A conducting ring is placed in a uniform magnetic field with its plane perpendicular to the field . An `emf` is induced in the ring if

Options

A. it is rotated about its axis.
B. it is rotated about its diameter.
C. it is not moved.
D. it is given translational motion in the field.

Explanation

To determine when an electromotive force (emf) is induced in a conducting ring placed in a uniform magnetic field with its plane perpendicular to the field, we need to analyze the conditions under which the magnetic flux linked with the ring changes.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- A conducting ring is placed in a uniform magnetic field, with the plane of the ring perpendicular to the direction of the magnetic field lines.

2. **Magnetic Flux**:
- The magnetic flux (Φ) through the ring is given by the formula:
\[ Φ = B \cdot A \cdot \cos(θ) \]
where \(B\) is the magnetic field strength, \(A\) is the area of the ring, and \(θ\) is the angle between the magnetic field and the normal to the surface of the ring. Since the plane of the ring is perpendicular to the magnetic field, \(θ = 0\) and thus \(cos(θ) = 1\).

3. **Conditions for Induced EMF**:
- According to Faraday's law of electromagnetic induction, an emf is induced in a circuit if there is a change in magnetic flux through the circuit. This can occur due to:
- Rotating the ring about its axis.
- Rotating the ring about its diameter.
- Translating the ring through the magnetic field.

4. **Analyzing Each Condition**:
- **Rotating about its axis**:
- If the ring is rotated about its own axis, the orientation of the ring does not change relative to the magnetic field. Therefore, the magnetic flux linked with the ring remains constant. **No induced EMF**.

- **Rotating about its diameter**:
- If the ring is rotated about its diameter, the orientation of the area vector of the ring changes with respect to the magnetic field. This results in a change in the magnetic flux linked with the ring. **Induced EMF occurs**.

- **Not moving**:
- If the ring is not moved at all, there is no change in the magnetic flux linked with the ring. **No induced EMF**.

- **Translating motion in the field**:
- If the ring is given a translational motion in the magnetic field, the area through which the magnetic field lines pass does not change, and thus the magnetic flux remains constant. **No induced EMF**.

5. **Conclusion**:
- The only condition under which an emf is induced in the conducting ring is when it is rotated about its diameter.

### Final Answer:
The induced emf occurs when the ring is rotated about its diameter.

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