A coil and a magnet moves with their constant speeds 6 m/sec and 2 m/sec respectively, towards each other, then induced emf in coil is 18 mV. If both are move in same direction , then induced emf in coil

Options

A. 5 mV
B. 7 mV
C. 3 mV
D. 9 mV

Explanation

To solve the problem, we need to analyze the situation using the principles of electromagnetic induction, particularly focusing on the concept of relative velocity between the coil and the magnet.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Speed of the coil (V_coil) = 6 m/s
- Speed of the magnet (V_magnet) = 2 m/s
- Induced EMF when moving towards each other (E) = 18 mV

2. **Calculate the Relative Velocity When Moving Towards Each Other:**
- When the coil and magnet move towards each other, their relative velocity (V_rel) is the sum of their speeds:
\[ V_{rel} = V_{coil} + V_{magnet} = 6 \, \text{m/s} + 2 \, \text{m/s} = 8 \, \text{m/s} \]

3. **Understanding the Induced EMF:**
- According to Faraday's law of electromagnetic induction, the induced EMF (E) is directly proportional to the relative velocity:
\[ E \propto V_{rel} \]

4. **Calculate the Relative Velocity When Moving in the Same Direction:**
- When both the coil and the magnet move in the same direction, the relative velocity is the difference of their speeds:
\[ V_{rel}' = V_{coil} - V_{magnet} = 6 \, \text{m/s} - 2 \, \text{m/s} = 4 \, \text{m/s} \]

5. **Set Up the Proportionality for Induced EMF:**
- Let E' be the induced EMF when both are moving in the same direction. Using the proportionality:
\[ \frac{E'}{E} = \frac{V_{rel}'}{V_{rel}} \]
- Substitute the known values:
\[ \frac{E'}{18 \, \text{mV}} = \frac{4 \, \text{m/s}}{8 \, \text{m/s}} \]

6. **Solve for E':**
- Cross-multiply to find E':
\[ E' = 18 \, \text{mV} \times \frac{4}{8} = 18 \, \text{mV} \times \frac{1}{2} = 9 \, \text{mV} \]

7. **Conclusion:**
- The induced EMF in the coil when both the coil and the magnet are moving in the same direction is **9 mV**.