V.4 No 1

27

Study of dynamic scalar potential

Actually, for example, Kalitievsky in [11] gives the following derivation for the interference of two in-phase plane waves in the far field: "To simplify, let us think the sources S₁   and S₂  radiating plane waves of equal amplitude E₀: such admission is legal, as the distance D (from the sources to the observer - authors) is much more than 2l  (the distance between the sources - authors). All oscillations are directed equally, so we can think our problem scalar. We have

The field E created by the total oscillation will take the following appearance:

[11, p. 129]. As we can see from (33), the total strength of the field has the shape of modulated oscillations whose amplitude and phase depends on the distances from the field sources to the observation point. Noting that in accordance with [1]

we can reduce the correspondence between (33) and the interference pattern of the studied dynamic gradient of scalar potential. We see that the Kalitievsky's expression for the electric field total strength presents the progressive wave whose amplitude and phase depend on the ratio of distances between the field sources. On the basis of (26) we can easily yield for the near field the expression similar in structure to (33), but with much more complicated relationship for the delay phases which will depend not only on the difference of distances from the sources but also on the wave attenuation in space and on the angular characteristics of dipole at the point of observation. This fully corroborates the conclusion made in [10] that the pattern of standing waves in the near field, derived by now mere formally, follows from the inaccurate trigonometric transformations. And intentional inaccuracy, caused by the wish to match the derivation of Pointing vector with the field distribution in the vicinity of dipole, obtained on the basis of Maxwell equations. In a dipole, as we could make sure, standing waves in the near field are not inherent.

The third important feature of presented diagrams is that we corroborated the complicated pattern of scalar potential variation in space and time; this does not allow us to neglect it in dynamic fields calculation. Even in case of half-wave dipole, where in the normal to the line of charges the scalar potential is identically zero in time, anyway the gradient of potential does not vanish. And zero value of potential along the normal means only that the gradient of potential on this line is strongly perpendicular to the wave propagation.

Thus, we see that

1. the field of dipole has the structure of progressive wave both in the near and far fields;

2. transverse wave is formed in the region of junction of half-waves of scalar potential and propagates in some sector having the axis on the normal to the line of dipole charges;

3. in this region the curl of gradient of scalar potential is not zero.

Speaking of features of distribution of scalar potential of dynamic field in space and time, we would like to emphasise one more important point. Despite their rigorous causation and associativeness, the presented diagrams essentially differ from the experimental studies of EM field described in the scientific literature (see, e.g., [12]- [14]), because of conditions, how the field strength is measured in the experiments. We can easily prove it. As this feature is highly important for understanding of dynamic processes in EM field, we select this subject into a separate item.