电各向异性介质中无限长矩形腔内电势分布

Potential Distribution in An Infinite Rectangular Cavity in Anisotropic Dielectric

电各向异性介质中无限长矩形腔内的电势分布,是拉普拉斯方程的边值问题.腔四壁处均满足第一类非齐次边界条件,不能直接应用分离变量法求解该边值问题.这时,可根据二阶线性齐次偏微分方程解的叠加原理,将该边值问题分解为4个能直接应用分离变量法求解的边值问题来进行求解.求解的方法可作为现有应用分离变量法求解电各向异性介质中拉普拉斯方程边值问题的补充.在令ε11=ε22=ε33=ε的情况下,所得的结果可适用于电各向同性介质.

Potential distribution in an infinite rectangular cavity in anisotropic dielectric is a boundary value problem of Laplace equation. Because the walls of the cavity meet the first nonhomogeneous boundary conditions, the Laplace equation boundary value problem cannot be solve directly by applying variable separation methods. According to the superposition principle of the solutions of the two order linear homogeneous partial differential equations, the boundary value problems which are divided into 4 boundary value problems can be solved directly by using method of separation of variables. The method can be used as a supplementary method for solving the boundary value problem of Laplace equation by applying method of separation of variables in anisotropic dielectric. The results can be applied to isotropic dielectric in the situation：ε11=ε22=ε33=ε.