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

Answer

To solve the problem of calculating the work done when a magnet with 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 Initial and Final Angles**:
- The initial angle \( \theta_1 \) can be considered as \( 0^\circ \) (the direction of the magnetic moment is aligned with the magnetic field).
- The final angle \( \theta_2 \) after rotating the magnet through \( 360^\circ \) is also \( 360^\circ \), which is equivalent to \( 0^\circ \) in terms of direction.

2. **Using the Work Done Formula**:
- The work done \( W \) in rotating a magnetic moment in a magnetic field is given by the formula:
\[ W = M B (\cos \theta_1 - \cos \theta_2) \]
- Here, \( B \) is the magnetic field strength, which in this case is given as \( H \).

3. **Substituting the Values**:
- Substitute \( B \) with \( H \):
\[ W = M H (\cos 0^\circ - \cos 360^\circ) \]

4. **Calculating the Cosine Values**:
- We know that:
\[ \cos 0^\circ = 1 \quad \text{and} \quad \cos 360^\circ = 1 \]
- Therefore, substituting these values into the equation gives:
\[ W = M H (1 - 1) = M H \cdot 0 \]

5. **Final Result**:
- Since the expression simplifies to zero:
\[ W = 0 \]
- Thus, the work done in rotating the magnet through \( 360^\circ \) in the magnetic field \( H \) is \( 0 \).

### Conclusion:
The work done when a magnet of magnetic moment \( M \) is rotated through \( 360^\circ \) in a magnetic field \( H \) is \( 0 \).