Vector potential and magnetic field of current-carying finite arc segment in analytical form, part II: Thin sheet approximation

Analytical expressions for the components of the vector potential and magnetic field of a thin circular conic cylinder segment of arbitrary azimuthal and axial length, and carrying a constant peripheral current are derived. All the expressions developed consist of known functions such as Jacobian elliptic functions, and complete and incomplete elliptic integrals of the first, second, and third kind and thus permit a new time-saving efficient computation algorithm.