ABSTRACT
In this chapter, the theory of 2D electrostatics in terms of complex variables is developed. The development begins by establishing the requirements for 2D analysis to be valid and introduces the 2D equivalent of Coulomb's law. In addition to the standard electromagnetic quantities and concepts, the complex variable treatment allows defining a complex potential. The complex potential is an analytic function with the real part equal to the electrostatic potential in regions free of charge. With the complex potential, the visualization of the electric field is accomplished with field maps. With the concept of field maps established, the method of curvilinear squares is then developed allowing the estimation of the capacitance and stored energy of different regions based on the field map of the region. Although the complex potential is only valid in regions that obey Laplace's equation, a method for transforming Poisson's equation into Laplace's equation is introduced which extends the use of the complex potential into regions containing charge.
