The complicated history of electric units : implications on SI expressions

The International System of Units has only existed since 1946 and it was developed after a very long process that depended on the evolution of our understanding of electromagnetism. Cet article vise à mettre en lumière les imbrications entre mécanique et électromagnétisme qui ont conditionnées les choix d’unités. This article aims to highlight the interconnections between mechanics and electromagnetism that have influenced the choice of units. it appears that the choice of electrical units was conditioned by the predominant use of the electromechanical measurement system based on magnetic force, CGS EMU, to the detriment of the measurement system based on electrostatic force, CGS ESU. These two systems were incompatible and had a ratio in the speed of light. Furthermore, the expressions for these forces failed to account for the solid angle \(4π\), which consequently appeared unjustifiably in Maxwell's equations; the rationalization proposed by Heaviside resolved this problem. The article shows that this rationalization and incompatibility between these two systems necessitated, during their unification, the use of two constants to adjust the expressions for Ampère and Coulomb forces to the electrical units defined in the CGS UEM system. We call these constants the permeability and permittivity of free space.