Q.
Two connectric and coplanar circular coils have radii $a\ and\ b$ as shown in figure. Resistance of the inner coil is R. Current in the other coil is increased from $O\ to\ i,$ then the total charge circulating the inner coil is
A) $\frac{\mu_{0}iab}{2\ R}$
B) $\frac{\mu_{0}i\ a\ \pi b^{2}}{2\ a\ b}$
C) $\frac{\mu_{0}\ ib}{2\ \pi\ R}$
D) $\frac{\mu_{0}\ i\ a^{2}}{2\ Rb}$
Explanation
(d) Initial flux linked with inner coil when $i = 0$ is zero. Final flux linked with inner coil when $i = i\ \ is\ \left( \frac{\mu_{0}i}{2\pi b} \right)\pi\ a^{2}\ $
$\therefore\ \ \ $ Change in flux, $\ d\phi = \ \left( \frac{\mu_{0}i}{2\pi b} \right)\pi\ a^{2}$
As $dq\ \ = \frac{d\phi}{R}\ $
$\therefore\ \ \ $Total charge circulating the inner coil is
= $\left( \frac{\mu_{0}i}{2\ \pi\ b} \right)\frac{\pi a^{2}}{R} = \ \frac{\mu_{0}i\ a^{2}}{2\ R\ b}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.