Abstract

There are two versions of Maxwell's equations. The classical version uses the Coulomb gauge and the relativistic version has electrodynamic potentials fulfilling the non-homogeneous equations for waves. With the use of the Lorenz gauge such equations have been obtained from the fourth Maxwell's equation and the equation for potentials of vector of electric intensity E. We show that the last equation after differentiation in time and multiplication by dielectric permittivity is similar to the fourth Maxwell's equation. We also show that after obvious corrections the equations are equivalent. We claim that in the fourth Maxwell's equation, instead of the vector of electric current density j, its irrotational component should only be applied. We also claim that in the equation for potentials of vector  E instead of vector A there should be only its solenoidal component. It is shown that the corrected form of these two equations is fully consistent with the rest of Maxwell's equations. As the result of replacing vectors j and A by their proper components the problem of different gauges disappeared. Only one gauge i.e. that of Lorenz with a changed sign is shown to be necessary. As the result of the proposed modification in the case of waves, the wave equations for the potentials - as well as for the field vectors - are homogeneous. It is not so in the relativistic version of Maxwell's equations. We claim that the classical Maxwell's equations in the proposed version are fully consistent, satisfactory and do not fit the Special Relativity Theory.