New Consideration of the Skin Effect in Electrodynamics

Abstract The article proposes an approach to solving the normal skin effect problem based on integral equations derived directly from Ampère's circuital law, Faraday's law of induction and Kirchhoff's circuit laws, in contrast to modern solutions based on Maxwell's equations of electrodynamics in differential form. It is shown that the skin effect is mainly due to the electromotive force of the wire self-induction, which depends on the distance to the surface, and the influence of eddy currents is either very small or absent. New equations, their solutions and formulas for the total current and impedance are proposed for various technically significant cases immediately taking into account the inductance of the external space and in two versions: taking into account only the self-induction of the conductor; taking into account both self-induction and eddy currents. On the example of a solid cylinder, it is shown that, in accordance with the formulas of the existing approach itself, the current density on the surface of the wire does not increase with increasing frequency, as it is stated in words. It is shown that, in fact, the solutions of the existing concept are based not on eddy currents, but on the uneven distribution of elementary self-induction currents over depth and are completely equivalent to the variant of the presented solutions, taking into account only self-induction. Power balances were obtained without the introduction of a frequency-dependent active resistance to alternating current in two versions: based on the total current, voltage and average electromotive force of induction; based on the integration of the balance of specific powers over the entire volume of the wire. The physical meaning of the visual increase of the active resistance with increasing frequency is revealed, but certainly not on the basis of a decrease in the effective cross section of the wire. Based on the symmetry of the distribution of eddy currents, the assumption is made that they are absent in galvanically closed wires, but present in open wires such as antennas. An experiment was carried out with a negative result on the detection of the alleged thermal separation in the wire, an explanation for this was proposed.