Computing the field near parallel straight conductors

Abstract

Incremental equations based on the conformal transformation (U+jV) = log (x+jy) are derived which enable the field near parallel straight conductors to be computed. Each line in the sets U = constant and V = constant is established by first fixing one point and then tracking along it. As an example, the magnetic field distribution near three straight conductors carrying symmetrical 3-phase currents at the instant when the current in one conductor is at its maximum, is derived. The method is extended to allow the potential gradient at any point in the field to be determined. This is illustrated by comparing the computed magnetic-field intensity between two parallel conductors, 2 m apart and carrying 1A (go and return), with that obtained by conventional theory. Other two-dimensional field problems can be dealt with in this way provided appropriate conformal transformations can be found. The method is particularly suitable for interactive computation with a graphical display facility.