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 use the formula for work done in a magnetic field:

### 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. **Understand the Angle of Rotation**:
- The magnet is rotated from the direction along the magnetic field (0 degrees) to the direction opposite to the magnetic field (180 degrees).
- Therefore, the angle \( \theta = 180^\circ \).

3. **Use the Work Done Formula**:
The work done \( W \) in rotating a magnetic moment in a magnetic field is given by the formula:
\[ W = -mB \cos \theta \]
Since we are rotating from \( \theta = 0^\circ \) to \( \theta = 180^\circ \), we can express this as:
\[ W = -mB (\cos 180^\circ - \cos 0^\circ) \]

4. **Calculate \( \cos 180^\circ \) and \( \cos 0^\circ \)**:
- \( \cos 180^\circ = -1 \)
- \( \cos 0^\circ = 1 \)

5. **Substituting Values**:
Substitute the values into the work done formula:
\[ W = -mB (-1 - 1) = -mB (-2) = 2mB \]

6. **Calculate the Work Done**:
Now, substituting the values of \( m \) and \( B \):
\[ W = 2 \times 2 \, \text{Am}^2 \times 5 \times 10^{-3} \, \text{T} \]
\[ W = 20 \times 10^{-3} \, \text{J} \]

7. **Final Answer**:
The work done in rotating the magnet is:
\[ W = 20 \times 10^{-3} \, \text{J} = 2 \times 10^{-2} \, \text{J} \]

### Conclusion:
The work done in rotating the magnet from the direction along the magnetic field to the direction opposite to the field is \( 20 \times 10^{-3} \, \text{J} \) or \( 2 \times 10^{-2} \, \text{J} \).