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MHT CET 2026 (15 Apr, Shift 2) · Mutual Inductance

Mutual Inductance question from MHT CET 2026 (15 Apr, Shift 2)

Q14MHT CET 2026 · 15 APR · SHIFT 2Easy

Mutual Inductance

Two concentric circular coils having radii $r_1$ and $r_2$ ( $r_2 \ll r_1$ ) are placed co-axially with centres coinciding. The mutual inductance of the arrangement is (Both coils have single turn, $\mu_0$ = permeability of free space)

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Answer: (d)

Field of outer coil at centre: $B = \dfrac{\mu_0 I}{2r_1}$ , uniform over inner coil since $r_2 \ll r_1$
Flux through inner coil: $\Phi = \dfrac{\mu_0 I}{2r_1}\pi r_2^2$
$M = \dfrac{\Phi}{I} = \dfrac{\mu_0 r_2^2\pi}{2r_1}$
So the answer is (d) $\dfrac{\mu_0 r_2^2\pi}{2r_1}$ .

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