Resolution of the inconsistency of the initial laws of electromagnetism, implications and perspectives

The inconsistency in the initial laws of electromagnetism inspired Maxwell, but it was not resolved because it was circumvented by the use of constants when creating the SI.The objective of this theoretical study is to resolve the inconsistency and fill this gap in electromagnetism. Cartesian analysis was used. After a historical summary that recalls how the inconsistency was circumvented without being resolved, we observe that the failure to consider the speed of light in the initial laws is the cause of its presence in the ”measurements” deduced from the expressions of these laws. This ”encystment” is the origin of the inconsistency between the CGS EMU and CGS ESU measurement systems. The incompatibility of these systems is then mathematically eliminated by identifying this inappropriate presence and removing it. It follows that the speed of light affects the intensity of the phenomena. The speed of light acts as a multiplier parameter for the electrostatic force and as a dividing parameter for the magnetostatic force. It is shown that the permeability and permittivity of vacuum are compound constants: µ0 =K/c and 1/ε0 = K.c and that the value of the vacuum impedance Z0 = K depends only on the construction of the unit system. The physical interpretation of these results and their implications are particularly interesting perspectives.