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MHT CET 2023 (10 May, Shift 2) · Mutual Inductance

Mutual Inductance question from MHT CET 2023 (10 May, Shift 2)

Q40MHT CET 2023 · 10 MAY · 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 induction of the arrangement is (Both coils have single turn, $\mu_0 =$ permeability of free space)

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Answer: (a)

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: $\Phi = \dfrac{\mu_0 I}{2r_1}\pi r_2^2$
$M = \dfrac{\Phi}{I} = \dfrac{\mu_0\pi r_2^2}{2r_1}$
So the answer is (a) $\dfrac{\mu_0\pi r_2^2}{2r_1}$ .

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