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Equations of Motion of Interacting Classical Charged Particles and the Motion of an Electron Outside a Long Solenoid

By Hanno Essén
Progress In Electromagnetics Research B, Vol. 100, 39-53, 2023


The equation of motion for a test particle moving in given fixed external fields is analyzed and compared to the corresponding equation of motion derived from the Darwin Lagrangian for a system of interacting charged particles. The two approaches agree as long as the part of the electric field that arises from the partial time derivative of the vector potential is taken into account. It is, however, only via the Darwin approach that the origin of this field can be understood as arising from a breakdown of the test particle approximation. Applying the formalism to an electron moving outside a long solenoid results in a classical analog of the Aharonov-Bohm effect.


Hanno Essén, "Equations of Motion of Interacting Classical Charged Particles and the Motion of an Electron Outside a Long Solenoid," Progress In Electromagnetics Research B, Vol. 100, 39-53, 2023.


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