When mathematics knocks physics or the true story of the layer copper factor

Summary form only given. In 1D analytical theories aimed at calculating winding losses in magnetic devices, one usually introduces a "layer copper factor" to account for layer porosity (i.e. several conductors per layer). The existence of this factor is accepted by anyone since 1966 although it leads to non-physical equations where the skin depth varies depending on the winding pitch. The author presents a theoretical discussion on the origin of the copper factor, and shows how it does not respect Maxwell equations, leading to non-physical conclusions such as a skin depth depending on winding pitch. The author also looks at non-physical models of the phenomena and shows via finite element analysis a specific 2D field effect occurring in typical round wire windings. The purpose of this paper is not to say that the layer copper factor cannot be used, but to show what it really is and that it comes from a tricky 1.5D model. Another purpose is to illustrate, as an interesting example, how theoretically wrong justifications have propagated from one paper to another during 35 years.