A note on the $δ$-singularities of the static electric and magnetic fields
The $δ-$singularities of the electric and magnetic fields in the static case are established based on the regularized $δ_\eps(\rvec)$ function introduced by Jackson.
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Publications and source records attributed to Constantin Vrejoiu.
The $δ-$singularities of the electric and magnetic fields in the static case are established based on the regularized $δ_\eps(\rvec)$ function introduced by Jackson.
The singularities of the electromagnetic field are derived to include all the point-like multipoles representing an electric charge and current distribution. Partial results obtained in a previous paper are completed to represent accurately all the terms included in these singularities.
Some pedagogical aspects of the formulation of electrodynamics independently of the system of units are commented. Only electrodynamics in vacuum is considered. It is pointed out the efficiency of using a notation system close to SI.
Compact general formulae for the energy, momentum and angular momentum radiated by confined systems of charges and currents are presented in terms of their multipole Cartesian tensors. Besides the usual electric and magnetic multipoles, a family of toroid (anapole) electromagnetic tensors, as well as some mean squared radii contributions are standed out through a method given in previous works of the authors.
Based on some previous results, one gives a general formula for introducing electromagnetic multipole expansions in terms of symmetric and traceless cartesian tensors.
A simple procedure for restoring the constants in physical equations is introduced by a consistent consideration of the correspondence between the symbols representing physical quantities and pairs formed by numerical values and unit symbols. This procedure is applied to the very used unit systems stressing also the direct relations between the atomic, natural systems and SI.