Electromagnetic Waves in Maxwell’s Theory

Abstract

The description of a plane traveling electromagnetic wave existing in the physical literature by identical solutions of wave equations for the strengths of electric and magnetic fields is physically incorrect, since such solutions contradict the physical meaning of Maxwell’s equations and violate the energy conservation law. The paper gives a physically correct description of electromagnetic waves in the framework of Maxwell’s theory. New solutions of Maxwell’s wave equations for traveling electromagnetic wave are proposed, in which the strength of its electric and magnetic components change in time with shifts of a quarter of the period and a quarter of the wavelength along coordinate. The solutions describe a traveling electromagnetic wave, in which the energy of the electrical component is sequentially converted into the energy of the magnetic component and vice versa; the total energy density of the lossless wave remains constant in space at any time; the mutual orientation of the intensity vectors of the electric, magnetic fields and phase velocity changes from a left-handed three to a right-handed three every quarter of the wavelength; the energy flux density of the traveling wave is described by the Umov vector. It is shown that the formation of a standing electromagnetic wave does not require the loss of half a wave of one of the components of the wave reflected at the interface between the media. In a standing wave, the total energy density remains constant in time, but it is a function of coordinates: there are points in space where the total energy density of the wave at any time is zero – these are nodes, and there are points where it has a maximum value – these are antinodes. Due to the inhomogeneity of the distribution of the total energy density of the wave in space, a standing electromagnetic wave cannot be considered as a harmonic oscillator, but a lossless traveling electromagnetic wave can.