Title: Nature of the electromagnetic force between classical magnetic dipoles,
Abstract: The Lorentz force law of classical electrodynamics states that the force F
exerted by the magnetic induction B on a particle of charge q moving with
velocity V is given by F=qVxB. Since this force is orthogonal to the direction
of motion, the magnetic field is said to be incapable of performing mechanical
work. Yet there is no denying that a permanent magnet can readily perform
mechanical work by pushing/pulling on another permanent magnet -- or by
attracting pieces of magnetizable material such as scrap iron or iron filings.
We explain this apparent contradiction by examining the magnetic Lorentz force
acting on an Amperian current loop, which is the model for a magnetic dipole.
We then extend the discussion by analyzing the Einstein-Laub model of magnetic
dipoles in the presence of external magnetic fields.