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) $\dfrac{l^2}{L}$
A current $I$ in the large loop gives a field at its centre $B = \dfrac{2\sqrt{2}\mu_0 I}{\pi L} \propto \dfrac{1}{L}$, nearly uniform over the small loop.
Flux through the small loop: $\phi = Bl^2 \propto \dfrac{l^2}{L}I$, so $M = \dfrac{\phi}{I} \propto \dfrac{l^2}{L}$.
Solution by Sreeraj P, M.Sc Physics