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) $\dfrac{R_2^2}{R_1}$
A current $I$ in the large loop gives a field $B = \dfrac{\mu_0 I}{2R_1}$ at the centre, which is nearly uniform over the small loop.
Flux through the small loop:
$$\phi = \frac{\mu_0 I}{2R_1}\pi R_2^2$$
$$M = \frac{\phi}{I} = \frac{\mu_0\pi R_2^2}{2R_1} \propto \frac{R_2^2}{R_1}$$
Solution by Sreeraj P, M.Sc Physics