Question

A current loop in a magnetic field :

• A. Can be in equilibrium in two orientations, one stable while the other is unstable.
• B. Experiences a torque whether the field is uniform or non uniform in all orientations
• C. Can be in equilibrium in one orientation
• D. Can be in equilibrium in two orientations, both the euilibrium states are unstable

Answer 1

The Correct Option is A

A current loop in a magnetic field experiences forces due to the interaction between the magnetic field and the current flowing through the loop. Let's examine the dynamics of this interaction to determine the correct option.

1. **Torque on a Current Loop**: When a current loop is placed in a magnetic field, it experiences a torque. The magnitude of this torque depends on the angle between the plane of the loop and the magnetic field.

The torque \(\tau\) acting on the loop is given by:

\(\tau = NIAB \sin \theta\)

where:

• N is the number of turns in the loop.
• I is the current through the loop.
• A is the area of the loop.
• B is the magnetic field strength.
• \(\theta\) is the angle between the normal to the loop and the magnetic field.

2. **Equilibrium Conditions**: The loop can reach equilibrium where the net torque becomes zero. This happens when:

• \(\theta = 0^\circ\) or
• \(\theta = 180^\circ\)

At these angles, \(\sin \theta = 0\), resulting in zero torque on the loop.

3. **Stability of Equilibrium**:

• At \(\theta = 0^\circ\), the torque will tend to restore the loop to its equilibrium position if disturbed, representing a stable equilibrium.
• At \(\theta = 180^\circ\), if the loop is slightly disturbed, it will move away from this position, indicating an unstable equilibrium.

4. **Conclusion**: From the above analysis, a current loop in a magnetic field can be in equilibrium in two orientations: one stable (\(\theta = 0^\circ\)) and the other unstable (\(\theta = 180^\circ\)).

Therefore, the correct answer is:

• Can be in equilibrium in two orientations, one stable while the other is unstable.