Complex Representation and Computation of Two-Dimensional Magnetic Fields

Abstract

The method of evaluating two-dimensional fields as analytic functions of a complex variable without resort to absolute values and complex conjugates is described and applied to the magnetic field produced by straight currents. Explicit formulas are derived suitable for numerical computation of vector and scalar potentials, of field components, and of field gradients for round and polygonal (including rectangular) conductors, current ribbons, and arrays thereof.