Analytic solution for the torque between two magnetic dipoles

Abstract

An analytic equation describing the torque between two magnetic dipoles is derived in this paper. We assume that the dipole sizes are small compared to their separation. Based on a previously derived force calculation between two magnetic dipoles, we derive an analytic expression for the torque. Note that the derived torque decreases with the third power of the distance between the dipoles. It is also interesting to note that the torque on the first dipole is not necessarily equal in magnitude and opposite in direction to the torque on the second dipole. This is due to the torque of both dipoles about a common center of mass.