Determination of the Magnetic Field around a Curved Conductor with Arbitrary Current Density Distribution

摘要

The paper presents an analytical method to determine the magnetic field around any circular cross section of a current carrying, curved conductor. The current density distribution over any cross sectional area is represented by a Fourier series which allows one to consider nonrotational distributions up to second order terms. By including the influence of the local channel curvature, the total magnetic field around such a conductor is expressed by the sum of short and far range fields. By means of this approach, one is able to relate the local conductor curvature and the current density distribution to the local, aximuthal magnetic field distribution and vice versa. The knowledge of this relation is important for determining static and dynamic effects on electrical, especially gaseous conductors. (Author)