A certain elastic conducting material is stretched into a circular loop. It is placed with its plane perpendicular to a uniform magnetic field $B = 0.8 T$ . When released the radius of the loop starts shrinking at a constant rate of 2 cms^-1.The induced emf in the loop at an instant when the radius of the loop is 10 cm will be ____________ mV.

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Detailed Solution

$\begin{array}{l} ε_{in} = B \frac{dA}{dt} \\ = B \frac{d}{dt} ({πr}^{2}) \\ = B \times 2 πr \frac{dr}{dt} \\ = 0.8 \times 2 \times π \times 0.1 \times 0.02 \\ = 0.010 V \\ = 10 mV \end{array}$

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