电偶极子和磁偶极子场分布相似性的一种解释

A Simple Explanation for the Similarity of Field Distributions of Electric Dipole and Magnetic Dipole

电偶极子电场与磁偶极子磁场具有相似的空间分布。然而,这种相似性并非显而易见:电偶极子由一对等量异号电荷组成,而磁偶极子则是一个电流回路。本文从矢量场边值问题的唯一性定理出发,得出了面散度源和面旋度源产生的矢量场分布的一种等价关系,进而对电偶极子电场与磁偶极子磁场空间分布的相似性进行了解释。

The electric field distribution of an electric dipole is similar with the magnetic field distribution of a mag- netic dipole. However, this similarity is not obvious and is difficult to be understood due to the fact that： an elec- tric dipole consists of a pair of separate electric charges with equal magnitude and opposite sign, but the magnetic dipole is a closed circulation of electric current. A kind of equivalent relationship between the vector field from a surface divergence source and that from a surface rotation source is obtained by using the uniqueness theorem of the boundary problem of a vector field. Based on this relationship, the similarity can be explained easily.