Evaluation of Current-Produced Two-Dimensional Magnetic Fields

Abstract

Formulas are developed for the two-dimensional magnetic field (and its derivatives of all orders) produced by a long straight conductor of uniform current density. These formulas are independent of whether the field point lies inside or outside the conductor and avoid ambiguities due to multiple values of the complex logarithm. Evaluation of the formulas can be done numerically, with the arbitrary conductor boundary approximated by a polygon, or graphically, or mechanically.