The force on a magnetic dipole

Abstract

The classical magnetic force on a magnetic dipole depends upon the model for the dipole. The usual electric current loop model for a magnetic dipole leads to the force F=∇(m⋅B) on a magnetic dipole m in a magnetic field B. The separated magnetic charge model for a magnetic dipole leads to the force F=(m⋅∇)B on a magnetic dipole. The latter expression is analogous to the force experienced by an electric dipole in an electric field. Here, some elementary examples are given where the force expressions yield entirely different forces on a magnetic dipole. Electromagnetism textbooks usually do not emphasize the difference between these force expressions; however, occasionally the difference is important for understanding experimental results. In the 1930s and 1940s the difference in force expressions was involved in a determination of the nature of the neutron dipole moment. At present, in the 1980s, the difference in the force expressions is central to a controversy over an experiment to test the proposed Aharonov–Casher effect.