Force and Hidden Momentum for Classical Microscopic Dipoles

Abstract

The concept of hidden momentum is reviewed and a rigorous derivation from Maxwell's equations is provided for the electromagnetic force on electrically small perfect electric conductors of arbitrary shape in arbitrarily time-varying fields. It is proven for the Amperian magnetic dipoles of these perfect conductors that a "hidden-momentum" electromagnetic force exists that makes the force on these Amperian magnetic dipoles equal to the force on magnetic-charge magnetic dipoles with the same magnetic dipole moment in the same externally applied fields. The exact Mie solution to the perfectly conducting sphere under plane-wave illumination is used to prove that the expressions for the total and hidden-momentum forces on the arbitrarily shaped electrically small perfect conductors correctly predict the forces on perfectly conducting spheres.