The c equivalence principle and the correct form of writing Maxwell's equations

Details The c equivalence principle and the correct form of writing Maxwell's equations The c equivalence principle and the correct form of writing Maxwell's equations

2010-12-06

arxiv.org/abs/1012.1067v1

Eur. J. Phys. 31, 1177-1185 (2010)

Physics

Classical Physics

Scientific paper

10.1088/0143-0807/31/5/018

It is well-known that the speed $c_u=1/\sqrt{\epsilon_0\mu_0}$ is obtained in the process of defining SI units via action-at-a-distance forces, like the force between two static charges and the force between two long and parallel currents. The speed $c_u$ is then physically different from the observed speed of propagation $c$ associated with electromagnetic waves in vacuum. However, repeated experiments have led to the numerical equality $c_u=c,$ which we have called the $c$ equivalence principle. In this paper we point out that $\nabla\times{\bf E}=-[1/(\epsilon_0\mu_0 c^2)]\partial{\bf B}/\partial t$ is the correct form of writing Faraday's law when the $c$ equivalence principle is not assumed. We also discuss the covariant form of Maxwell's equations without assuming the $c$ equivalence principle.

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