A simple derivation for the skin effect in a round wire

The skin effect in a round wire is an important electromagnetic phenomenon with practical consequences; however, it is usually not presented in any detail at the undergraduate level but reserved for graduate study. The purpose of this paper is to remedy this situation by providing a simple derivation for the skin effect in a round wire that only requires background usually familiar to these students: Maxwell's equations in integral form, integral calculus (specifically integration of a power) and some elementary properties of series. Graphical results are used to clearly show the current concentrating near the surface as the frequency increases and the accompanying increase in the resistance and decrease in the inductance of the wire. A brief review of the history of the subject shows that several of the scientists familiar to students made contributions to our understanding of the skin effect in a round wire; they include J C Maxwell, Lord Rayleigh, Lord Kelvin, O Heaviside and J J Thomson. The validity of the theory is demonstrated by comparing results from the theory with resistances and inductances measured by some of the early pioneers of wireless communication. (paper)