ABSTRACT
This chapter focuses primarily on potential functions that can be described by the superposition of individual line charges. Both indirect and direct methods are developed. Indirect methods describes the approach where the potential function is known and the physical situation it describes needs to be found. Direct methods describes the approach where the physical problem and boundary conditions are known and the potential function needs to be found. Indirect methods are demonstrated through the use of the complex potential for a single line charge and two opposite line charges. For direct methods, Green's functions are introduced. The primary method for obtaining the required Green's function is the method of images. The largest obstacle when applying the method of images is determining the location and value of each image charge. The method of ray tracing is developed to overcome this obstacle for planar boundaries. Although this approach is only useful for planar boundaries, the development of conformal mapping in subsequent chapters allows extending the results to other geometries.
