On the exact electric and magnetic fields of an electric dipole

TL;DR

This paper derives exact expressions for the electric and magnetic fields of a time-dependent electric dipole using multipole expansion from Jefimenko's equations, providing clarity beyond typical textbook explanations.

Contribution

It introduces a precise derivation of the fields of an electric dipole with arbitrary time dependence from fundamental equations, clarifying common misconceptions.

Findings

Exact formulas for electric and magnetic fields of a time-dependent dipole

Comparison with standard textbook expositions

Insights into the multipole expansion approach

Abstract

We derive from Jefimenko's equations a multipole expansion in order to obtain the exact expressions for the electric and magnetic fields of an electric dipole with an arbitrary time dependence. A few comments are also made about the usual expositions found in most common undergraduate and graduate textbooks as well as in the literature on this topic.