Laws of conservation of momentum and angular momentum in classical electrodynamics of material media

TL;DR

This paper investigates the conservation laws of momentum and angular momentum in classical electrodynamics of material media, emphasizing the necessity of considering elementary charges with infinite fields for fundamental consistency.

Contribution

It demonstrates that the conservation laws are upheld only when elementary charges are modeled as point-like with infinite fields, challenging the universality of continuous charge distributions.

Findings

Conservation of angular momentum appears violated without infinite fields at elementary charges.

Inclusion of infinite fields at charge locations restores conservation laws.

Continuous charge distributions are insufficient for fundamental descriptions of electromagnetic media.

Abstract

We analyze the laws of conservation of momentum and angular momentum in classical electrodynamics of material media with bound charges, and explore the possibility to describe the properties of such media via a discrete set of point-like charges of zero size (as imposed by special relativity), and via continuous charge/current distributions. This way we put a question: do we have to recognize the infinite fields at the location of elementary charges as the essential physical requirement, or such infinite fields can be ignored via introduction of continuous charge distribution? In order to answer this question, we consider the interaction of a homogeneously charged insulating plate with a compact magnetic dipole, moving along the plate. We arrive at the apparent violation of the angular momentum conservation law and show that this law is re-covered, when the electric field at the location of each elementary charge of the plate is taken infinite. This result signifies that the description of electromagnetic properties of material media via the continuous charge and current distributions is not a universal approximation, and at the fundamental level, we have to deal with a system of elementary discrete charges of zero size, at least in the analysis of laws of conservation of momentum and angular momentum.