多极矩分析的教与学探讨

Discussion on teaching and learning of multipole analysis

多极矩展开是一种重要的分析方法,由静态电磁场多极矩展开得到的电多极子和磁多极子是基础而重要的物理模型.多极矩展开表示方法、多极子模型与多极子以及电磁场相互作用是多极矩分析教学的核心内容.本文从上述三个方面展开探讨:给出静态电场和静态磁场的内部和外部多极展开;讨论多极矩展开的不同表示的关系;强调多极子是基于远源处电磁势对源进行的等效点源替代;最后,从受力与力矩方面考察电多极子和磁多极子与外电磁场的相互作用.

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.