39 - 40 - 41

On longitudinal electromagnetic waves

(Moreover, by the condition of the field calculation   r >> l , consequently,  r  does not vanish, as it exceeds the limits of solution reliability).

Proceeding from that, (2-3-10) has to take a normal form

As we can see, (33) describes the progressive wave; it means that the longitudinal component of the field  _r has, none the less, the wave nature, and in the view of progressive nature of wave propagation it is illegitimate to divide the field of radiator into the near and far fields. Both in the near and far fields the wave is progressive.

One would think: having determined such important characteristic, we can consider the Pointing vector for a longitudinal wave:

However here we are running into a double complication caused again by the invalid simplifications and omissions. First, if we try substituting the corrected system (33) into the system of Maxwell equations, this will not work because of phase shift by  /2  between (t - r)  and  (t - r) . For example, when substituting (33) into the equality

in the left-hand part of the sum the uncompensated term

appears, and it must be equalised to zero with all consequences. Given the derivation of field equations, conducted by Kugushev and based on the standard field theory formalism, coincides in its technique with that conventional, the incorrectness of simplifications was caused not by the author's inattention but it was a compulsory action to retain the structure of the formalism based on Maxwell's equations. This conclusion can be corroborated simply by way of analysing the second pair of Maxwell's equations

41

by analogy with the pair of Maxwell's equations

Second, the vectors  _r  and    anyway must not be combined, because    was created by way of variation of   , i.e., of the transversal wave vector. So for   the Pointing vector

is true.

The vector of the magnetic field strength  _?   created by  _r  was not present in the consideration at all, though, as we pointed above, according to Maxwell's equations,

and if  _r  had the wave pattern,  _?   must exist and must have the form of solenoidal vector around the force lines   _r   (see Fig. 3).  _?  was absent in the consideration just due to its axial nature, because conventionally the only component of magnetic field    is a linear vector.