Two coil A and B have coefficient of mutual inductance M=2H. The magnetic flux passing through coil A charges by 4 Weber in 10 seconds due to the change in current in B. Then

Options

A. change in current in `B` in this time interval is `0.5 A`
B. change in current in `B` in this time interval is `2 A`
C. change in current in `B` in this time interval is `8 A`
D. a change in current of `1A` in coil `A` will produce a change in flux passing through by `4` Weber.

Explanation

To solve the problem, we need to find the change in current in coil B, given the change in magnetic flux through coil A and the mutual inductance between the two coils.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Coefficient of mutual inductance, \( M = 2 \, \text{H} \)
- Change in magnetic flux through coil A, \( \Delta \Phi = 4 \, \text{Wb} \)
- Time interval, \( t = 10 \, \text{s} \)

2. **Use the Formula for Mutual Inductance:**
The relationship between the change in magnetic flux and the change in current in coil B is given by the formula:
\[ \Delta \Phi = M \cdot \Delta I_B \]
where \( \Delta I_B \) is the change in current in coil B.

3. **Rearrange the Formula to Find \( \Delta I_B \):**
We can rearrange the formula to solve for \( \Delta I_B \):
\[ \Delta I_B = \frac{\Delta \Phi}{M} \]

4. **Substitute the Known Values:**
Substitute the values of \( \Delta \Phi \) and \( M \) into the equation:
\[ \Delta I_B = \frac{4 \, \text{Wb}}{2 \, \text{H}} = 2 \, \text{A} \]

5. **Conclusion:**
The change in current in coil B over the time interval of 10 seconds is:
\[ \Delta I_B = 2 \, \text{A} \]

### Final Answer:
The change in current in coil B is \( 2 \, \text{A} \).

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