Generalized integral formulation of electromagnetic Cartesian multipole moments

TL;DR

This paper develops a comprehensive integral formulation for electromagnetic multipole moments in Cartesian coordinates, including volume and surface integrals, and introduces a new type of dipole moment within the same framework.

Contribution

It presents a generalized integral approach for electromagnetic multipole moments and introduces a novel dipole moment concept in Cartesian coordinates.

Findings

Derived volume and surface integral expressions for multipole moments.

Established relationships between different integral formulations.

Introduced a new dipole moment concept similar to existing multipole moments.

Abstract

We study integral expressions of electromagnetic multipole moments of arbitrary order in Cartesian coordinates. The volume and surface integrals of charge-induced and current-induced multipole moment tensors are formulated and the relationship between them is discussed. Full surface integral expressions for the multipole moment are also obtained. We further extend the formulation to introduce another kind of dipole moment, which is similar to the charge-induced and current-induced multipole moments and is found in a vector decomposition formula.