Introduction to Numerical Electrostatics Using MATLAB

3Introduction to the Method of Moments Technique for Electrostatics

3.1 Fundamental Equations

Our plan in this chapter is to approximate the charge distribution over a small region of an electrode as a constant and then to combine many of these approximations in a manner that results in a useful approximation to the exact solution of Poisson’s equation over all of space. The method of moments (MoM) technique breaks conductor surfaces into small planar regions, assumes a constant charge distribution on each region, approximates Poisson’s equation by a set of algebraic equations, and then creates an approximate solution by (exactly) solving these equations.

The term method of moments is derived from the use of moment, as in momentum, as a weighting function for multiplying a set of variables by before adding (or integrating) them. Sadiku traces the term back to a Russian literature origin.¹ It was popularized in the United States by Harrington, who used the name in the title of his seminal text on the subject.² The method of moments is a much more general technique than its application here portrays; the interested reader is encouraged to follow up with either of the above mentioned references.

Consider an unbounded space with a finite total area of ideal conductors present. Practically, of course, unbounded means everywhere, but the conductors that we are not considering are so far away as to be irrelevant to our discussion. The conductors can be either ideally thin (two-dimensional) ...