电各向异性介质中泊松方程的具体形式

The Specific Expressions of Poisson Equation in Anisotropic Dielectric

泊松方程是研究电各向异性介质静电场的核心方程.文章从泊松方程并矢表达式出发,应用张量分析的矩阵方法,推导出电各向异性介质中泊松方程在球坐标系和柱坐标下的具体形式,即A1+A2+A3+A4=-ρ和B1+B2+B3+B4=-ρ.并得出介电常数张量ε→→具有坐标系下的不变性,这有助于加深对电各向导性介质的介电属性的了解.

Poisson equation is the core equation of electrostatic field in anisotropic dielectric. Starting from the dyadic of Poisson Equation,the specific expressions of Poisson equation：A, ＋A2 ＋A3 ＋A4 =-p and B1 ＋B2 ＋B3 ＋B4 =-p were deduced in the spherical coordinate system and in the cylindrical coordinate system with matrix method of tensor analysis.The coordinate invariance of the dielectric tensor can be discovered,which helps to understand the dielectric properties of anisotropic dielectric deeply.