For a magnetic dipole μ in a uniform field B, the potential energy when μ is parallel to B is which of the following?

• A. U = − μ B
• B. U = μ B
• C. U = 0
• D. U = − μ B cos 60°

Answer: (A)

The potential energy of a magnetic dipole in a uniform magnetic field is given by U = − μ · B = − μ B cos θ. When the dipole moment points parallel to the field, the angle is zero, so cos θ = 1 and U = − μ B. This is the lowest possible energy, meaning the system is most stable in this alignment. If the dipole pointed opposite to the field, the energy would be + μ B, and if it were perpendicular, the energy would be zero. So, for parallel alignment, the energy is − μ B.