2021 Electromagnetic InductionMutual Inductance Medium Question 1 of 2 in Mutual Inductance

Two conducting circular loops of radii $R_1$ and $R_2$ are placed in the same plane with their centres coinciding. If $R_1\gg R_2$, the mutual inductance $M$ between them will be directly proportional to:

A $\frac{R_2}{R_1}$
B $\frac{R_1^2}{R_2}$
C $\frac{R_2^2}{R_1}$
D $\frac{R_1}{R_2}$

The answer is C.

Solution

Field at the centre due to the large loop: $B_1 = \frac{\mu_0 I_1}{2R_1}$ (nearly uniform over the small loop since $R_1 \gg R_2$) $M = \frac{\phi_{12}}{I_1} = \frac{B_1A_2}{I_1} = \frac{\mu_0}{2R_1}\pi R_2^2$ $M \propto \frac{R_2^2}{R_1}$

Concept mutual inductance of coplanar loops

Mutual Inductance in past papers

2 questions from this chapter have appeared across 2 exam years.