Abstract: 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.

Key words: electric dipole, polarization charges, equipotential line, electric field line