V.4 No 1

3

On gradient of potential function

2. Gradient of scalar potential of point pulsing potential source of field

Let in unbounded homogeneous space free of charges and currents be a point source. Let us put to this point the origin of spherical reference frame, and let the charge of this source vary in time harmonically.

At the first glance, such statement of problem can seem unrealisable practically, though this is not so. For example, if we consider as such source a system of radial dipoles whose charges shift synchronously, as we can see it in Fig. 1, we will obtain a practical analogue of considered model.

Fig. 1. Radially located dipoles: positive charges are shown in red, and negative charges - in blue

Actually, if in this system of radial dipoles the maximal length of each dipole is equal to a half-length of radiated wave, then on the surface of sphere enveloping this system of dipoles we will observe the synchronous variation of charge in time. Looking now at this sphere at much more distance than its size, we will yield a practically ideal analogue of the above pulsing point source.