Singular behaviour of the electromagnetic field

TL;DR

This paper investigates the singularities in electromagnetic fields caused by point-like multipoles, extending the analysis from static to dynamic cases with a straightforward method for the generalization.

Contribution

It provides a comprehensive derivation of electromagnetic field singularities for all point-like multipoles, including a simple transition from static to dynamic scenarios.

Findings

Derived singularities for static multipoles

Generalized results to dynamic multipoles

Established a simple transition procedure

Abstract

The singularities of the electromagnetic field are derived to include all the point-like multipoles representing an electric charge and current distribution. Firstly derived in the static case, the result is generalized to the dynamic one. We establish a simple procedure for passing from the first, to the second case.