Numerical calculation for the magnetic field in current-carrying circular arc filament

This paper introduces numerical calculations for the vector potential and the magnetic field in current-carrying circular arc filaments of arbitrary length. The analytical expressions which are derived in Cartesian coordinates for the vector potential and magnetic field consist of only complete and incomplete elliptic integrals of the first and second kinds and thus permit an efficient computation algorithm by applying arithmetic-geometric mean (AGM) numerical integrals.