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

### Step-by-Step Solution:

1. **Understand the Setup**: We have a cylindrical bar magnet placed along the axis of a circular coil. The north pole of the magnet is at one end and the south pole at the other.

2. **Rotation of the Magnet**: The problem states that the magnet is rotated about its own axis. This means that the orientation of the magnet remains the same relative to the coil, but the magnet itself is spinning.

3. **Magnetic Flux Consideration**: The magnetic flux (Φ) through the coil is given by the product of the magnetic field (B) and the area (A) of the coil, along with the cosine of the angle (θ) between the magnetic field and the normal to the coil's surface. Since the magnet is rotating about its axis, the angle θ does not change, and thus the magnetic field strength and the area remain constant.

4. **Apply Faraday's Law of Electromagnetic Induction**: According to Faraday’s law, the induced electromotive force (EMF) in a closed loop is equal to the negative rate of change of magnetic flux through the loop:
\[ E = -\frac{d\Phi}{dt} \]
Since the magnetic flux (Φ) is constant (as established in the previous step), the rate of change of magnetic flux (dΦ/dt) is zero.

5. **Conclusion on Induced EMF**: If the rate of change of magnetic flux is zero, then the induced EMF (E) is also zero:
\[ E = 0 \]

6. **Induced Current Calculation**: The induced current (I) can be calculated using Ohm's law:
\[ I = \frac{E}{R} \]
Since E is zero, the induced current (I) will also be zero:
\[ I = 0 \]

7. **Final Answer**: Since no current is induced in the coil when the magnet is rotated about its axis, the correct conclusion is that no current will be induced in the coil.

### Summary of Options:
- Option 1: Incorrect (current will not be induced)
- Option 2: Correct (no current will be induced)
- Option 3: Incorrect (neither EMF nor current will be induced)
- Option 4: Incorrect (none of these)

Thus, the correct answer is Option 2.

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