A coil and a magnet moves with their constant speeds `5m//sec` and `3m//sec`. Respectively , towards each other, then induced emf in coil is 16 m V . If both are moves in same direction , then induced emf in coil :-

Options

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

Answer

To solve the problem step by step, we need to understand the relationship between induced EMF and the relative speeds of the coil and the magnet.

### Step 1: Identify the given data
- Speed of the coil (v1) = 5 m/s
- Speed of the magnet (v2) = 3 m/s
- Induced EMF when moving towards each other (E) = 16 mV

### Step 2: Calculate the relative speed when moving towards each other
When the coil and the magnet are moving towards each other, the relative speed (Vr) is the sum of their speeds:
\[ Vr = v1 + v2 = 5 \, \text{m/s} + 3 \, \text{m/s} = 8 \, \text{m/s} \]

### Step 3: Calculate the relative speed when moving in the same direction
When both the coil and the magnet are moving in the same direction, the relative speed (Vr') is the difference of their speeds:
\[ Vr' = v1 - v2 = 5 \, \text{m/s} - 3 \, \text{m/s} = 2 \, \text{m/s} \]

### Step 4: Establish the relationship between induced EMF and relative speed
The induced EMF is directly proportional to the relative speed. Therefore, we can set up the following ratio:
\[ \frac{E'}{E} = \frac{Vr'}{Vr} \]
Where:
- \(E'\) is the induced EMF when moving in the same direction.
- \(E\) is the induced EMF when moving towards each other.

### Step 5: Substitute the known values into the equation
We know:
- \(E = 16 \, \text{mV}\)
- \(Vr' = 2 \, \text{m/s}\)
- \(Vr = 8 \, \text{m/s}\)

Substituting these values into the equation:
\[ \frac{E'}{16 \, \text{mV}} = \frac{2 \, \text{m/s}}{8 \, \text{m/s}} \]

### Step 6: Solve for \(E'\)
Cross-multiplying gives:
\[ E' = 16 \, \text{mV} \times \frac{2}{8} \]
\[ E' = 16 \, \text{mV} \times \frac{1}{4} \]
\[ E' = 4 \, \text{mV} \]

### Conclusion
The induced EMF in the coil when both are moving in the same direction is **4 mV**.

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