Q 12-06-009NEETNEET 2021Top questionMedium
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 :
Answer: (A) $\dfrac{R_2^2}{R_1}$
Concept. Pass current through the large loop; its centre field is nearly uniform over the small loop, and $M = \dfrac{\phi}{I}$.
Step 1. Field at the centre. $B = \dfrac{\mu_0I}{2R_1}$.
Step 2. Flux through the small loop. $\phi = \dfrac{\mu_0I}{2R_1}\pi R_2^2$.
Step 3. Mutual inductance.
$$M = \frac{\mu_0\pi R_2^2}{2R_1} \propto \frac{R_2^2}{R_1}$$
Answer. $\dfrac{R_2^2}{R_1}$ (Option A).
Solution by Sreeraj P, M.Sc Physics