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