Research on the orientation of z-axis of the cylindrical coordinate system in the Sommerfeld integral

Abstract

In this paper, the z-axis orientation of the cylindrical coordinate system in the Sommerfeld integral is discussed. By the way of the rotation of coordinate system, the magnetic vector potentials of the current element in the homogeneous medium infinite space expressed by the Sommerfeld integral in different cylindrical coordinate systems are calculated, and verify that the z-axis don't have to be in the same direction as the current element. Furthermore, the expressions of the electric field intensity are deduced based on the magnetic vector potentials with the z-axis of cylindrical coordinate system parallel to the current element and perpendicular to the current element, and then a numerical example is given to demonstrate the orientations of the z-axis. The analyses contribute to understanding the mathematical meaning of the Sommerfeld integral and have the guiding meaning to solve the radiation problems of the current element.