An emf of 96 mV is induced in the windings of a coil when a current in a nearby coil is increasing at the rate of 1.20 A/s. What is the mutual inductance of the two coil?

Answer

To find the mutual inductance (M) of the two coils, we can use the formula that relates the induced electromotive force (emf) in one coil to the rate of change of current in the nearby coil. The relationship is given by:

\[ e = -M \frac{di}{dt} \]

Where:
- \( e \) is the induced emf (in volts),
- \( M \) is the mutual inductance (in henries),
- \( \frac{di}{dt} \) is the rate of change of current (in amperes per second).

### Step-by-Step Solution:

1. **Identify the given values:**
- Induced emf, \( e = 96 \, \text{mV} = 96 \times 10^{-3} \, \text{V} \)
- Rate of change of current, \( \frac{di}{dt} = 1.20 \, \text{A/s} \)

2. **Rearrange the formula to solve for mutual inductance (M):**
\[ M = -\frac{e}{\frac{di}{dt}} \]
Since we are interested in the magnitude, we can ignore the negative sign.

3. **Substitute the known values into the equation:**
\[ M = \frac{96 \times 10^{-3}}{1.20} \]

4. **Calculate the mutual inductance:**
\[ M = \frac{96 \times 10^{-3}}{1.20} = 80 \times 10^{-3} \, \text{H} \]
\[ M = 80 \, \text{mH} \]

### Final Answer:
The mutual inductance of the two coils is \( M = 80 \, \text{mH} \).

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