Exact dipolar moments of a localized electric current distribution

TL;DR

This paper derives new exact formulas for calculating dipolar moments of localized electric currents, improving precision over traditional small-source approximations and including polarization-specific cases.

Contribution

It introduces exact expressions for dipolar moments of localized currents, extending beyond standard approximations and incorporating polarization effects.

Findings

Exact formulas for dipolar moments derived

Higher order terms can be easily computed

Includes expressions for polarization-specific dipoles

Abstract

The multipolar decomposition of current distributions is used in many branches of physics. Here, we obtain new exact expressions for the dipolar moments of a localized electric current distribution. The typical integrals for the dipole moments of electromagnetically small sources are recovered as the lowest order terms of the new expressions in a series expansion with respect to the size of the source. All the higher order terms can be easily obtained. We also provide exact and approximated expressions for dipoles that radiate a definite polarization handedness (helicity). Formally, the new exact expressions are only marginally more complex than their lowest order approximations.