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(B) The moving electron constitutes a current $i = \frac{e}{T} = \frac{e \omega}{2\pi}$.The magnetic field at the center of the orbit due to this curr

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$\frac{\mu_0 e r^2}{4R} \alpha$

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(B) The moving electron constitutes a current $i = \frac{e}{T} = \frac{e \omega}{2\pi}$.The magnetic field at the center of the orbit due to this current is $B = \frac{\mu_0 i}{2R} = \frac{\mu_0 e \omega}{4\pi R}$.The magnetic flux $\phi$ linked with the smaller loop of radius $r$ is $\phi = B \cdot A = \left( \frac{\mu_0 e \omega}{4\pi R} \right) (\pi r^2) = \frac{\mu_0 e r^2 \omega}{4R}$.The induced $e.m.f.$ is given by Faraday's law: $\varepsilon = -\frac{d\phi}{dt} = -\frac{\mu_0 e r^2}{4R} \frac{d\omega}{dt}$.Since the angular acceleration is $\alpha = \frac{d\omega}{dt}$,the magnitude of the induced $e.m.f.$ is $\varepsilon = \frac{\mu_0 e r^2 \alpha}{4R}$.

An electron is moving in a circular orbit of radius $R$ with an angular acceleration $\alpha$. At the centre of the orbit is kept a conducting loop of radius $r$ $(r \ll R)$. The $e.m.f.$ induced in the smaller loop due to the motion of the electron is

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