A coil has an inductance of 0.03H. Calculate the emf induced when current in the coil changes at a rate of 200 A/s.

Explanation

To solve the problem of calculating the induced EMF in a coil with a given inductance when the current changes at a specific rate, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- Inductance (L) = 0.03 H (Henry)
- Rate of change of current (di/dt) = 200 A/s (Amperes per second)

2. **Use the formula for induced EMF:**
The induced EMF (ε) in a coil is given by the formula:
\[ \epsilon = -L \frac{di}{dt} \]
where:
- ε is the induced EMF,
- L is the inductance,
- di/dt is the rate of change of current.

3. **Substitute the known values into the formula:**
\[ \epsilon = -0.03 \, \text{H} \times 200 \, \text{A/s} \]

4. **Calculate the induced EMF:**
\[ \epsilon = -0.03 \times 200 = -6 \, \text{V} \]

5. **Interpret the result:**
The negative sign indicates the direction of the induced EMF according to Lenz's law, which states that the induced EMF will oppose the change in current. However, the magnitude of the induced EMF is:
\[ |\epsilon| = 6 \, \text{V} \]

### Final Answer:
The induced EMF is 6 volts.

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