A note on the $\delta$-singularities of the static electric and magnetic fields

TL;DR

This paper investigates the delta-function singularities present in static electric and magnetic fields using a regularization approach based on Jackson's delta function.

Contribution

It provides a detailed analysis of the delta-singularities in static fields, utilizing a specific regularization method to clarify their mathematical structure.

Findings

Identifies the form of delta-singularities in static fields

Uses regularized delta functions to analyze singularities

Clarifies the mathematical nature of field singularities

Abstract

The $\delta-$singularities of the electric and magnetic fields in the static case are established based on the regularized $\delta_\eps(\rvec)$ function introduced by Jackson.