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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

Step-by-Step Solution

According to the sources, a current-carrying loop with magnetic moment m\mathbf{m} in a uniform magnetic field B\mathbf{B} experiences a torque given by τ=m×B\boldsymbol{\tau} = \mathbf{m} \times \mathbf{B}, where the magnitude is τ=mBsinθ\tau = mB \sin \theta . Equilibrium occurs when the net torque is zero, which happens when the magnetic moment is either parallel (θ=0\theta = 0^\circ) or antiparallel (θ=180\theta = 180^\circ) to the magnetic field .

  1. Stable Equilibrium: At θ=0\theta = 0^\circ, the potential energy U=mB=mBU = -\mathbf{m} \cdot \mathbf{B} = -mB is at its minimum. In this orientation, any small displacement results in a restoring torque that brings the loop back to its original position .
  2. Unstable Equilibrium: At θ=180\theta = 180^\circ, the potential energy U=+mBU = +mB is at its maximum. Any small displacement from this position will cause the loop to rotate away to reach the stable state .

Thus, the loop can be in equilibrium in two orientations: one stable and one unstable.

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