TECHNIQUES FOR EVALUATING THE UNIFORM CURRENT VECTOR POTENTIAL AT THEISOLATED SINGULARITY OF THE CYLINDRICAL WIRE KERNEL

The cylindrical wire kernel possesses a singularity which must be prop erly treated in order to evaluate the uniform current vector potential . Traditionally, the singular part of the kernel is extracted resultin g in a slowly varying function which is convenient for numerical integ ration. This paper provides some new accurate and computationally effi cient methods for evaluating the remaining singular integral. It is sh own that this double integral may be converted to a single integral wh ich no longer possesses a singular integrand and consequently may be e fficiently evaluated numerically. This form of the integral is indepen dent of the restrictions involving wire length and radius which are in herent in various approximations. Also presented is a highly convergen t exact Series representation of the integral which is valid except in the immediate vicinity of the singularity. Finally, a new approximati on is derived which is found to be an improvement over the classical t hin wire approximation. It is demonstrated that each of these methods provides extremely accurate as well as efficient results for a wide ra nge of wire radii and field point locations.