Two coils of self-inductance $2 ext{ mH}$ and $8 ext{ mH}$ are placed so close together that the effective

Question

Two coils of self-inductance $2 	ext{ mH}$ and $8 	ext{ mH}$ 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:

Accepted Answer

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:**
*   $L_1 = 2 	ext{ mH}$
*   $L_2 = 8 	ext{ mH}$
*   $k = 1$

$$ M = 1 	imes \sqrt{2 	imes 8} $$
$$ M = \sqrt{16} $$
$$ M = 4 	ext{ mH} $$

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