Find the mutual inductance in the arrangement, when a small circular… | JEE Main 2023 (29 Jan, Shift 1)

Q45JEE Main 2023 · 29 JAN · SHIFT 1Medium

Mutual Inductance

Find the mutual inductance in the arrangement, when a small circular loop of wire of radius ' $R$ ' is placed inside a large square loop of wire of side $L \ (L \gg R)$ . The loops are coplanar and their centres coincide:

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Answer: (c)

Field at the centre of the square loop: $B = 4 \times \frac{\mu_0 I}{4\pi (L/2)} \times 2\sin 45^\circ = \frac{2\sqrt{2}\,\mu_0 I}{\pi L}$
Flux through the small circle ( $R \ll L$ ): $\phi = B \pi R^2 = \frac{2\sqrt{2}\,\mu_0 I R^2}{L}$
$M = \phi / I = \frac{2\sqrt{2}\,\mu_0 R^2}{L}$
So the answer is (c).

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