电偶极子位于均匀介质球中时球外电场的研究

采用分离变量法求解了电偶极子位于均匀介质球中时复连通域的拉普拉斯方程和泊松方程,求出了球内外两种不同介质的电势分布和球面上的极化电荷分布;通过求解二阶非线性微分方程得到了球外的电场线函数;利用计算软件Math-ematica 5.0,作出了相应的相互正交的等势线簇图形和电场线簇图形,并且进行了必要的讨论.

Research on the electrostatic field outside of an isotropic dielectric spheroid which an electric dipole located on

The solutions of Laplace and Poisson equations for electrostatic field belong to the multiply connected domain composed of an isotropic dielectric spheroid which an electric dipole located on are obtained by using the separation variable method.The distribution of potential inner and exterior of dielectric spheroid,as well as polarization charges appearing the surface of sphere are given.By means of the solution of the second-order nonlinear differential equation and the software package facility of Mathematica 5.0,we get the function of electric field lines outside of an isotropic dielectric spheroid and plot figures of the relative equipotential and electric field lines.Finally,the results are discussed.