On a hypothetical explanation of the Aharonov-Bohm effect

I study in detail a proposal made by T. H. Boyer in all attempt to explain classically the Aharonov-Bohm (AB) effect. Boyer claims that in an AB experiment, the perturbation the external incident particle produces on the charge and current distributions within the solenoid will affect back the motion of the external particle. With a qualitative analysis based on energetic considerations, Boyer seemed to arrive at the conclusion that this perturbation could give account of the AB effect. In this paper I make explicit calculations which show that Boyer's conjecture fails. Indeed I find that the perturbation produced on the solenoid and then its effect on the external charge, is independent of the solenoid current and consequently cannot account for the AB effect, which is current dependent.