V.4 No 1

21

Study of dynamic scalar potential

Actually, in accordance to [9],

where (r, , , t)  is some vector of dynamic flux, and is the unit vector of direction of wave propagation. If in this problem

(where we intentionally have put in the right-hand part the dynamic gradient of potential, emphasising the dynamic pattern of this vector and that we have to find it, noting the features described in [1]), then, substituting (28) into (27), we yield

Because in the above region of normal to the line of charges

the right-hand part of (27) will not vanish, as was to be shown.

It is easy to visualise this feature of dynamic fields, plotting the dynamic diagram of gradient of potential on the basis of the same initial data, for which we plotted the diagram in Fig. 5. For it, we have to take the same transforming grid and to deform each node not in direction of axis z, as in case of scalar potential, but in the same plane XY  - in direction of gradient of potential at each studied point. If on the chosen scale the amplitude of shift of grid nodes is proportional to the value of gradient of potential at the corresponding points, the resulting diagram will clearly show the gradient direction in space and time in the selected region.

Fig. 6. General appearance of non-excited transforming grid having quadratic calculated cells, with the difference in scale of the image in axes x   and y  (1:5)

In Fig. 6 we show such non-excited grid of the field with the fixed points of dipole charges location, on whose basis we will below plot the diagram of dynamic potential distribution. For the purpose of visualisation of transverse gradient of potential, it is desirable to show both the near and far fields in direction of normal to the axis of dipole charges; so we arranged the nodes in the area of grid irregularly. In this connection, though, as we said above, we calculated on the grid with quadratic cells, the visual representation has been transformed in relation 1:5; in our case it does not essentially affect the visualisation of field regularities, but enables us to see the maximally possible field of radiation in the direction of our interest.