Final answer:
The direction of the magnetic moment in stable equilibrium is along the z-axis represented by the unit vector when the ring is free to rotate around any diameter.
Step-by-step explanation:
If the ring were free to rotate around any diameter, the direction in which the magnetic moment points when the ring is in a state of stable equilibrium would be parallel to the applied magnetic field. This is due to the fact that the torque on a magnetic moment in a magnetic field is given by τ = μ × B where μ is the magnetic dipole moment and B is the magnetic field.
In stable equilibrium, the torque is zero, which occurs when μ is aligned with B. The orientation of μ in such a stable equilibrium would therefore be in the same direction as the magnetic field. Assuming the magnetic field is in the direction of the z-axis ( unit vector), the magnetic moment μ would point along the positive z-axis for stable equilibrium. Therefore, in unit vector notation, we can express the direction of the magnetic moment in stable equilibrium as . That is, μ/μ = .