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The Aharonov-Bohm phase shift in a particle interference pattern whenelectrons pass a long solenoid is identical in form with the opticalinterference pattern shift when a piece of retarding glass is introduced intoone path of a two-beam optical interference pattern. The particleinterference-pattern deflection is a relativistic effect of order 1/c^2, thoughthis relativity aspect is rarely mentioned in the literature. Here we give athorough analysis of the classical electromagnetic aspects of the interactionbetween a solenoid or toroid and a charged particle. We point out the magneticLorentz 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 backFaraday fields on the charge, the analysis in the inertial frame in which thecharge is initially at rest involves forces due to only electric fields whereforces are equal in magnitude and opposite in direction. The classical analysisis made using the Darwin Lagrangian. We point out that the classical analysissuggests an angular deflection independent of Planck's constant where thedeflection magnitude is identical with that given by the traditional quantumanalysis, but where the deflection direction is unambiguous.

Classical Electromagnetic Interaction of a Charge with a Solenoid or Toroid