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A thin non-conducting ring of mass `m` carrying a charge `q` can freely rotate about its axis. At `t = 0`, the ring was at rest and no magnetic field was present. Then suddenly a magnetic field `B` was set perpendicular to the plane. Find the angular velocity acquired by the ring.

Text Solution

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Due to the sudden chrage in flux, an electirc field is set up and the ring experiences an impulsive torque and suddenly acquires an angular velocity.
`E = (r )/(2)(dB)/(dt)`

Force experiences by an element of ring `dF = dqE`
Torque experiences by this element of ring `dtau = dFr = dq Er`
Total torque experienced by ring: `tau = qEr`
angular impulse experienced
`L = int tau dt = (qr^(2))/(2) int(dB)/(dt)dt = (qr^(2))/(2)B`
`L = Iomega` `rarr` `mr^(2)omega = (qr^(2))/(2)B` `rarr` `omega = (qB)/(2m)`
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