Q: An electron is moving in a circular orbit of radius R with an angular acceleration  α. At the center of the orbit is kept a conducting loop of radius r , (r < < R). The e.m.f induced in the smaller loop due to the motion of the electron is

(A) zero, since charge on electron in constant

(B) $\displaystyle \frac{\mu_0 e r^2}{4 R} \alpha $

(C) $\displaystyle \frac{\mu_0 e r^2}{4 \pi R} \alpha $

(D) none of these

Solution : $\displaystyle \phi = \frac{\mu_0 i}{2R} (\pi r^2) $

$\displaystyle \phi = \frac{\mu_0 e r^2}{4 R} \alpha t $

$\displaystyle e = \frac{d \phi}{dt} = \frac{\mu_0 e r^2}{4 R} \alpha $