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Two coils of self-inductance $L_1$ and $L_2$ are placed close to each other so that the total flux in one coil is completely linked with the other. If $M$ is the mutual inductance between them, then

1. $M=\sqrt{L_1L_2}$
2. $M=\dfrac{L_1L_2}{2}$
3. $M=L_1L_2$
4. $M=\dfrac{L_1+L_2}{2}$

Correct answer: $M=\sqrt{L_1L_2}$

Solution

When all the flux produced by one coil links the other, the coupling coefficient is unity. The mutual inductance is then $M=\sqrt{L_1L_2}$. This is the standard maximum possible mutual inductance for two coils.

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