How to introduce the magnetic dipole moment

Abstract

We show how the concept of the magnetic dipole moment can be introduced in the same way as the concept of the electric dipole moment in introductory courses on electromagnetism. Considering a localized steady current distribution, we make a Taylor expansion directly in the Biot–Savart law to obtain, explicitly, the dominant contribution of the magnetic field at distant points, identifying the magnetic dipole moment of the distribution. We also present a simple but general demonstration of the torque exerted by a uniform magnetic field on a current loop of general form, not necessarily planar. For pedagogical reasons we start by reviewing briefly the concept of the electric dipole moment.