A circular coil and a bar magnet placed nearby are made to move in the same direction. The coil covers a distance of `1m` in `0.5 sec` and the magnet a distance of `2 m` in `1 sec`. The induced emf produced in the coil

Options

A. zero
B. 1V
C. 0.5V
D. cannot be determined from the given infromation

Answer

To solve the problem, we need to analyze the situation step by step.

### Step 1: Calculate the velocity of the coil
The coil covers a distance of 1 meter in 0.5 seconds. We can calculate the velocity (v_coil) using the formula:

\[ v_{\text{coil}} = \frac{\text{distance}}{\text{time}} = \frac{1 \text{ m}}{0.5 \text{ s}} = 2 \text{ m/s} \]

### Step 2: Calculate the velocity of the magnet
The magnet covers a distance of 2 meters in 1 second. We can calculate the velocity (v_magnet) using the same formula:

\[ v_{\text{magnet}} = \frac{\text{distance}}{\text{time}} = \frac{2 \text{ m}}{1 \text{ s}} = 2 \text{ m/s} \]

### Step 3: Compare the velocities
Now that we have both velocities:
- Velocity of the coil (v_coil) = 2 m/s
- Velocity of the magnet (v_magnet) = 2 m/s

Both the coil and the magnet are moving at the same velocity.

### Step 4: Analyze the relative motion
Since both the coil and the magnet are moving in the same direction at the same speed, the distance between them remains constant. If the initial distance between the coil and the magnet is X, it does not change as they move together.

### Step 5: Determine the induced EMF
According to Faraday's law of electromagnetic induction, an electromotive force (EMF) is induced in a coil when there is a change in magnetic flux through it. Since the distance between the coil and the magnet remains constant, there is no change in magnetic flux through the coil.

Thus, the induced EMF (ε) in the coil is:

\[ \text{Induced EMF} = 0 \text{ V} \]

### Final Answer
The induced EMF produced in the coil is **0 V**.

---