[Paper Review] About the Abraham force in a conducting medium

Yurii A. Spirichev|arXiv (Cornell University)|May 26, 2017

Quantum and Classical Electrodynamics3 references3 citations

TL;DR

This paper derives the Abraham force in a conducting medium from the electromagnetic energy-momentum tensor, demonstrating its vortical nature due to non-collinear current density and vector potential. The study confirms that the force exhibits rotational characteristics in both conducting and dielectric media, resolving long-standing ambiguities in momentum transfer in moving media.

ABSTRACT

The article is devoted to the Abraham force in a conducting medium. From the energy-momentum tensor of the electromagnetic field interaction with moving charges the equation for the Abraham force is obtained. It is shown that the Abraham force in a conducting medium, as well as in a dielectric medium, has vortical character. Current density vectors and vector potential must be non-collinear

Motivation & Objective

• To clarify the nature of the Abraham force in moving conducting media.
• To resolve inconsistencies in momentum transfer in moving dielectric and conducting media.
• To derive the Abraham force from the electromagnetic energy-momentum tensor in a conducting medium.
• To establish the vortical character of the force in conducting media, analogous to dielectric media.

Proposed method

• Derives the Abraham force using the electromagnetic energy-momentum tensor in the presence of moving charges.
• Analyzes the interaction of the electromagnetic field with current-carrying media.
• Identifies the condition for vortical force: non-collinearity between current density vector and vector potential.
• Applies classical field theory to conductors with moving charges, focusing on momentum conservation.
• Compares the force structure in conducting and dielectric media to highlight similarities.
• Uses tensor formalism to ensure consistency with relativistic electrodynamics.

Experimental results

Research questions

• RQ1 What is the form of the Abraham force in a conducting medium, derived from the energy-momentum tensor?
• RQ2 Why does the Abraham force exhibit a vortical character in conducting media?
• RQ3 How do the current density and vector potential influence the force structure?
• RQ4 Is the vortical nature of the Abraham force preserved in conducting media as in dielectrics?
• RQ5 What conditions must be met for the force to have a non-zero curl in a conducting medium?

Key findings

• The Abraham force in a conducting medium is derived directly from the electromagnetic energy-momentum tensor, confirming its theoretical foundation.
• The force exhibits a vortical structure, indicating rotational momentum transfer in the medium.
• Non-collinearity between the current density vector and the vector potential is a necessary condition for the vortical force to arise.
• The vortical character of the Abraham force is preserved in conducting media, similar to dielectric media.
• The force vanishes when current density and vector potential are parallel, confirming the role of vector misalignment.
• The analysis confirms consistency with momentum conservation in moving media, resolving prior ambiguities.