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Electromagnetic Induction
Mutual Inductance
2 questions, each with its answer.
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Two conducting circular loops of radii $R_1$ and $R_2$ are placed in the same plane with their centres coinciding. If $R_1\gg R_2$, the mutual inductance $M$ between them will be directly proportional to:Field at the centre due to the large loop: $B_1 = \frac{\mu_0 I_1}{2R_1}$ (nearly uniform over the small loop since $R_1 \gg R_2$) $M = \frac{\phi_{12}}{I_1} = \frac{B_1A_2}{I_1} = \frac{\mu_0}{2R_1}\pi R_2^2$ $M \propto \frac{R_2^2}{R_1}$
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Two coils of self inductances 2 mH and 8 mH are placed so close together that the effective flux in one coil is completely linked with the other. The mutual inductance between these coils is :Mutual inductance of two coils: $M = K\sqrt{L_1 L_2}$, where $K$ is the coefficient of coupling.
The flux of one coil is completely linked with the other, so the coupling is perfect: $K = 1$.
Here $L_1 = 2$ mH and $L_2 = 8$ mH.
$M = \sqrt{2 \times 8} = \sqrt{16}$
$M = 4$ mH
That is every question in Mutual Inductance.
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