A magnetic dipole μ is placed in a uniform magnetic field B. What is the torque on the dipole, and what is the potential energy?

A magnetic dipole μ is placed in a uniform magnetic field B. What is the torque on the dipole, and what is the potential energy?

• A. Torque τ = μ × B; potential energy U = − μ · B
• B. Torque τ = μ × B; potential energy U = μ · B
• C. Torque τ = − μ × B; potential energy U = − μ · B
• D. Torque τ = μ × B; potential energy U = 0

Answer: (A)

A magnetic dipole in a uniform magnetic field experiences a torque that tends to rotate the dipole so its moment aligns with the field. The torque is given by the cross product τ = μ × B, which has magnitude τ = μ B sin θ and points perpendicular to the plane formed by μ and B, with the direction found by the right-hand rule. The orientation energy of the dipole in the field is U = − μ · B = − μ B cos θ, meaning the energy is lowest when μ points in the same direction as B (θ = 0) and highest when μ points opposite (θ = π). In a uniform field there is no net force on the dipole—only a torque, since the forces on the two charges cancel.

A magnetic dipole in a uniform magnetic field experiences a torque that tends to rotate the dipole so its moment aligns with the field. The torque is given by the cross product τ = μ × B, which has magnitude τ = μ B sin θ and points perpendicular to the plane formed by μ and B, with the direction found by the right-hand rule. The orientation energy of the dipole in the field is U = − μ · B = − μ B cos θ, meaning the energy is lowest when μ points in the same direction as B (θ = 0) and highest when μ points opposite (θ = π). In a uniform field there is no net force on the dipole—only a torque, since the forces on the two charges cancel.