  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.
