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A conducting loop of radius R is present in a uniform magnetic field B perpendicular to the plane of ring. If radius R varies as a function of time t as $R = R_{0} + t^{2}$ . The emf induced in the loop is

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2 π Bt (R_{0} + t^{2}) clock wise

4 π {Bt}^{2} (t^{2} + R_{0}) anti clock wise

4 π Bt (t^{2} + R_{0}) clock wise

4 π Bt (t^{2} + R_{0}) anti clock wise

answer is C.

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Detailed Solution

R = R_{0} + t^{2}

$e = \frac{d ϕ}{dt} = \frac{d}{dt} (BA) = B \frac{d}{dt} (π R^{2})$

$= π B \frac{d}{dt} {(R_{0} + t^{2})}^{2} = π B 2 (R_{0} + t^{2}) 2 t$

$= 4 π Bt (R_{0} + t^{2})$

Anticlock wise direction according to Lenz’s law

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