When a loop moves towards a stationary magnet with speed `v`, the induced emf in the loop is `E`. If the magnet also moves away from the lop with the same speed, then the emf inducted in the loop is

Options

A. `E`
B. `2E`
C. `E/2`
D. zero

Explanation

To solve the problem, we need to analyze the two scenarios presented:

1. When the loop moves towards a stationary magnet.
2. When both the loop and the magnet move away from each other with the same speed.

### Step-by-Step Solution:

**Step 1: Understand the first scenario.**
- In the first scenario, the loop is moving towards the stationary magnet with speed `v`. This motion causes a change in magnetic flux through the loop, which induces an electromotive force (emf) `E` in the loop.

**Step 2: Apply Faraday's Law of Electromagnetic Induction.**
- According to Faraday's Law, the induced emf (E) in a loop is given by:
\[ E = -\frac{d\Phi}{dt} \]
where \(\Phi\) is the magnetic flux through the loop.

**Step 3: Analyze the second scenario.**
- In the second scenario, both the loop and the magnet are moving away from each other at the same speed `v`. This means that the distance between the loop and the magnet is increasing, but since both are moving at the same speed, the relative speed between the loop and the magnetic field created by the magnet is zero.

**Step 4: Determine the change in magnetic flux.**
- Since the loop is moving away from the magnet at the same speed as the magnet is moving away from the loop, the magnetic field lines that pass through the loop do not change. Therefore, there is no change in magnetic flux (\(d\Phi = 0\)).

**Step 5: Calculate the induced emf in the second scenario.**
- Applying Faraday's Law again, since there is no change in magnetic flux:
\[ E = -\frac{d\Phi}{dt} = 0 \]
Thus, the induced emf in the loop when both the loop and the magnet move away from each other with speed `v` is zero.

### Final Answer:
The induced emf in the loop when the magnet moves away from it with the same speed `v` is **0**.

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