A varying current at the rate of `3A//s` in a coil generates an e.m.f. of `8mV` in a nearby coil. The mutual inductance of the two coils is

Options

A. `2.66xx10^(-3) H`
B. `2.66xx10^(-3)mH`
C. `2.66H`
D. `0.266H`

Explanation

To find the mutual inductance of the two coils, we can use the formula for mutual inductance (M) which relates the induced electromotive force (e.m.f.) in one coil to the rate of change of current in the other coil. The formula is given by:

\[ \text{e.m.f.} = -M \frac{dI}{dt} \]

Where:
- \(\text{e.m.f.}\) is the induced electromotive force in volts (V),
- \(M\) is the mutual inductance in henries (H),
- \(\frac{dI}{dt}\) is the rate of change of current in amperes per second (A/s).

### Step-by-Step Solution:

1. **Identify the given values**:
- The induced e.m.f. (\(\text{e.m.f.}\)) = 8 mV = \(8 \times 10^{-3}\) V
- The rate of change of current (\(\frac{dI}{dt}\)) = 3 A/s

2. **Rearrange the formula to solve for mutual inductance (M)**:
\[ M = -\frac{\text{e.m.f.}}{\frac{dI}{dt}} \]

3. **Substitute the values into the formula**:
\[ M = -\frac{8 \times 10^{-3} \text{ V}}{3 \text{ A/s}} \]

4. **Calculate the mutual inductance**:
\[ M = -\frac{8 \times 10^{-3}}{3} \approx -2.67 \times 10^{-3} \text{ H} \]

5. **Since mutual inductance is a scalar quantity, we can take the absolute value**:
\[ M \approx 2.67 \text{ mH} \]

### Final Answer:
The mutual inductance of the two coils is approximately \(2.67 \text{ mH}\).