Classical theory of the Aharonov-Bohm effect
Keywords:
Aharonov-Bohm effect, virtual work principleAbstract
The intention of constructing a classically-electrodynamic theory of the Aharonov-Bohm effect (ABE) was a driving force to conduct the study presented in this paper. The ABE has been detailed by R. P. Feynman; it is a phenomenon in which an electrically charged particle (electron) passing by a very long and extremely thin magnetized filament is affected by a force, despite the fact that both the magnetic field and electric field are zero along the particle trajectory. The fact that nonzero vector potential exists around a magnetized filament turned out to be sufficient to give rise the quantum-mechanical explanation of this effect by Aharonov and Bohm in 1959. However, among the theorems of classical physics, the virtual work principle can be found, which represents one facet of the energy conservation law. This principle asserts that if the energy of a set of physical objects varies with the location of some object, then this object is subjected to a force, which can be calculated from the energy gradient at the point of the object location. This paper presents a classically-electrodynamic theory of the Aharonov-Bohm effect. The proposed theory uses the virtual work principle to determine the force acting on a point charge. The calculated value of the transverse momentum of an electron passing by an infinitely long solenoid is opposite in sign to that calculated by a quantum-mechanical method. The need for new, reasonably set up experiments is justifiedReferences
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