SELF

6

S.B. Karavashkin and O.N. Karavashkina

To connect the second summand in (10) with the vector potential, it will be sufficient if we assume for this model

to yield (1) in substitution (11) into (10). With it, (11) will satisfy the known relation [5, p. 106]

So we see in particular case of pulsing source, (1) is exact not only because the solutions yielded on its basis satisfy the divergence theorem in dynamic fields, but because this expression immediately follows from transformation of gradient of scalar potential in dynamic fields. With it the expression for the field strength can be written in general case as

where the right-hand part depends both on the field space distribution and on time.

3. Gradient of scalar potential of oscillating potential source

In the previous item we marked that a mismatched half-wave oscillator can be in general case considered as a superposition of point pulsing sources and shifting sources. Let us study the field created by the source oscillating along the axis x around its balance position, as shown in Fig. 4.

Fig. 4. Radiation of the source moving along the axis x

We can see from the drawing that as the result of source motion, not only the time delay between the near equipotential lines arises but also the direction of equipotential lines changes. As the result, the direction of gradient will coincide not with the extension of direction from the source S₀   to the point  P₀ , but with direction which it had when the source was at the point S₁ , and its equipotential line is at the moment at the point P₁ . Furthermore, we cannot now write down the equality similar to (9), since S₁P₀  S₀P₀ and, consequently,