Copper wire is used to make a circular ring which is placed completely inside uniform magnetic field in such a manner that plane of ring is perpendicular to magnetic field. Emf is induced in the circular loop if

Options

A. loop is crushed
B. loop is translated
C. loop is rotated about its axis
D. loop is rotated about its diameter

Explanation

To determine when an electromotive force (EMF) is induced in a circular copper wire ring placed in a uniform magnetic field, we can analyze the situation using Faraday's law of electromagnetic induction. Here's the step-by-step solution:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a circular ring made of copper wire.
- The ring is placed completely inside a uniform magnetic field.
- The plane of the ring is perpendicular to the magnetic field.

2. **Applying Faraday's Law**:
- According to Faraday's law, EMF (E) is induced in a loop when there is a change in magnetic flux (Φ) through the loop over time. The relationship is given by:
\[ E = -n \frac{d\Phi}{dt} \]
- Here, \(n\) is the number of turns (which is 1 for a single loop), and \(\Phi = B \cdot A\) (where \(B\) is the magnetic field strength and \(A\) is the area of the loop).

3. **Identifying Conditions for Induction**:
- For EMF to be induced, there must be a change in magnetic flux, which can occur if:
- The area \(A\) of the loop changes.
- The angle \(\theta\) between the magnetic field \(B\) and the area vector \(A\) changes.
- The strength of the magnetic field \(B\) changes.

4. **Analyzing Each Option**:
- **Option A: Loop is crushed**:
- Crushing the loop reduces its area \(A\). Since the magnetic field \(B\) is uniform, a decrease in area leads to a decrease in magnetic flux, thus inducing EMF.
- **Conclusion**: EMF is induced.

- **Option B: Loop is translated**:
- Translating the loop does not change the area \(A\) or the angle \(\theta\) between \(B\) and \(A\). Therefore, the magnetic flux remains constant.
- **Conclusion**: EMF is not induced.

- **Option C: Loop is rotated about its axis**:
- Rotating the loop about its own axis does not change the area \(A\) or the angle \(\theta\) between \(B\) and \(A\). Thus, the magnetic flux remains constant.
- **Conclusion**: EMF is not induced.

- **Option D: Loop is rotated about its diameter**:
- Rotating the loop about its diameter changes the angle \(\theta\) between the magnetic field \(B\) and the area vector \(A\). This results in a change in magnetic flux.
- **Conclusion**: EMF is induced.

5. **Final Answer**:
- EMF is induced in the circular loop if:
- The loop is crushed (Option A).
- The loop is rotated about its diameter (Option D).