A current loop of magnetic dipole moment `vec(M)` is placed in uniform magnetic field B. Initially the angle between `vec(M) and vec(B) " is " theta_(1)`. Find the work done by magnetic field as the angle is increased from `theta_(1) " to " theta_(2)`

Explanation

To find the work done by the magnetic field as the angle between the magnetic dipole moment \(\vec{M}\) and the magnetic field \(\vec{B}\) is increased from \(\theta_1\) to \(\theta_2\), we can follow these steps:

### Step 1: Understand the Torque on the Current Loop
The torque \(\tau\) acting on a current loop with a magnetic dipole moment \(\vec{M}\) in a magnetic field \(\vec{B}\) is given by the formula:
\[ \tau = \vec{M} \times \vec{B} = MB \sin \theta \]
where \(M\) is the magnitude of the magnetic dipole moment, \(B\) is the magnitude of the magnetic field, and \(\theta\) is the angle between \(\vec{M}\) and \(\vec{B}\).
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