So we all need math, well its complicated to model a 3 dimensional wave, esp when the modelling work for 2 dimensional waves is not complete enough to fully understand them and they are simple in comparison.
But luckily there is a simplier method, obviously removing the negative value was not simple enough, so we need to explain why we are removing the negative.
The first and most important factor to understand is this statement.
Maxwell's equations measure the CHANGE in the magnetic field. They do not measure or assume the magnetic structure which is causing the change.
You see Maxwell was working with a very basic to non existent understanding of the atomic structure.
He assumed as would anyone that since the induced current wave was produced by a dipole, that the changes that were occuring were also due to a rotating dipole.
Since we all took chemistry, we should all be aware of the electron shells of all atoms. As each shell rotates around the poloidal axis it becomes 1 pole of the quadrupole. As we can see in the attached image this results in a magnetic structure that changes polarity every 90°. As can be seen by the red & blue colour change on each lobe of the quadrupole. The changing magnetic field observed by Maxwell is the combination of the 2 north or positive poles being 180° opposite each other.
If we use Maxwell's equations to determine the value placed on each quadrant around the 360° rotation, then we find that the quadrupoles are valued as positive in the electric field then 90° further in rotation we find the positive value has moved to the magnetic field that is 90° to the electric. This implies that Maxwell assumed that a dipole was rotating 360° to produce the changes observed, an obvious assumption to make given a rotating dipole was the source of the change in the first place.
However since new understanding has come to light over 200 years and a slightly improved ability to see the atomic structure, we must examine what has previously been considered absolute.
Essentially Maxwell was out by a factor of 2, he measure 180° as 360°. We know this to be true because each action has an equal and opposite reaction. Light, electricity and magnetism follow this rule because they are all double helical waves. If you dont know what a double helixs is then i suggest looking at DNA.
If im wrong, then why do....
Electrons travel in pairs?
Photons travel in pairs?
2 electrons per orbital?
A pair of Electrons have a trajectory of 1.1°?
Why do 2 electrons spin in opposite directions inside the same shell? P.s. just like a quadrupole does.
Why do planets and stars also produce the same quadrupoles?
So the math? If we look at the first 90° of rotation of the atomic structure. Ie the 2 points where the electric field is positive rotating towards a positive value for the magnetic field. At 90° into the rotation we find that we have a positive value for the magnetic field ie, it is north. Maxwell's mathimatical matrix now says that the electric field is zero in both directions. While the opposite direction has a value of negative. This value suggests that a south pole exists at this location, while it does NOT to the orginal observer who noticed the positive change in the first instance. It most certainly does look like a south pole to the observer at 180°, thus maxwell determined this to be the opposite force to his frame of reference, but it wasnt the opposite force. It was the same force travelling in the opposite direction.
Now we can quickly look at the quadrupole of an atom (attached) and notice this is not true for a quadrupole aka a double helixs. Note, these are the same thing. A "pole" is 180° of the sinusoidal wave, so if we double the number of waves we get 4 poles. Sorry i better add the maths in, some ppl dont want walls of txt. Oops...
(2 x 180°) + (2 x 180°) = 4, again the 180° comes from half a full rotation, ie 360°, sinusoidal waves are a product of rotation. In this case from observing the rotation around the toroidal axis perpendicular to the Poloidal axis. The mathimatical matrix built around this is a product of perspective. Just because 2 observers view the force/rotation of something as completely opposite does not mean they are, unless you have considered any change in perspective as well. This change in perspective has been entirely ignored for 25 pages now. Ive been telling you from the beginning to look at the situation from the opposite perspective.
The double helical compression wave that forms an endless loop around the toroid of the plasma reactor or Sun is being utilised to further compress the plasma in the z pinch. This is due to the reverse of the inverse square law. Waves curving around any object undergo compression on the inside edge (quadrant) and expansion on the outside edge. This results in different energy densitys in the opposite side of each quadrant of the toroid.
Compression waves grow exponentially when the wave opposite is in the same phase. This produces what is called the Z-pinch or Theta-pinch. It can be found at the center of every rotating wave around a coil of wire. Or every rotating wave around a plasma toroid. Does the medium make a difference to inductance of current? Ie is iron better than air? & Is "superionic" plasma better than iron?
The maths to actually model the interaction of the same wave travelling in 3 dimensions would crash the best supercomputer on the planet. Its a straggering amount of data to input into 1 model. You need to know everything. Speed, density, angle of convergence with itself in every plain, what point the wave convergence reaches its limit, the changing density of the medium as it travels outward, the inverses square law outward, the square law inward, how much faster does the wave travel as it reaches the Poloidal axis? and not to mention every other electromagnetic wave inside the larger system. Ie you cant model the planet, without including the Sun, and you cant model the Sun, without including the Galaxy. There is no point even trying to work on the complicated maths, simply because it's useless to anyone until they understand the helical wave of motion and what the current math is telling you. Take the conservative of energy, does a travelling ocean wave lose energy? Or does the energy expand? The reverse of this is obviously also true and results in the square law for waves travelling inward.
We have to go back to basics and ask what is the diff difference between a North and South pole, how are they related to positive and negative? All these answers have been provided many times. If you dont get it and arent willing to put the work in, then give up. Take the blue pill and go back to sleep.
For those willing to take the red pill, i will give you all my spare time to help you understand.
To those who dont understand the electrostatic potential energy inside a compressed fluid, and think "heat" will some how magical make fusion energy possible. I have 2 little words for you "heat expands".
If Compression with a small expansion from electromagnetic waves (heat) = fusion
And Compression with a large expansion from non linear electromagnetic waves (current) = you have no energy source..... haha, the good news is; most of you are hiding behind avatars. The bad news is; the double helixs is why we have quadrupoles as oppose to monopoles inside either end of a dipoles. Remember the term equal and opposite reaction.... identical motion 180° apart. Its a rotating plasma universe, and the plasma reactor is designed to allow the energy of the compressed plasma to expand. Just like the compression waves inside a screw compressor. They might be made of metal, but they are still helical compression waves, thus the term compressor. Potential difference in a fluid dynamics is like cracking the valve open on an air receiver, It induces current. The plasma reactor is a big air receiver with the helical compression waves built in.
Please also try to consider that every looping magnetic wave eventually creates an endless current loop. Energy is not lost or gained ever. So long as coulomb's force fights electrostatic force the universe will exist.
No beginning and no end, the magnetic field is the universes power source, an endless current loop.