)(BecauseV=E×d)...(i)
ByFaraday'slawofEMI;
Theinducedemf=rateofchangeofmagneticflux
=rateofchangeofmagneticfield×area
=Bπa2t...(ii)
FromEqs.(i)and(ii),wehave;
2πbE=emf=Bπa2t
Step 2: Since,thechargedringexperiencedanelectricforce=QE
Thisforcetriestorotatethecoil,andthetorqueisgivenby;
Torque=b×Force
=QEb=QBπa22πbtb
=QBa22t
Step 3:IfListhechangeinangularmomentum.
L=Torque×t=QBa22
Since,initialangularmomentum=0
Now,since,Torque×t=Changeinangularmomentum
Finalangularmomentum=mb2ω=QBa22
ω=QBa22mb2
Onrearrangingtheterms,wehavetherequiredexpressionofangularspeed.