What is the force on a magnetic dipole?

Abstract

We show that attempts to modify the force on a magnetic dipole by introducing either hidden momentum or internal forces are not correct. The standard textbook result ${\bf F=\nabla(\bmu\cdot B)}$ is correct even in the presence of time dependent electromagnetic fields. Using this expression for the force, overall momentum (the sum of mechanical and electromagnetic momentum) is conserved in changing electromagnetic fields.

This version presents a more compelling argument that the textbook equation for the force on a magnetic dipole is correct, and is needed to preserve overall momentum conservation