A coil and a magnet moves with their constant speeds 10 m/sec and 5 m/sec respectively, towards each other, then induced emf in coil is 12mV. If both are move in same direction , then induced emf in coil

Options

A. 15 mV
B. 4 mV
C. 64 mV
D. zero

Explanation

To solve the problem of induced EMF in a coil when a magnet and the coil are moving towards each other and then in the same direction, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information:**
- The speed of the coil (Vc) = 10 m/s
- The speed of the magnet (Vm) = 5 m/s
- Induced EMF (E1) when they move towards each other = 12 mV

2. **Calculate the Relative Velocity When Moving Towards Each Other:**
- When the coil and magnet move towards each other, the relative velocity (VCM1) is given by:
\[ VCM1 = Vc + Vm = 10 \, \text{m/s} + 5 \, \text{m/s} = 15 \, \text{m/s} \]

3. **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 (VCM2) is given by:
\[ VCM2 = Vc - Vm = 10 \, \text{m/s} - 5 \, \text{m/s} = 5 \, \text{m/s} \]

4. **Use Faraday's Law of Electromagnetic Induction:**
- According to Faraday's law, the induced EMF is directly proportional to the relative velocity:
\[ \frac{E1}{E2} = \frac{VCM1}{VCM2} \]
- Rearranging gives us:
\[ E2 = E1 \times \frac{VCM2}{VCM1} \]

5. **Substituting the Values:**
- Substitute the known values into the equation:
\[ E2 = 12 \, \text{mV} \times \frac{5 \, \text{m/s}}{15 \, \text{m/s}} = 12 \, \text{mV} \times \frac{1}{3} = 4 \, \text{mV} \]

6. **Conclusion:**
- The induced EMF in the coil when both the coil and the magnet are moving in the same direction is **4 mV**.