The work done in rotating a magnet from the direction of uniform field to the opposite direction of the field is W. Find work done in rotating the magnet from the field direction to half the maximum couple position

Explanation

To solve the problem of finding the work done in rotating a magnet from the direction of a uniform magnetic field to half the maximum couple position, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Torque in a Magnetic Field**:
The torque (\( \tau \)) on a magnetic dipole in a magnetic field is given by the formula:
\[
\tau = \mathbf{m} \times \mathbf{B} = mB \sin \theta
...