A small square loop of wire of side l is placed inside a large square… | JEE Main 2022 (25 Jul, Shift 1)

Q48JEE Main 2022 · 25 JUL · SHIFT 1Medium

Mutual Inductance

A small square loop of wire of side $l$ is placed inside a large square loop of wire $L (L \gg l)$ . Both loops are coplanar and their centres coincide at point $O$ as shown in figure. The mutual inductance of the system is:

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Answer: (c)

Field at the centre of the big square: $B = \frac{2\sqrt{2}\,\mu_0 I}{\pi L}$ (four sides, each $\frac{\mu_0 I}{4\pi (L/2)} \cdot 2\sin 45^\circ$ ).
Since $l \ll L$ , flux through the small square: $\phi = B l^2 = \frac{2\sqrt{2}\,\mu_0 I l^2}{\pi L}$
$M = \phi / I = \frac{2\sqrt{2}\,\mu_0 l^2}{\pi L}$
So the answer is (c).

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Mutual Inductance question from JEE Main 2022 (25 Jul, Shift 1)

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