V.4 No 1

19

Study of dynamic scalar potential

We can yield the similar result, considering the sound propagation from an ideal point source. According to Jeffreys [8], "The equation of sound propagation in 3 D space is

where   is the potential of velocity" [8, p. 138]. Noting that the momentary velocity of elementary volumes of linear continuum v is connected with the momentary shift by a simple relationship

(where is the momentary shift of elementary volumes of continuum from the position corresponding to the non-excited state), we can easily make sure that the modelling equations (19) and (20) are identical; this shows that the laws of wave process are general, irrespectively of the nature of medium in which it propagates.

The function of the kind

is the solution of (19), where C  is some constant having in the international system of units the following dimension:

To determine the value of this constant, we have to note that in the limiting case at 0 , (22) has to transform into Coulomb law

from which

where in this case q  determines the amplitude of charge variation of the pulsing potential source.

On the basis of yielded solution (22) for a single source, we can write down the expression for pulsing dipole. We should only note that the charges in the dipole change in anti-phase. Then for the model of dipole shown in Fig. 1, the total potential will be described as follows:

The connection between r₁  and   r₂ will be determined by (2), which together with (26) allows us, using the method of deformed grid, to plot the pattern of dynamic scalar potential produced in space by the dipole pulsing in time.