New closed form expressions for calculating the magnetic field of thin conductors with longitudinal current direction introduction

In this paper, we present relatively simple expressions in the analytical form in order to calculate the magnetic fields of thin cylindrical finite conductors with current in longitudinal direction. The derivation presented here can be employed usefully to calculate the magnetic fields in more complicated geometries. They may also be used for computation of self and mutual inductances for systems with thin conductors [9]. The reduction of the mathematical complexity based on the above expressions makes it desirable for calculation of magnetic fields in various problems. The expressions, obtained in the analytical form, allow easy solving of fields at singular locations. The presented method can be simply applied to derive expressions for the computation of magnetic fields of various thin conductors with the current flow in the longitudinal directions, and whose angular lengths are arbitrary. In this case, all mathematical procedures will be expressed over incomplete elliptic functions of the first, second, and third kinds [8].