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Q.

A metallic horizontal ring of mass m and radius r falling under gravity in a region having magnetic field. If z is the vertical direction, the z-component of magnetic field is  B01+az where B0 and a are constants. If R is the resistance of the ring, the terminal velocity of the ring is

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a

mgRπr2aB02

b

mgR2πr2aB0

c

mgRπr2B02

d

2mgRπr2aB02

answer is A.

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Detailed Solution

When the ring fall with terminal velocityRate of the heat produced in the ring = rate of loss of gravitation potential energy of the ring⇒I2R=mgv→(1)Induced Current, I=ER=1Rdϕdt=1Rπr2dBdt⇒I=πr2RB0avFrom equation (1),πr2B0a2v2R2×R=mgv⇒v=mgRπr2B0a2
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