Vector potential and magnetic field of current-carrying finite arc segment in analytical form, Part III: Exact computation for rectangular cross section

Analytical expressions for the components of the vector potential and magnetic field of a circular arc segment of a current-carrying conductor of rectangular cross section and arbitrary azimuthal length are derived. Components of the field gradient are also calculated. All the expressions developed consist of known functions such as Jacobian elliptic functions, complete and incomplete elliptic integrals of the first, second, and third kind, and thus permit a new timesaving efficient computation algorithm.