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Q.

A conducting circular loop is placed in a uniform magnetic field of induction B tesla with its plane normal to the field. Now, radius of the loop starts shrinking at the rate (dr/dt). Then the induced e.m.f at the instant when the radius is r, is

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a

πrBdrdt

b

2πrBdrdt

c

πr2Bdrdt

d

πBr22drdt

answer is B.

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Detailed Solution

If the radius is r at a time t, then the instantaneous magnetic flux ϕ is given byϕ=πr2BNow, induced e.m.f. e is given bye=−dϕdt=−ddtπr2B=−πB2rdrdt=−2πrBdrdt
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A conducting circular loop is placed in a uniform magnetic field of induction B tesla with its plane normal to the field. Now, radius of the loop starts shrinking at the rate (dr/dt). Then the induced e.m.f at the instant when the radius is r, is