Two inductor coils of self inductance, $L_1$ and $L_2$, having same length and same area of cross-section are placed so close that effective flux in one coil is completely linked with the other. The mutual inductance between them, is equal to

$\sqrt{L_1 L_2}$

The correct answer is Option (4) → $\sqrt{L_1 L_2}$

Given:

Two coils with self-inductances $L_1$ and $L_2$, same length and area, placed so that all flux of one links the other completely.

Mutual inductance: $M = k \sqrt{L_1 L_2}$, where $k$ = coefficient of coupling

For complete coupling, $k = 1$

∴ $M = \sqrt{L_1 L_2}$

∴ Mutual inductance between the coils = $M = \sqrt{L_1 L_2}$