A magnet of magnetic moment M is rotated through `360^(@)` in a magnetic field H, the work done will be

Options

A. `MH`
B. `2MH`
C. `2piMH`
D. Zero

Explanation

To find the work done when a magnet with a magnetic moment \( M \) is rotated through \( 360^\circ \) in a magnetic field \( H \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Work Done by a Magnetic Field**:
The work done \( W \) on a magnetic dipole in a magnetic field when it is rotated from an angle \( \theta_1 \) to \( \theta_2 \) is given by the formula:
\[ W = -M \cdot B \cdot (\cos \theta_2 - \cos \theta_1) \]
where \( M \) is the magnetic moment, \( B \) is the magnetic field strength, and \( \theta \) is the angle between the magnetic moment and the magnetic field.

2. **Setting the Initial and Final Angles**:
In this case, we are rotating the magnet through \( 360^\circ \). We can set:
- \( \theta_1 = 0^\circ \) (initial position)
- \( \theta_2 = 360^\circ \) (final position)

3. **Calculating Cosine Values**:
Now, we calculate the cosine values for these angles:
- \( \cos(0^\circ) = 1 \)
- \( \cos(360^\circ) = 1 \)

4. **Substituting Values into the Work Done Formula**:
Substitute \( \theta_1 \) and \( \theta_2 \) into the work done formula:
\[ W = -M \cdot B \cdot (\cos(360^\circ) - \cos(0^\circ)) = -M \cdot B \cdot (1 - 1) \]

5. **Simplifying the Expression**:
This simplifies to:
\[ W = -M \cdot B \cdot 0 = 0 \]

6. **Conclusion**:
Therefore, the work done when the magnet is rotated through \( 360^\circ \) in the magnetic field \( H \) is:
\[ W = 0 \]

### Final Answer:
The work done is \( 0 \).

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