A current loop is a magnetic field is in equilibrium in two orientations one is stable and another unstable.
∵τ=M×B=MBsinθ
If θ=0o⇒τ=0    (stable)
If θ=π⇒τ=0     (unstable)
Do not experience a torque in some orientations

A current loop in a magnetic field

A current loop is a closed path through which an electric current flows. When a current loop is placed in a magnetic field, it experiences a torque, which is a rotational force that tends to change its orientation. The torque on the loop is given by the equation:

τ = NIABsinθ

where τ is the torque, N is the number of turns in the loop, I is the current flowing through the loop, A is the area of the loop, B is the magnetic field strength, and θ is the angle between the normal to the loop and the magnetic field.

Effect of uniform and non-uniform magnetic fields

- Uniform magnetic field: In a uniform magnetic field, the magnetic field strength and direction are the same at all points. In this case, the torque experienced by the current loop is constant and does not depend on its orientation. Therefore, the current loop always experiences a torque in a uniform magnetic field.

- Non-uniform magnetic field: In a non-uniform magnetic field, the magnetic field strength and/or direction vary at different points. In this case, the torque experienced by the current loop depends on its orientation. The torque tends to align the loop with the magnetic field direction. If the loop is not aligned with the field, it will experience a torque that tries to align it. Therefore, the current loop always experiences a torque in a non-uniform magnetic field as well.

Equilibrium orientations

- One equilibrium orientation: The equilibrium orientation occurs when the torque on the current loop is zero. This happens when the loop is aligned with the magnetic field, so that the angle θ is zero. In this orientation, the torque equation becomes τ = 0, and the loop is in equilibrium.

- Two equilibrium orientations: In some cases, the current loop can have two equilibrium orientations. One of the equilibrium orientations is stable, meaning that if the loop is slightly displaced from this orientation, it will experience a torque that brings it back to the equilibrium position. The other equilibrium orientation is unstable, meaning that if the loop is slightly displaced from this orientation, it will experience a torque that further displaces it from the equilibrium position.

The correct answer

In the given question, option D states that a current loop can be in equilibrium in two orientations, one stable while the other is unstable. This statement is correct. The stable equilibrium occurs when the loop is aligned with the magnetic field, while the unstable equilibrium occurs when the loop is anti-aligned with the magnetic field. In the stable equilibrium, any small displacement from the aligned position will result in a torque that tries to bring it back to the aligned position. In the unstable equilibrium, any small displacement from the anti-aligned position will result in a torque that further displaces it from the anti-aligned position. Therefore, option D is the correct answer.

Overall, a current loop always experiences a torque in a magnetic field, whether the field is uniform or non-uniform. It can be in equilibrium in one orientation when aligned with the field, and in two orientations when aligned and anti-aligned with the field, with one of them being stable and the other being unstable.