The mutual inductance ($M$) between two coils with self-inductances $L_1$ and $L_2$ is related by the formula: $M = k \sqrt{L_1 L_2}$ Where $k$ is the coefficient of coupling, which ranges from 0 to 1.

Condition: The problem states that the effective flux in one coil is completely linked with the other. This implies perfect coupling, so $k = 1$ .

Calculation: $L_1 = 2 \text{ mH}$ $L_2 = 8 \text{ mH}$

• $k = 1$

$M = 1 \times \sqrt{2 \times 8}$ $M = \sqrt{16}$ $M = 4 \text{ mH}$