Two coils of self inductance 100 mH and 400 mH are placed very closed to each other. Find maximum mutual inductance between the two when 4 A current passes through them.

Options

A. `200 mH`
B. `300 mH`
C. `100sqrt2 mH`
D. None of these

Explanation

To solve the problem of finding the maximum mutual inductance between two coils with given self-inductances, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Self-inductance of the first coil, \( L_1 = 100 \, \text{mH} = 100 \times 10^{-3} \, \text{H} \)
- Self-inductance of the second coil, \( L_2 = 400 \, \text{mH} = 400 \times 10^{-3} \, \text{H} \)

2. **Understand the Formula for Maximum Mutual Inductance:**
- The formula for maximum mutual inductance \( M \) between two coils is given by:
\[ M_{\text{max}} = \sqrt{L_1 \times L_2} \]

3. **Substitute the Values into the Formula:**
- Substitute \( L_1 \) and \( L_2 \) into the formula:
\[ M_{\text{max}} = \sqrt{(100 \times 10^{-3}) \times (400 \times 10^{-3})} \]

4. **Calculate the Product:**
- First, calculate the product:
\[ 100 \times 400 = 40000 \]
- Then, include the powers of ten:
\[ 40000 \times 10^{-6} = 40 \times 10^{-3} = 0.04 \]

5. **Take the Square Root:**
- Now, take the square root:
\[ M_{\text{max}} = \sqrt{0.04} = 0.2 \, \text{H} = 200 \, \text{mH} \]

6. **Final Answer:**
- Therefore, the maximum mutual inductance \( M_{\text{max}} \) between the two coils is:
\[ \boxed{200 \, \text{mH}} \]