Algorithm for the Fast Calculation of Magnetic Fields Generated by Arc-Shaped Conductors with Rectangular Cross Section

This paper presents a novel procedure for the fast numerical integration of magnetic field produced by arc-shaped conductors, characterized by rectangular cross section. Available procedures are based on the analytical integration of Biot-Savart\u2019s law but most of them exploit the analytical integration along one coordinate, and then perform a two-dimensional numerical integration. In the proposed procedure, the analytical integration was performed along two coordinates, obtaining a one-dimensional integrand (thus avoiding the use of Elliptic Integrals), very easy to process using a state-of-the-art numerical quadrature library. The result is very satisfactory in terms of high speed and precision, particularly on conductor surface, and when its cross dimensions are very uneven