ABSTRACT
This chapter focuses on two-dimensional solutions using finite-element methods with triangular elements. Integral relationships applied over the elements lead to a set of coupled difference equations for electrostatic potential values at the vertices. The chapter reviews principle of electrostatics and covers Coulomb's law, the foundation of electrostatics. It shows how to represent forces resulting from large numbers of charged particles. The chapter applies Gauss’ law to small volumes to find differential relationships, the electrostatic Maxwell equations. It introduces the computational mesh, where the solution volume is divided into elements. The chapter shows how the application of Gauss’ law in Cartesian coordinates over the elements surrounding a vertex yields a simple difference relationship between the potential at the point and its neighbors. The resulting set of coupled linear equations can be solved on a digital computer. The chapter extends the derivation to three-dimensional systems with cylindrical symmetry.
