Field of a Multilayer and Multiturn Coil with Analytically Set Laws of Variations in the Distances between Layers and Turns

Abstract

Design formulas for three-dimensional magnetic fields generated with a complex system of circular currents, which compose a multilayer and multiturn coil are derived. The distribution of a vector field in any spatial domain can be obtained by setting the analytic function that establishes the distances between turns and/or layers. It is revealed that under uniform winding and equal densities of surface currents, the magnetic fluxes of a single-layer coil and equidimensional axial magnetized cylinder are identical. The magnetic flux of the cylinder is calculated by the demagnetizing factor.