We begin this chapter by examining a two-dimensional (2d) rectangular structure. Extending the analysis to three-dimensional (3d) structures in rectangular, cylindrical, or spherical coordinates is straightforward and will be discussed later. Also, for now consider only prescribed voltage boundary conditions.

Laplace’s equation in rectangular coordinates is

(8.1)

For a uniform structure infinitely long in the Z direction, all partial derivatives with respect to Z vanish, leaving us with the 2d equation

(8.2)

Figure 8.1 shows a rectangular grid of points in 2d space.

The lines in the figure are just for our eyes to follow easily. Of interest are the intersections of these lines, which we’ll call nodes. The X-axis separation of nodes is h_{x} [equation (8.3)]; the Y-axis separation of nodes is h_{y} [equation (8.4)]:

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