Two coils of self-inductance `2mH` 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 coil is

Options

A. 16 mH
B. 10 mH
C. 6 mH
D. 4 mH

Explanation

To find the mutual inductance between the two coils, we can use the formula for mutual inductance when one coil is completely linked with another. The formula is given by:

\[ M = \sqrt{L_1 \cdot L_2} \]

where:
- \( M \) is the mutual inductance,
- \( L_1 \) is the self-inductance of the first coil,
- \( L_2 \) is the self-inductance of the second coil.

### Step 1: Identify the self-inductances
We are given:
- \( L_1 = 2 \, \text{mH} = 2 \times 10^{-3} \, \text{H} \)
- \( L_2 = 8 \, \text{mH} = 8 \times 10^{-3} \, \text{H} \)

### Step 2: Substitute the values into the formula
Now we substitute the values of \( L_1 \) and \( L_2 \) into the mutual inductance formula:

\[ M = \sqrt{(2 \times 10^{-3}) \cdot (8 \times 10^{-3})} \]

### Step 3: Calculate the product
Calculating the product inside the square root:

\[ M = \sqrt{(2 \cdot 8) \times (10^{-3} \cdot 10^{-3})} = \sqrt{16 \times 10^{-6}} \]

### Step 4: Calculate the square root
Now, we take the square root:

\[ M = \sqrt{16} \cdot \sqrt{10^{-6}} = 4 \cdot 10^{-3} = 4 \, \text{mH} \]

### Final Answer
Thus, the mutual inductance \( M \) between the two coils is:

\[ M = 4 \, \text{mH} \]

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