A cylindrical bar magnet is kept along the axis of a circular coil. If the magnent is rotated about its axis, then

Options

A. A current will be induced in the coil
B. No current will be induced in the coil
C. An emf and a current both will be induced in the coil
D. None of these

Answer

To solve the question, we need to analyze the situation where a cylindrical bar magnet is rotated about its axis while being positioned along the axis of a circular coil. We will determine whether this action induces any current in the coil.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a cylindrical bar magnet placed along the axis of a circular coil.
- The magnet is rotated about its own axis.

2. **Magnetic Field Characteristics**:
- The magnetic field produced by a cylindrical magnet is uniform along its axis and does not change with rotation about that axis.
- The magnetic field strength (B) at the location of the coil remains constant as the magnet is rotated.

3. **Induced EMF and Current**:
- 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 the coil.
- The magnetic flux (Φ) through the coil is given by the product of the magnetic field (B) and the area (A) of the coil: \( Φ = B \cdot A \).
- Since the magnetic field (B) is constant and the area (A) of the coil does not change, the magnetic flux (Φ) through the coil also remains constant.

4. **Calculating Change in Flux**:
- The induced EMF (ε) in the coil is given by the formula:
\[ ε = -\frac{dΦ}{dt} \]
- Since the magnetic flux (Φ) is constant (as established in the previous step), the rate of change of flux (\( \frac{dΦ}{dt} \)) is zero.

5. **Conclusion**:
- Since there is no change in magnetic flux through the coil, the induced EMF (ε) is zero.
- Consequently, no current (I) will flow in the coil.

### Final Answer:
- The correct answer is: **No current will be induced in the coil.**