A bar magnet of magnetic moment `vec(M)` is placed in a magnetic field of induction `vec(B)` . The torque exerted on it is

Options

A. `vec(M).vec(B)`
B. `-vec(M).vec(B)`
C. `vec(M)xxvec(B)`
D. `vec(B)xxvec(M)`

Answer

To find the torque exerted on a bar magnet placed in a magnetic field, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Magnetic Moment and Magnetic Field**:
- The magnetic moment of a bar magnet is represented as \(\vec{M}\) and is defined as the product of the pole strength and the distance between the poles.
- The magnetic field induction is represented as \(\vec{B}\).

2. **Torque on a Magnetic Dipole**:
- The torque \(\vec{\tau}\) experienced by a magnetic dipole in a magnetic field is given by the vector cross product of the magnetic moment and the magnetic field:
\[ \vec{\tau} = \vec{M} \times \vec{B} \]

3. **Magnitude of Torque**:
- The magnitude of the torque can be expressed as:
\[ \tau = MB \sin \theta \]
where \( \theta \) is the angle between the magnetic moment \(\vec{M}\) and the magnetic field \(\vec{B}\).

4. **Direction of Torque**:
- The direction of the torque vector is given by the right-hand rule, which states that if you point the fingers of your right hand in the direction of \(\vec{M}\) and curl them towards \(\vec{B}\), your thumb will point in the direction of \(\vec{\tau}\).

5. **Final Expression**:
- Therefore, the final expression for the torque exerted on the bar magnet in the magnetic field is:
\[ \vec{\tau} = \vec{M} \times \vec{B} \]