The Laws of Interaction of Currents and Charges and the Determination of Magnetic Field

Abstract

Different versions of the interaction of current elements and moving charges, written in vector form, starting from the Ampère theory, are considered. It is shown that from the point of view of the classical two-body problem the most adequate is the Gauss-GrassmannNeumann theory. An expression is obtained for magnetic induction created by a moving current element, which, in addition to usual Biot-Savart-Laplace law, includes additional terms due to both the electron spin and the mutual displacement of elements.