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 the magnetic field produced by arc-shaped conductors, which are characterized by a rectangular cross section. Available procedures are based on the analytical integration of Biot-Savart's law, but most of them exploit the analytical integration along one coordinate and then perform a 2-D numerical integration. In the proposed procedure, the analytical integration was performed along two coordinates, obtaining a 1-D integrand (thus avoiding the use of elliptic integrals), which is 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 the conductor surface, and when its cross dimensions are very uneven.