Modification to Maxwell's Equations

Abstract

A fixed electric charge is an electric current relative to a moving magnetic field, so that it is subjected to the force of the moving magnetic field. This means that not only time-varying magnetic field produces electric field, but moving magnetic field produces electric field as well. Maxwell neglected this fact in deriving his equations for the description of dynamical behavior of electromagnetic field so that the two equations (A) $\nabla\cdot\bfE=\epsln_0^{-1}\rho$ and (B) $\partial_t\bfE-\epsln_0^{-1}\mu_0^{-1}\nabla\times\bfB=-\epsln_0^{-1}\bfJ$ are incorrect. In this paper we modify the equation (A) into $\nabla\cdot(\bfE+\overline{\bfu}\times\bfB)= \epsln_0^{-1}\rho$, where $\overline{\bfu}$ denotes the mean velocity of the charges in the electric current, and the equation (B) is correspondingly modified. The modified equations are invariant under Galilean transformation. As a byproduct of this work, we see that Einstein's theory of special relativity is wrong.