It is pointed out that the wave equation of electrodynamics contradicts the law of conservation of energy and therefore the solution of the system of Maxwell's equations must and can be replaced by another one in which this law is observed. This solution allows us to determine the vector potential, as a consequence of the system of Maxwell's equations. It turns out that, in the general case, the existence of a vector potential contradicts the system of Maxwell's equations. However, nevertheless, there is one case - an electromagnetic wave without longitudinal strengths. In this case, the vector potential exists and becomes proportional to the magnetic strength vector. The calibration of the vector potential, which introduces subjective arbitrariness into physics, becomes unnecessary.