For a current loop with magnetic moment mu = I A n_hat in a uniform B field, what are the potential energy and torque?

For a current loop with magnetic moment mu = I A n_hat in a uniform B field, what are the potential energy and torque?

• A. U = mu · B; tau = mu × B
• B. U = - mu · B; tau = - mu × B
• C. U = - mu · B; tau = mu × B
• D. U = mu × B; tau = mu · B

Answer: (C)

When a magnetic dipole such as a current loop sits in a uniform magnetic field, its orientation relative to the field determines its energy and how it will rotate. The energy is lowest when the magnetic moment μ points in the same direction as the field, which is captured by U = - μ · B (equivalently U = - μ B cos θ). The torque acts to rotate the dipole to align μ with B and is given by τ = μ × B, with magnitude τ = μ B sin θ and a direction perpendicular to both μ and B, determined by the right-hand rule. Since μ for a current loop is μ = I A n̂, the same relations apply: the energy is - μ · B and the torque is μ × B. This means when μ is parallel to B, the energy is at a minimum and the torque vanishes; when μ is perpendicular to B, the energy is higher and the torque is at its maximum.

When a magnetic dipole such as a current loop sits in a uniform magnetic field, its orientation relative to the field determines its energy and how it will rotate. The energy is lowest when the magnetic moment μ points in the same direction as the field, which is captured by U = - μ · B (equivalently U = - μ B cos θ). The torque acts to rotate the dipole to align μ with B and is given by τ = μ × B, with magnitude τ = μ B sin θ and a direction perpendicular to both μ and B, determined by the right-hand rule.

Since μ for a current loop is μ = I A n̂, the same relations apply: the energy is - μ · B and the torque is μ × B. This means when μ is parallel to B, the energy is at a minimum and the torque vanishes; when μ is perpendicular to B, the energy is higher and the torque is at its maximum.