## Field Map Applications

This chapter presents a graphical procedure for generating two-dimensional field maps for uniform two-conductor circular geometries. The mathematics to create such maps is validated through the generation of field line graphs for two distinct fragments of a coaxial line. For this, an arrangement in parallel on the same plane of two of the infinite lines one with ρ, and the other with -ρ_{l}, can be used to model a two-wire transmission line. The potential field of this assembly is given by ()f=?l2?elnR2R1. Locating pairs of infinite lines at whichever angular plane, and assuming for the time being that the set of equipotential surfaces generated by the whole arrange as circles of any radius, eccentric at every line, then the distances R_{1} and R_{2}, in rectangular coordinates, may be expressed by ()R1=[x-(2b+p)cos ?]2+[y-(2b+p)sin ?]2()R2=(x-pcos ?)2+(y-psin ?)2. Where b is the distance from either line to origin O, p is an eccentric point that serves as new origin and axis of rotation.