Q. O is the centre of two coplanar concentric circular conductors, A and B, of radii r and R respectively as shown in the figure. Here, r <<< R. the mutual inductance of the system of the conductors can be given by
A) $\frac{\mu_{0}\pi r^{2}}{2R}$
B) $\frac{\mu_{0}\pi R^{2}}{2r}$
C) $\frac{\pi R^{2}}{\mu_{0}r}$
D) $\frac{\mu_{0}\pi r}{2R}$
Explanation
(a) Mutual inductance for two concentric coplanar circular coils,
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ M = \frac{\pi\mu N_{1}N_{2}r^{2}}{2R}$
Here, $\ \ \ \ \ \ \ \ N_{1} = N_{2} = 1$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ M = \frac{\pi\mu_{0}r^{2}}{2R}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.