The Bar Magnet

To solve this problem, we need to calculate the work done in rotating a bar magnet from its most stable position (parallel to the magnetic field) to its most unstable position (antiparallel to the magnetic field). The formula for the work done in rotating a magnetic dipole in a magnetic field is given by:

where PE (Potential Energy) is calculated using:

Here, is the magnetic moment, is the magnetic field, and is the angle with the magnetic field.

1. **Most Stable Position**: The magnetic dipole is aligned with the magnetic field. Therefore, .

2. **Most Unstable Position**: The magnetic dipole is antiparallel to the magnetic field. Thus, .

Substituting these into the formula for work done:

3. **Substitute Given Values**: and .

Therefore, the work done in rotating the magnet is .

The correct option is: .