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JEE Main 2021 (31 Aug, Shift 1) · Mutual Inductance

Mutual Inductance question from JEE Main 2021 (31 Aug, Shift 1)

Q52JEE Main 2021 · 31 AUG · SHIFT 1Medium

Mutual Inductance

A small square loop of side 'a' and one turn is placed inside a larger square loop of side b and one turn (b >> a). The two loops are coplanar with their centres coinciding. If a current I is passed in the square loop of side 'b', then the coefficient of mutual inductance between the two loops is:

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Answer: (a)

Field at the centre of the big square of side $b$ : $B = \frac{2\sqrt{2}\,\mu_0 I}{\pi b}$
Flux through the small square: $\phi = B a^2 = \frac{2\sqrt{2}\,\mu_0 I a^2}{\pi b}$
$M = \frac{2\sqrt{2}\,\mu_0 a^2}{\pi b} = \frac{\mu_0}{4\pi}\cdot 8\sqrt{2}\,\frac{a^2}{b}$
So the answer is (a).

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