Explanation notes on the multipole expansions of the electromagnetic field

TL;DR

This paper examines the multipole expansions of electromagnetic fields derived from Jefimenko's equations, discussing power calculations, approximation criteria, reference point invariance, and tensor descriptions of moments.

Contribution

It provides detailed commentary on the mathematical and physical aspects of multipole expansions, emphasizing consistent approximation and tensor representations.

Findings

Clarifies the use of symmetric and trace-free tensors for moments

Discusses invariance of physical results under reference point changes

Analyzes the calculus of radiated power in multipole expansions

Abstract

Starting from Jefimenko's equations, we consider the multipole expansions of electric and magnetic fields for a confined system of charges and currents. We analyze and comment on the calculus of radiated power, on the consistent use of approximation criteria, on the invariance of physical results when changing the point of reference, as well as on the use of electric and magnetic moments described by symmetric and trace free tensors.