Two concentric circular coils with radii 1 cm and 1000 cm, and number… | JEE Main 2023 (6 Apr, Shift 2)

Q46JEE Main 2023 · 6 APR · SHIFT 2Medium

Mutual Inductance

Two concentric circular coils with radii $1\text{ cm}$ and $1000\text{ cm}$ , and number of turns 10 and 200 respectively are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be ___________ $\times 10^{-8}\text{ H}$ . (Take, $\pi^2 = 10$ )

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

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Answer: 4

Field of the big coil at its centre: $B = \frac{\mu_0 N_2 I}{2 r_2}$ ; flux through the small coil: $N_1 B \pi r_1^2$ .
$M = \frac{\mu_0 N_1 N_2 \pi r_1^2}{2 r_2} = \frac{4\pi\times10^{-7}\times 10 \times 200 \times \pi \times 10^{-4}}{2\times 10}$
$M = 4\pi^2 \times 10^{-7} \times 0.01 = 40\times10^{-9} = 4\times10^{-8}\text{ H}$
So the answer is 4.

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