A magnetic field in a certain region is given by $B = B_0 cm (\omega t) \hat {k}$ and a coil of radius "a" with resistance R is placed in the x - y plane with its centre at the origin in the magnetic field, as shown in the fig. Find the magnitude and th direction of the current at (a, 0, 0) at $t = \frac {\pi}{2\omega} \; and \; t = \frac {3 \pi}{2 \omega}$

Question

(a) at t = $\frac {\pi}{2\omega}, I = \frac {B \pi a^2 \omega}{R}\; along \; \hat{i}$ at t = $\frac {\pi}{\omega}, I = 0$ at t = $\frac {3 \pi}{\omega}. I = \frac {B \pi a^2 \omega}{R}\; along \; \hat {-i}$
(b) at t = $\frac {\pi}{2\omega}, I = \frac {B \pi a^2 \omega}{R}\; along \; \hat{j}$ at t = $\frac {\pi}{\omega}, I = 0$ at t = $\frac {3 \pi}{\omega}. I = \frac {B \pi a^2 \omega}{R}\; along \; \hat {-j}$
(c) at t = $\frac {\pi}{2\omega}, I = \frac {B \pi a^2 \omega}{R}\; along \; \hat{-i}$ at t = $\frac {\pi}{\omega}, I = 0$ at t = $\frac {3 \pi}{\omega}. I = \frac {B \pi a^2 \omega}{R}\; along \; \hat {i}$
(d) at t = $\frac {\pi}{2\pi}, I = \frac {B \pi a^2 \omega}{R}\; along \; \hat{-j}$ at t = $\frac {\pi}{\omega}, I = 0$ at t = $\frac {3 \pi}{\omega}. I = \frac {B \pi a^2 \omega}{R}\; along \; \hat {j}$