In the thread Rain static I referred to a closed surface which is
clearly
defined by Gauss's law. Let us now look at a time vary field applied to

a dielectric. I fht efield is applied for the shortest of time the
charges
will stay on the surface. If time is longer than the shortest space of
time
then charges will openetrate the closed surface. If the surface is an
insulator type then it takes a long while to penetrate but if the
surface
is a good conductor then the charges will penetrate very quickly so
we can associate the time constant of penetration to the subject of
skin depth. If we are to associate the time varying field to a
gaussian field
all the excess charges must be on the surface by law. Or in other words
the time evolved must be shorter than the time required to begin
penetration.
Thus for a short space of time all charges are on the surface and the
charges
have a magnhe radiating eneetic and electric field vectors. Just having
charges is not enough to convert to a gaussian field in that a gaussian
field must be in equilibrium thus a cluster of elements
must have the direction of the surface charges change in unison. For a
cluster of elements to do this they must all be resonant such that the
charges reach the ends of the elements at the same time. Resonance of
an element is determined by its diameter and its length and because it
is coupled to other elements in the cluster the coupling must be taken
into account to secure resonance of not only the individual elements
but of the cluster as a whole. When this is accomplished the charges on
the surface of the closed volume are in equilibrium but onty for that
shortest of short time and where that time is added to the gaussian
formulae for the transition to be complete. For the Gaussian field or
volume we can say the energy inside the gaussian field is equal to that
supplied by flux to the outside of the border and remember the flux
inside consists of magnetic and electric vectoirs. We now can say that
in a moment of time the flux produced from each element that breaches
the border in summation with the other elements is equal to the
radiating field outside of the border when each element energy makes
the transmittion. Thus the summation of each of the clustered elements
individual energy when the vectors are given a value
must equal the flux on the outside of the border that produces
radiation. We also know that if we have a cluster of elements that are
clustered together we can obtain radiation by just applying a time
varing field to just one of the elements and by virtue of intercoupling
all the radiating energy
will leave the near field. Thus we have two different methods of
determining the value of the radiated field
! radiation from the clustered within a Gaussian field and
2 radiation from an array of coupled elements
Since the elements within the cluster are all of the same "Q'" the
determination of all factors
in the resulting equation are simplified to Ohms law and where the
laborious coupling calculations
are omitted. The above describes in first principles as to how a
Gaussian field in a short space of time can be equated to a radiating
cluster using existing laws of the masters which also embraces NEC
code. Now many have said I have no understanding of radiation concepts
so go ahead and tear this apart and have a merry Xmas doing it
Art Unwin KB9MZ..........XG