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

Explanation

To find the mutual inductance between two coils with given self-inductances, we can use the formula:

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

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-by-Step Solution:

1. **Identify the Self-Inductances**:
- Given:
- \( L_1 = 2 \, \text{mH} = 2 \times 10^{-3} \, \text{H} \)
- \( L_2 = 8 \, \text{mH} = 8 \times 10^{-3} \, \text{H} \)

2. **Substitute the Values into the Formula**:
- Using the formula for mutual inductance:
\[ M = \sqrt{L_1 \cdot L_2} = \sqrt{(2 \times 10^{-3}) \cdot (8 \times 10^{-3})} \]

3. **Calculate the Product**:
- First, calculate the product of \( L_1 \) and \( L_2 \):
\[ L_1 \cdot L_2 = 2 \times 10^{-3} \cdot 8 \times 10^{-3} = 16 \times 10^{-6} \, \text{H}^2 \]

4. **Take the Square Root**:
- Now, take the square root of the product:
\[ M = \sqrt{16 \times 10^{-6}} = 4 \times 10^{-3} \, \text{H} = 4 \, \text{mH} \]

5. **Final Answer**:
- The mutual inductance \( M \) between the two coils is:
\[ M = 4 \, \text{mH} \]