Abstract: The multipole expansion is an important analysis method, which defines basic and important physical models: electric as well as magnetic multipoles. The representations of the multipole expression, the multipoles, and the interaction between multipoles and an external electromagnetic field are the core aspects of teaching multipole analysis. In this paper, firstly multipole expansions for both the static electric field and the static magnetic field are given, the relationship between their Cartesian representation and spherical harmonics representation is discussed. Secondly, it is emphasized that multipoles are ideal point models based on the equivalent of electromagnetic potential rather than real charge or current distributions. Finally, the forces and torques due to interactions between multipoles and the external field are reviewed.

Key words: multipole expansion, multipoles, electric scale potential, magnetic vector potential, electrodynamics