  The concept of hidden momentum is reviewed and the first rigorous derivation
from Maxwell's equations is provided for the electromagnetic force on
electrically small perfect electric conductors of arbitrary shape in
bandlimited but otherwise 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 time varying
Amperian magnetic dipoles equal to the force on magnetic-charge magnetic
dipoles with the same time varying magnetic dipole moment in the same time
varying 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. Remarkably, it is found that the quadrupolar fields at the
surface of the sphere are required to obtain the correct total force on the
sphere even though the quadrupolar moments are negligible compared to the
dipole moments as the electrical size of the sphere approaches zero.
