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S.B. Karavashkin

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which gives after the transformation

where  ₀ = t - (x/c), and denotes an unit-vector from dV '  to the observation point, "because the charge density is taken at the same moment at all points of the system" [1, p. 105].

This enables Levich to conclude the following [1, p. 106]:

It automatically follows from (4) that when   is at right angles to , the scalar potential of charges system vanishes, though   is non-zero.

Show that just this regularity was the basis to derive the EM wave pure transversal, though we can notice that in the view of general potential equation the inference (4) is not obvious. Actually, it is no less known that a charge system to produce a monochromatic radiation, all elementary regions of the picked out region V ' must be in resonance. Given

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(where is the velocity of charges density shift in an elementary region dV ' ), we can require the synchronism of  ()  for all elementary regions dV '   and deal with some averaged characteristic  (₀). Then the second equation of (1) takes the following form:

So we come to the basically other result which in case of perpendicular to remains the value of scalar potential, only reflecting the fact of perpendicularity of   to but not vanishing , and this is more logic.

It is interesting that this result fully coincides with the inference for the field potential of an arbitrarily moving unit charge [1, p. 98]:

where ₀ is the vector potential of momentary velocity of the charge. Hence there are two regularities between the potential in the conventional field theory:

the Lorenz calibration

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and

We can add that, as by the statement of problem the studied region V '  does not move and the radiation is produced on the account of space redistribution of the charges density, (, t)  and (₀)  are interrelated through a definite regularity. Therefore, in the absence of charge density shift in the region V ', their shift velocity is absent too and scalar potential remains constant. In other words, we can introduce the condition that at

Basing on the yielded, follow the derivation of condition of the EM wave transverseness by Landau: "Consider a plane wave going in a positive direction of the axis x. In such wave all values, and in that number, are the functions only of  (t - (x/c)) . From the formulas

we find that

where the prime means the differentiation with respect to   (t - (x/c))  and   is the unit vector along the wave propagation. Substituting the first equation by the second, we yield