An elliptical loop having resistance $$R$$, of semi major axis $$a$$, and semi minor axis $$b$$ is placed in a magnetic field as shown in the figure. If the loop is rotated about the $$x$$-axis with angular frequency $$\omega$$, the average power loss in the loop due to Joule heating is:

A

$$\frac{\pi^2 a^2 b^2 B^2 \omega^2}{2R}$$

B

zero

C

$$\frac{\pi bB\omega}{R}$$

D

$$\frac{\pi^2 a^2 b^2 B^2 \omega^2}{R}$$