SELF

22

S.B. Karavashkin and O.N. Karavashkina

For this plot, we can conveniently calculate the values of gradient of potential numerically, determining them in a small vicinity of each studied point per each axis x   and y , and then taking use of formulas

where x₀ , y₀ are the coordinates of nodes of non-excited grid, x₁, y₁ are the coordinates of corresponding nodes of transformed grid, x, y are the shifts in the coordinates x and y whose smallness is determined from the condition x, y << being the wavelength of radiation (in our problem we chose the shifts equal to 0,01), C_m is the scale factor, and r is the distance from the centre of dipole to the studied node of the grid. Furthermore, for better visualisation of general pattern of the field, in (31) we multiplied the deforming part into the distance of the studied node of grid from the centre of dipole.

We preferred the numerical technique to find the gradient before that analytical shown in [1], because of simpler and faster calculation. The numerical calculation of (31) allows to take into account immediately and quite accurately the variation of phase of gradient of dynamic field scalar potential without mathematical complicacy that appears with analytical technique shown in [1], and to avoid the discussion of legitimacy of such or other way to find the gradient of scalar potential. But in deeper study, the analytical technique is preferable, of course.

The results of this plotting are shown in Fig. 7.

Fig. 7. Dynamic diagram of gradient of scalar potential of dynamic dipole having the length equal to the half of wavelength

In this diagram we can clearly see the angle forming in the normal of dipole, in whose limits the wave with transverse gradient propagates. With it, seemingly, the varying inclination of gradient of potential has to be smoother with the growing angle from the normal of dipole, but the transition is quite clear. We can find the answer in the scalar potential distribution in Fig. 5. Looking at the region of transition, we see, the half-waves coincide in a limited region in the vicinity of normal to the line of charges. This transition region just forms the angle within which the transverse wave forms. We should mark that we had to increase a little the scale factor in (31) in order to visualise better the transverse wave; this caused small distortions in the line of dipole charges. In reality, there is no front in this region and the velocity of excitation propagation is equal to the propagation velocity of transverse wave towards the normal to dipole, as we can see it in Fig. 5.