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  4. A magnetic field B is confined to a region r le a and points out of the paper (the z-axis), r = 0 being the centre of the circular region. A 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 Δ The angular velocity ω t of the ring after the field vanishes, is

Q. A magnetic field is confined to a region and points out of the paper (the -axis), being the centre of the circular region. A charged ring (charge = ) of radius and mass lies in the 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 The angular velocity of the ring after the field vanishes, is

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Solution:

Let is the electric field generated around the charged ring of radius , then


or
Torque acting on the ring

[Using (i)]
If is change in angular momentum of the charged ring, then



As initial angular momentum,

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