Magnetic field evaluation for thick annular conductors

The three-dimensional integration of the Biot-Savart law for conductors in annular sector shape, in which only a constant-density θ-directed current flows, is reported. The expressions obtained allow a quick and accurate evaluation of the components of the vector potential of the stationary magnetic field and of the magnetic induction due to this type of conductor, in iron-free media. The relations presented, together with similar expressions that are valid for other shapes of conductor and current distributions, can be useful for evaluating the magnetic fields in complex, linear, iron-free structures when the geometry can be well approximated with a series of current elements of elementary shape, for which the solution of Laplace´s equation is known in closed form