Fast Calculation of Magnetic Fields Produced by Rectangular Cross Section, Arc-Shaped Conductors

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