The work done in rotating a magent of the magnetic moment `2Am^(2)` in a magnetic field of induction `5 xx 10^(-3)T` from the direction along the magnetic field to the direction opposite to the field , is

Options

A. zero
B. `2 xx 10^(-2)J`
C. `10^(-2)J`
D. `10J`

Answer

To solve the problem of calculating the work done in rotating a magnet from the direction along the magnetic field to the direction opposite to the field, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Magnetic moment \( M = 2 \, \text{Am}^2 \)
- Magnetic field induction \( B = 5 \times 10^{-3} \, \text{T} \)

2. **Determine the Angle of Rotation**:
- The magnet is rotated from the direction along the magnetic field to the direction opposite to the field. This means the angle \( \theta \) is \( 180^\circ \).

3. **Use the Work Done Formula**:
- The work done \( W \) in rotating a magnetic moment in a magnetic field is given by the formula:
\[ W = M \cdot B \cdot (1 - \cos \theta) \]

4. **Calculate \( 1 - \cos \theta \)**:
- For \( \theta = 180^\circ \):
\[ \cos 180^\circ = -1 \]
- Therefore,
\[ 1 - \cos 180^\circ = 1 - (-1) = 2 \]

5. **Substitute the Values into the Formula**:
- Now substitute \( M \), \( B \), and \( 1 - \cos \theta \) into the work done formula:
\[ W = 2 \, \text{Am}^2 \cdot (5 \times 10^{-3} \, \text{T}) \cdot 2 \]

6. **Calculate the Work Done**:
- Performing the multiplication:
\[ W = 2 \cdot 5 \times 10^{-3} \cdot 2 = 20 \times 10^{-3} \, \text{J} \]
- This can be rewritten as:
\[ W = 2 \times 10^{-2} \, \text{J} \]

7. **Final Answer**:
- The work done in rotating the magnet is:
\[ W = 2 \times 10^{-2} \, \text{J} \]

### Conclusion:
The work done in rotating the magnet from the direction along the magnetic field to the direction opposite to the field is \( 2 \times 10^{-2} \, \text{J} \).