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

Answer

To solve the problem, we will use the concept of mutual inductance and the relationship between magnetic flux, mutual inductance, and change in current.

### Step-by-Step Solution:

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

2. **Use the Formula for Change in Flux:**
The relationship between the change in magnetic flux (\( \Delta \Phi \)), mutual inductance (\( M \)), and change in current (\( \Delta I \)) is given by:
\[ \Delta \Phi = M \Delta I \]

3. **Rearrange the Formula to Find \( \Delta I \):**
To find the change in current (\( \Delta I \)), we can rearrange the formula:
\[ \Delta I = \frac{\Delta \Phi}{M} \]

4. **Substitute the Known Values:**
Now, substitute the values we have into the equation:
\[ \Delta I = \frac{4 \, \text{Wb}}{2 \, \text{H}} = 2 \, \text{A} \]

5. **Conclusion:**
The change in current in coil B is \( \Delta I = 2 \, \text{A} \).

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

---