Faraday versus Maxwell ________________________________________________ 561
For the last not yet explained terms at first are written down the vectors b and j as
abbreviation. With equation 27.13 we in this way immediately look at the well-known law
of Ampere (1
st
Maxwell equation). The comparison of coefficients (27.15) in addition
delivers a useful explanation to the question, what is meant by the current density j: it is a
space charge density consisting of negative charge carriers, which moves with the
velocity v for instance through a conductor (in the x-direction).
The current density j and the to that dual potential density b mathematically seen at first
are nothing but alternative vectors for an abbreviated notation. While for the current
density j the physical meaning already could be clarified from the comparison with the
law of Ampere, the interpretation of the potential density b still is due. From the
comparison with the law of induction (eq. 27.1*) we merely infer, that according to the
Maxwell theory this term is assumed to be zero. But that is exactly the Maxwell
approximation and the restriction with regard to the new and dual field approach, which
roots in Faraday.
In that way also the duality gets lost with the argument that magnetic monopoles (div B)
in contrast to electric monopoles (div D) do not exist and until today could evade every
proof. It thus is overlooked that div D at first describes only eddy currents and div B only
the necessary anti-vortex, the potential vortex. Spherical particles, like e.g. charge carriers
presuppose both vortices: on the inside the expanding (div D) and on the outside the
contracting vortex (div B), which then necessarily has to be different from zero, even if
there hasn't yet been searched for the vortices dual to eddy currents, which are expressed
in the neglected term.
Assuming, a monopole concerns a special form of a field vortex, then immediately gets
clear, why the search for magnetic poles has to be a dead end and their failure isn't good
for a counterargument: The missing electric conductivity in vacuum prevents current
densities, eddy currents and the formation of magnetic monopoles. Potential densities and
potential vortices however can occur. As a result can without exception only electrically
charged particles be found in the vacuum (derivation in chapter 4.2 till 4.4).
Because vortices are more than monopole-like structures depending on some boundary
conditions, only the vortex description will be pursued further consequently.
Let us record: Maxwell's field equations can directly be derived from the new dual
field approach under a restrictive condition. Under this condition the two approaches
are equivalent and with that also error free. Both follow the textbooks and can so to speak
be the textbook opinion.
The restriction (b = 0) surely is meaningful and reasonable in all those cases in which the
Maxwell theory is successful. It only has an effect in the domain of electrodynamics. Here
usually a vector potential A is introduced and by means of the calculation of a complex
dielectric constant a loss angle is determined. Mathematically the approach is correct and
dielectric losses can be calculated. Physically however the result is extremely
questionable, since as a consequence of a complex s a complex speed of light would result
(according to the definition
With that electrodynamics offends against all
specifications of the textbooks, according to which c is constant and not variable and less
then ever complex.
But if the result of the derivation physically is wrong, then something with the approach is
wrong, then the fields in the dielectric perhaps have an entirely other nature, then
dielectric losses perhaps are vortex losses of potential vortices falling apart?
562
Derivation of the potential vortices
•
Maxwell's field equations:
•
describe the special case for b = 0 resp. div B = 0
The physical meaning of the introduced
abbreviations b and j is:
•
the current density
(27.15)
•
with Ohm's law
(27.16)
•
the potential density
, (27.17)
•
with the eddy current time constant
(27.16* >
•
and with the potential vortex time constant
The complete field equations (27.12 and 27.13) read, with the time
constants
of the respective field vortex:
• completely extended law of induction (with B = H): (27.18)
(27.20)
• and the well-known law of Ampere (with D = E): (27.19)
(27.21)
Fig. 27.10: The extension of the law of induction for
vortices of
the electric field (potential vortices].
: see also fig. 5.1
Faraday versus Maxwell
563
27.10 Derivation of the potential vortices
Is the introduction of a vector potential A in electrodynamics a substitute of neglecting the
potential density b? Do here two ways mathematically lead to the same result? And what
about the physical relevance? After classic electrodynamics being dependent on working
with a complex constant of material, in what is buried an unsurmountable inner
contradiction, the question is asked for the freedom of contradictions of the new approach.
At this point the decision will be made, if physics has to make a decision for the more
efficient approach, as it always has done when a change of paradigm had to be dealt with.
The abbreviations j and b are further transformed, at first the current density in Ampere's
law j = -
(27.15), as the movement of negative electric charges. By means of
Ohm's law j=
E and the relation of material D= E the current
density j also can be
written down as dielectric displacement current with the characteristic relaxation time
constant
(eq. 27.16) for the eddy currents. In this representation of the law of
Ampere (eq. 27.21) clearly is brought to light, why the magnetic field is a vortex field,
and how the eddy currents produce heat losses depending on the specific electric
conductivity
As one sees we, with regard to the magnetic field description, move
around completely in the framework of textbook physics.
Let us now consider the dual conditions. The comparison of coefficients (eq. 27.12 +
27.17) looked at purely formal, results in a potential density b in duality to the current
density j, which with the help of an appropriate time constant founds vortices of the
electric field. I call these potential vortices (in eq. 27.20).
In contrast to that the Maxwell theory requires an irrotationality of the electric field,
which is expressed by taking the potential density b and the divergence B equal to zero.
The time constant thereby tends towards infinity. This Maxwell approximation leads to
the circumstance that with the potential vortices of the electric field also their propagation
as a scalar wave gets lost, so that the Maxwell equations describe only transverse and no
longitudinal waves. At this point there can occur contradictions for instance in the case of
the near-field of an antenna, where longitudinal wave parts can be detected measuring
technically, and such parts already are used technologically in transponder systems e.g. as
installations warning of theft in big stores.
It is denominating, how they know how to help oneself in the textbooks of high-frequency
technology in the case of the near-field zone
. Proceeding from the Maxwell equations
the missing potential vortex is postulated without further ado, by means of the
specification of a ,,standing wave" in the form of a vortex at a dipole antenna. With the
help of the postulate now the longitudinal wave parts are ,,calculated", like they also are
being measured, but also like they wouldn't occur without the postulate as a result of the
Maxwell approximation.
There isn't a way past the potential vortices and the new dual approach, because no
scientist is able to afford to exclude already in the approach a possibly authoritative
phenomenon, which he wants to calculate physically correct!
: Zinke, Brunswig: Lehrbuch der Hochfrequenztechnik, 1. Bd., 3. Auflage 1986
Springer-Verlag Berlin, Seite 335