Magnetic field and forces in a pair of parallel conductors

Abstract

The article provides a comprehensive idea of the calculating the magnetic field and forces in a pair of parallel solid conductors. The conductors are connected to a sinusoidal voltage source of a frequency that does not exceed 1 MHz. Thus the current density over the conductor cross sections is not constant. Its distribution depends on the distance of the conductors and their resistivity, on the shape of conductor cross sections, and on the voltage source frequency. The distribution of current density over the conductor cross sections affects not only the magnetic field produced by the conductors but also the forces acting on the conductors. For the acting forces, general conclusions are derived that hold for conductors of arbitrary shape of cross section. Specifically, pairs of conductors of rectangular, circular and triangular cross section are examined.