Question

A current loop in a magnetic field

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

Answer 1

The Correct Option is D

To solve this question, we need to understand the behavior of a current loop in a magnetic field. When a current-carrying loop is placed in a magnetic field, it experiences a torque. This torque tends to rotate the loop until the loop reaches an equilibrium position.

Let's analyze the options based on the concept:

1. The first option states that a current loop experiences a torque in all orientations, whether the magnetic field is uniform or non-uniform. This is incorrect because, in certain positions relative to the field lines, the net torque can be zero, leading to equilibrium.
2. The second option suggests that the loop can be in equilibrium in one orientation. While the loop can certainly be in equilibrium, it doesn't restrict to just one orientation.
3. The third option states that the loop can be in equilibrium in two orientations, both of which are unstable. While two equilibrium positions are possible, they include one stable and one unstable configuration, not two instables.
4. The correct option is the fourth: A current loop can be in equilibrium in two orientations, one stable and the other unstable. This is correct because:

A current loop in a magnetic field can align itself to minimize its potential energy. There are typically two distinct orientations:

• Stable equilibrium: Here, the plane of the loop is parallel to the field lines. In this position, the magnetic moment of the loop is aligned with the magnetic field, and if disturbed, the torque will try to bring it back to this position.
• Unstable equilibrium: In this orientation, the plane of the loop is perpendicular to the field lines. Here, the magnetic moment is opposite the magnetic field, and if disturbed slightly, the torque will increase its displacement from this position.

The presence of both stable and unstable equilibriums validates the correct answer: a current loop can indeed be in equilibrium in two orientations, with one stable and the other unstable.