Crossed Field Antenna Theory

Dr. KABBARY's NEW EM EQUATIONS

NEW ElectromagneticEquations
CFA Antenna group - RGIT

This is to show that the present Electromagnetic Equations of Jim Clerk Maxwell are in trouble and in need for major corrections to find the solutions for many unsolved applied physics applications as the present uncontrollable nuclear fusion projects (e.g., the previous JET project) to save more future decades of years will be consumed trying to solve the plasma dynamic stability problems,where the present shape of Maxwell's equations were the reason behind the delay of success of these projects and many other projects .

We can offer solutions when requested from us.

This article can also explain the atomic radiation mechanism , nd will show that the displacement current D' is the only source of the magnetic field H .This was proven by our antenna group and been published 15 years ago in IJEEE, OCT. 1990 .

Also, it is well known that Einstein was defeated to prove the wave particle duality because he used the present (uncorrected) Maxwell's equations. Maxwell's equations were hard to solve because the fourth Maxwell equation was not correct , to use the conduction current as a source of the magnetic field , it is naturally one source for H was proven as D'.

This work was started by our antenna group of Scotland (kabbary , Stewart and Hately ) , and had reached its final stage later in Egypt.

The present antenna theory is full of the well known many approximations, assumptions and the unknown near field mechanism of field reaction of building wave propagation or power radiation, only the assumed far field, and its magnetic vector potential related to the assumed sinusoidal (of no proof) current distribution on the antenna elements, using moment methods and mode theory; both full of the severe approximations of the phase relationship in both macro and the neglected microscopic level, this microscopic level in which field reactions occurs. The near field mechanism is unknown by antenna scientists , and the NEAR pure real radiation is impossible to measure .

When one can measure the magnetic vector potential A , sure he will be able to measure the near pure radiating field , but now it is the mixtureof induction and radiating field which is measured by PI or other field strength devices .

The major discovery we have reached was that the displacement current ( time varying electric field ) has appeared in D.C. circuits, while all textbooks have shown that the displacement current is zero in D.C. circuits, but we found it is not zero! This was enough to put the fourth Maxwell's equation in trouble and needs major correction , confirming that the direct source of the magnetic field is the displacement current ( D' ) , not the conduction current ( J ) for both D.C. and AC circuits, and the ( J ) term is not any more a source of any field, but only is the current flow rate no more.

We shall confirm now that Ampere's law does not exist, i.e. the J conduction current became not anymore the source of the magnetic field H for either D.C. circuit or A. C. circuit .

Ampere has discovered his phenomenon which was magnetic field lines wereappeared as circles around the current passing in a conductor; this was before Maxwell's time, then Maxwell came and was worried about charge conservation problem, ignoring energy conservation, and he mathematically turned Ampere's phenomenon into real law as follows ::

Ampere's law: ( J = curl H ), was

added it to Maxwell's law: (D' = curl H) ,

to give his fourth equation: (J + D' = curl H)

How naturally or physically the magnetic field is produced form two different Mother sources J and D' , it is elegant Nature to get some have one Mother D' , not more.

This means that either J term or D' term has to be dropped form the fourth Maxwell's equation to have only one source for the magnetic field, and not having doubled measured magnetic field H.

Theory:

Consider a fixed point P (stationary frame) close to one moving charge at constant velocity v in the z direction , in microscopic level, i.e., D.C. condition, as shown in the figure 1 drawn below.

Through the fixed frame point P, gives rise to time-varying electric field and thus displacement current D' appears at that point P (see figure 1) located inside the conductor under D.C. condition. So, in D.C., the AC component D' has appeared; while textbooks have considered D' is zero for D.C.

From Maxwell's Law, the resulting magnetic field distribution surrounding the moving charge is evaluated from the vector reaction equation.

D' > curl H

This is to show that the direct source of the magnetic field H is the displacement current D' not J in D.C. circuits , as well as D' has appeared in D.C., which is a new discovery too. This is exactly equal to the magnetic field created when D.C. current J was moving in the conductor.

So, for D.C circuits . Ampere's law becomes Maxwell law and Ampere's law does not exist anymore. This means the fourth Maxwell 's equation has been reduced to Maxwell law and J became useless term for radiation or wave propagation.

The new electro-magnetic equations became now, for the century:

p > div D

0 > div B

B' > - curl E

D' > curl H

(The J term is defined as nqv but can not be a source of magnetic field ,it is only charge flow rate)

The above four equations are causality equations , mainly the third and fourth equations , which are also field reaction equations, but not equality equations as made by Maxwell himself .

Maxwell did great efforts, in his time , in gathering the most important laws of previous scientists and then he put them in the equality form .These causality new equations form is the only way for solving all problems of major applied physics projects.

J - term was behind all physics problems, century ago, when added to field equations .

In conclusion, the above is further illustrated in Figure 1 below: