Faraday Induction and the Current Carriers in a Circuit

TL;DR

This paper presents a particle-based perspective on Faraday induction, using explicit calculations from point-charge fields, and explores how the behavior of current carriers depends on interactions within a circuit.

Contribution

It introduces a novel particle-based approach to electromagnetic induction, contrasting with traditional field-based methods, and analyzes the effects of particle interactions on induced fields.

Findings

Induced fields depend on particle mass and charge for non-interacting particles.

Mutual interactions dominate in multi-particle circuits, nullifying individual particle properties.

Energy transfer shifts from kinetic to magnetic energy in interacting systems.

Abstract

In this article, it is pointed out that Faraday induction can be treated from an untraditional, particle-based point of view. The electromagnetic fields of Faraday induction can be calculated explicitly from approximate point-charge fields derived from the Li\'enard-Wiechert expressions or from the Darwin Lagrangian. Thus the electric fields of electrostatics, the magnetic fields of magnetostatics, and the electric fields of Faraday induction can all be regarded as arising from charged particles. Some aspects of electromagnetic induction are explored for a hypothetical circuit consisting of point charges which move frictionlessly in a circular orbit. For a small number of particles in the circuit (or for non-interacting particles), the induced electromagnetic fields depend upon the mass and charge of the current carriers while energy is transferred to the kinetic energy of the particles. However, for an interacting multiparticle circuit, the mutual electromagnetic interactions between the particles dominate the behavior so that the induced electric field cancels the inducing force per unit charge, the mass and charge of the individual current carriers become irrelevant, and energy goes into magnetic energy.