  The classical electromagnetic interaction of a point charge and a magnet is
discussed by first calculating the interaction of point charge with a simple
model magnetic moment and then suggesting a multiparticle limit. The Darwin
Lagrangian is used to analyze the electromagnetic behavior of the model
magnetic moment (composed of two oppositely charged particles of different mass
in an initially circular orbit) interacting with a passing point charge. The
changing mangetic moment is found to put a force back on a passing charge; this
force is of order 1/c^2 and depends upon the magnitude of the magnetic moment.
It is suggested that in the limit of a multiparticle magnetic toroid, the
electric fields of the passing charge are screened out of the body of the
magnet while the magnetic fields penetrate into the magnet. This is consistent
with our understanding of the penetration of electromagnetic velocity fields
into ohmic conductors. Conservation laws are discussed. The work corresponds to
a classical electromagnetic analysis of the interaction which is basic to
understanding the controversy over the Aharonov-Bohm and Aharonov-Casher phase
shifts and represents a refutation of the suggestions of Aharonov, Pearle, and
Vaidman.
