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A thin conducting wire is bent into a circular loop of radius r and placed in a time dependent magnetic field of magnetic induction.
$$\overrightarrow {\bf{B}} \left( t \right) = {B_0}{e^{ - \alpha t}}{{\bf{\hat e}}_z},\,\,\left( {{B_0} > 0{\text{ and }}\alpha > 0} \right)$$
such that, the plane of the loop is perpendicular to $$\overrightarrow {\bf{B}} \left( t \right).$$ Then the induced emf in the loop is

A thin conducting wire is bent into a circular loop of radius r and placed in a time dependent magnetic field of magnetic induction.
$$\overrightarrow {\bf{B}} \left( t \right) = {B_0}{e^{ - \alpha t}}{{\bf{\hat e}}_z},\,\,\left( {{B_0} > 0{\text{ and }}\alpha > 0} \right)$$
such that, the plane of the loop is perpendicular to $$\overrightarrow {\bf{B}} \left( t \right).$$ Then the induced emf in the loop is Correct Answer πr<sup>2</sup> αB<sub>0</sub> e<sup>-αt</sup>

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