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. 200mH
B. 300mH
C. `100sqrt(2)mH`
D. none of these

Explanation

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

### Step 1: Identify the Self-Inductances
We are given the self-inductances of the two coils:
- \( L_1 = 100 \, \text{mH} = 100 \times 10^{-3} \, \text{H} \)
- \( L_2 = 400 \, \text{mH} = 400 \times 10^{-3} \, \text{H} \)

### Step 2: Use the Formula for Maximum Mutual Inductance
The maximum mutual inductance \( M \) between two coils can be calculated using the formula:
\[ M = \sqrt{L_1 \cdot L_2} \]

### Step 3: Substitute the Values into the Formula
Now, we substitute the values of \( L_1 \) and \( L_2 \) into the formula:
\[ M = \sqrt{100 \times 10^{-3} \cdot 400 \times 10^{-3}} \]

### Step 4: Calculate the Product
Calculating the product inside the square root:
\[ 100 \times 400 = 40000 \]
Thus,
\[ M = \sqrt{40000 \times 10^{-6}} = \sqrt{0.04} = 0.2 \, \text{H} \]

### Step 5: Convert to Millihenry
Since we need the answer in millihenries, we convert:
\[ 0.2 \, \text{H} = 200 \, \text{mH} \]

### Conclusion
The maximum mutual inductance between the two coils is:
\[ M = 200 \, \text{mH} \]

### Final Answer
Thus, the correct option is **200 mH**.

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