  It is shown that the well-known procedure for proving the equivalence of the
expressions for the electric field calculated using the Lorentz and Coulomb
gauges is incorrect. The difference between the two gauges is due to the
difference in the speed of propagation of a disturbance of the scalar
potential. As an auxiliary result, it is proven that the solution for the
electric field cannot be obtained directly from the Maxwell equations, i.e.
without introducing the scalar and vector potentials.
