Preface to the lecture, 1

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?

 

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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

 

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