Q. Two conducting circular loops of radii $R_{1}\ and\ R_{2}$ are placed in the same plane with their centres coinciding. If $R_{1} > R_{2},$ the mutual inductance M between them will be directly proportional to
A) $\frac{R_{1}}{R_{2}}$
B) $\frac{R_{2}}{R_{1}}$
C) $\frac{R_{1}^{2}}{R_{2}}$
D) $\frac{R_{2}^{2}}{R_{1}}$
Explanation
(d) Magnetic field at the centre of primary coil $B = \mu_{0}i_{1}/2R_{1}$. Considering it to be uniform, magnetic flux passing through secondary coil is
$\phi = BA = \frac{\mu_{0}i_{1}}{2R_{1}}\left( \pi R_{2}^{2} \right)$
Now, $M = \frac{\phi_{2}}{i_{1}} = \frac{\mu_{0}\pi R_{2}^{2}}{2R_{1}}$
$\therefore\ \ M \propto \frac{R_{2}^{2}}{R_{1}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.