A small square loop of wire of side l is placed inside a large square… | JEE Main 2024 (31 Jan, Shift 1)

Q35JEE Main 2024 · 31 JAN · SHIFT 1Medium

Mutual Inductance

A small square loop of wire of side $l$ is placed inside a large square loop of wire of side $L \left(L = l^2\right)$ . The loops are coplanar and their centers coincide. The value of the mutual inductance of the system is $\sqrt{x} \times 10^{-7}\text{ H}$ , where $x =$ _________.

Numerical answer type. Work it out, then open the answer.

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Answer: 128

For a small square inside a large square (centres coinciding): $M = \frac{2\sqrt{2}\,\mu_0 l^2}{\pi L}$
With $L = l^2$ : $M = \frac{2\sqrt{2}\,\mu_0}{\pi} = \frac{2\sqrt{2}\times 4\pi\times10^{-7}}{\pi} = 8\sqrt{2}\times10^{-7}\text{ H}$
$8\sqrt{2} = \sqrt{128}$ , so $M = \sqrt{128}\times10^{-7}\text{ H}$
So $x = 128$ .

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