Simple methods for converting equations between the SI, Heaviside–Lorentz and Gaussian systems

Abstract

School and undergraduate students are almost always taught the equations of electromagnetism using a set of conventions that are described as the SI. More advanced students are often introduced to different conventions that produce different equations for the same relationships, using either the Gaussian or Heaviside-Lorentz systems. In general, the connection between these equations is not simple. However, if the basis of each system is understood, conversion from SI equations to either Gaussian or Heaviside-Lorentz ones is very straightforward. The reverse processes are less straightforward, but more comprehensible when the fundamental differences are understood. Simple methods for these processes are presented, using a novel application of dimensional analysis, without factors of ε01/2 or (4πε0)1/2 appearing. It is also shown that when different physical quantities are given different symbols, and these are used consistently, the SI can be seen to provide general equations, with the Gaussian and Heaviside-Lorentz ones being simplifications of them. This removes any need for ‘system-independent’ versions of electromagnetic equations, with additional parameters that take different values in the different systems, which have been proposed in various forms over many decades.