Electrostatic Boundary-Value Problems

This chapter deals with more advanced techniques than those discussed in Chapter 2 to solve electrostatic problems. The techniques presented in the chapter include the method of images, the multi-pole expansion, analytical methods, and some numerical methods, which may be invoked as an alternative techniques or when the analytical solution for a particular problem is not available. The method of images and multi-pole expansion techniques are applied to analyze the problems involving charges near a perfectly electric conducting or dielectric interfaces. For the media that are subject to certain boundary conditions, the electrostatic problem is modeled by Poisson's or Laplace's equation then solved analytically or numerically. Analytical solutions for the Laplace's equation in different coordinate systems are presented in details. The method of moments and finite difference method are presented as examples of numerical techniques for the solution of Poisson's or Laplace's equation. The discussions of the topics in the chapter are supported by illustrative examples, figures, solved problems, and computer programs in addition to homework problems at the end of the chapter.