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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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$4 π B t (R_{0} + t^{2})$ Clockwise

$2 π B t (R_{0} + t^{2})$ Clockwise

$4 π B t (R_{0} + t^{2})$ Anticlockwise

$2 π B t (R_{0} + t^{2})$ anticlockwise

answer is C.

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Detailed Solution

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

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

$e = πB 2 (R_{0} + t^{2}) 2 t$

as downward flux is increasing the induced current will produce magnetic field upward so current will be anticlockwise.

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