  The Aharonov-Bohm phase shift in a particle interference pattern when
electrons pass a long solenoid is identical in form with the optical
interference pattern shift when a piece of retarding glass is introduced into
one path of a two-beam optical interference pattern. The particle
interference-pattern deflection is a relativistic effect of order 1/c^2, though
this relativity aspect is rarely mentioned in the literature. Here we give a
thorough analysis of the classical electromagnetic aspects of the interaction
between a solenoid or toroid and a charged particle. We point out the magnetic
Lorentz force which the solenoid or toroid experiences due to a passing charge.
Although analysis in the rest frame of the solenoid or toroid will involve back
Faraday fields on the charge, the analysis in the inertial frame in which the
charge is initially at rest involves forces due to only electric fields where
forces are equal in magnitude and opposite in direction. The classical analysis
is made using the Darwin Lagrangian. We point out that the classical analysis
suggests an angular deflection independent of Planck's constant where the
deflection magnitude is identical with that given by the traditional quantum
analysis, but where the deflection direction is unambiguous.
