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S.B. Karavashkin and O.N. Karavashkina

In this view, consider the acoustic field producing in a gas medium by the system of sources radiating in anti-phase, as shown in Fig. 1. According to the vector diagram presented in this figure, the resulting displacement of gas molecules is perpendicular to the propagation direction of the resulting acoustic wave. This effect is conditioned neither by viscosity nor by the presence of solid bounds, and it is not limited by the close region of acoustic near field. If the studied region was at a large distance r  from the presented acoustic dipole, then for each half of dipole we can write [5, p.38]:

where ₁  and ₂  are the unit vectors from the half-oscillators to the observation point.

Summing (5) vectorially, we yield

where   is the unit vector of resulting velocity of molecules vibration in an elementary region. With symmetrical location of ₁ and ₂  relatively to the perpendicular to the resulting wave propagation direction (see Fig. 1) and with v₁ = v₁ , the vector   is perpendicular to too.

Thus, on one hand the resulting sound field remains potential, since it is produced by linear superposition of strongly potential fields, but on the other hand, the resulting velocity of molecules vibration is perpendicular to the wave propagation direction. Consequently, in the conventional viewpoint, this sound field, being vortical, cannot exist in gas medium.

When studying electromagnetic fields, we see the contrary. As is known, just the transversal waves correspond to them, and the induction pair of Maxwell equations has non-zero right part for the region free of sources and currents:

where c  is the light velocity in vacuum. At the same time, ''an electrical dipole whose charges alternate in time under an extraneous source action can be presented as a system of two metallic spheres connected by a conductor to whose middle the extraneous source is included... The alternating charge is equivalent to the alternating current in the connecting conductor. Due to it, the field produced by a variable-momentum electrical dipole will coincide with the field produced by a l-long conductor in which the extraneous current runs... Such dipole field radiation offers to solve the problems of analysis and synthesis of antennas, as we can consider them as dipole systems'' [6, pp.96-97]. The same, ''an oscillating dipole is equivalent to an antenna with the current J = J₀ cos t  uniformly distributed along the entire length l of antenna'' [7, p.432]. Noting that each charge separate radiation is potential for such dipole, we come to the same problem otherwise. On one hand, the resulting transversal EM field is formed by two potential sources of an electrical field, so it must be potential. But on the other hand, the field itself is transversal, therefore it must be vortex by its definition. It leads to the fact that with an electrostatic field strong potentiality, ''the time-alternating electric field, unlike electrostatic fields, has, generally speaking, vortical pattern'' [8, p.34]. And the electrical field lines have been closed with the consideration that ''electric field lines cannot begin or finish in the empty space'' [9, p.291].

In this paper we will show that these problems in many respects are caused by the difference between stationary and dynamical lines of force, which was studied by the example of divergence of vector in [10]. We can expect that the curl of vector determining the field to be solenoidal will reveal in dynamical cases the peculiarities different from those known - the peculiarities that up to now were disregarded, because the conventional vector algebra basic regularities were limited by stationary fields.