Q 12-06-010NEETJEE MainEAMCET 2006 (Engineering)Medium
A small square loop of wire of side $l$ is placed inside a large square loop of side $L$ ($L \gg l$). If the loops are coplanar and their centres coincide, the mutual inductance of the system is directly proportional to
Answer: (D) $\dfrac{l^2}{L}$
Concept. Current in the large loop gives a centre field $\propto \dfrac{I}{L}$, nearly uniform over the small loop; $M = \dfrac{\phi}{I}$.
Step 1. Field. $B = \dfrac{2\sqrt2\mu_0I}{\pi L} \propto \dfrac{1}{L}$.
Step 2. Flux and $M$. $\phi = Bl^2$, so $M \propto \dfrac{l^2}{L}$.
Answer. $\dfrac{l^2}{L}$ (Option D).
Solution by Sreeraj P, M.Sc Physics