A coil of radius ' r ' is placed on another coil (whose radius is R and current flowing through it is changing) so that their centres coincide (R r). If both the coils are coplanar then the mutual inductance between them is ( μ₀ = permeability of free space) (a) (μ₀ π R²)/(2 r) (b) (μ₀ π r²)/(2 R) (c) (μ₀ π r²)/(R) (d) μ₀ π R²

Answer: (b). Field of big coil at centre: B = (μ₀ I)/(2R), uniform over the small coil ( R r) Flux through small coil: Φ = (μ₀ I)/(2R)π r² M = Φ/I = (μ₀π r²)/(2R) So the answer is (b) (μ₀π r²)/(2R).

A coil of radius ' r ' is placed on another coil (whose radius is R… | MHT CET 2023 (11 May, Shift 1)

Q39MHT CET 2023 · 11 MAY · SHIFT 1Easy

Mutual Inductance

A coil of radius ' $r$ ' is placed on another coil (whose radius is $R$ and current flowing through it is changing) so that their centres coincide $(R \gg r)$ . If both the coils are coplanar then the mutual inductance between them is ( $\mu_0 =$ permeability of free space)

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Answer: (b)

Field of big coil at centre: $B = \dfrac{\mu_0 I}{2R}$ , uniform over the small coil ( $R \gg r$ )
Flux through small coil: $\Phi = \dfrac{\mu_0 I}{2R}\pi r^2$
$M = \dfrac{\Phi}{I} = \dfrac{\mu_0\pi r^2}{2R}$
So the answer is (b) $\dfrac{\mu_0\pi r^2}{2R}$ .

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Mutual Inductance question from MHT CET 2023 (11 May, Shift 1)

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