Ivor Catt makes the statement that Charge and current are mathematical constructs in electromagnetism.
Earnshaws calculation showed that if charge did exist it would not form static stable aggregations. Thus induction diagrams are anomalous to that law. What is really going on is that wave dynamics are occurring at the surface of materials, and conductors are extremely good at concentrating magneto dynamic wave structures in themselves and their environs, the electro dynamic structures actually prefer dielectric materials. Magneto dynamic wave structures are strongest in the rare earth and mineral elements in the periodic table
It is obvious that charge is a fundamental concept of the current electromagnetic theory, so how did this happen?
Briefly, because I have discussed ths st length before, the electric behaviour was secondary to the magnetic behaviour , but related in Gilbert's analysis. He coined the term magnetic poles to describe concentrations of magnetic ubstance. This substance was an invisible fluid, of which air is an example. The flowing of this fluid explained the observed effects. However Electra behaviour seemed different.
Researchers like Robert Boyle etc , continental and British scientists found Electra of interest and used this same fluid substance as a model. However, invisible fluids, infernal experimentation, and Alchemy did not go down very well with the religious authorities at the time, so. Secretive communications and alternative code words were used, among which charge beamed a popular analogy with the power released in gunpowder etc, by a spark!
Both in metalwork and in polishing industries the spark was a common occurrence, and the invisible model had to account for this Tribo electric and Tribo magnetic phenomenon and empirically observed and experimentally demonstrated behaviours.
2 fluid substances were proposed as being applied to a neutral corpuscle called matter. Discussion, experiment, and exposition narrowed this down to one fluid that remained attached to the neutral matter and the other that moved between objects, increasing or decreasing" charge". This notion was made popular by Benjamin Franklin. Charge was given a symbol to denote whether the fluid was in excess or in defect. Charge was not quantised until the Leyden jar enabled a unit of Quantity to be visualised.
In the meantime, the fluid analogy automatically lead to the notion of charge flowing from one body to another. By rights this flow should have been just on the surface of the objects. It was clear that certain substances allowed an easier flow than others and these were called conductors in the real sense that they guided the flow of this fluid called charge.
Faraday observed what he called induction. This means "to lead into". Thus it became unclear whether the charge flowed on the surface or through a body, but this was of little significance, the fluid flowed! What maxwell did was then invent the term current for this flow of charge "in a conductor". He was not principally concerned about how it flowed , but more about its inability to stop flowing unless it encountered an insulator!
So with these models Maxwell built a fluid dynamic description of charge flow, in which he does posit flow as only being on the conductors surface., but later plumbers likened it to fluid flow in a pipe. This was due to Eddington using copper pipes filled with tar as transmission cables for direct "current" electricity as he called it.
The flow of this new commodity electricity was the source of commercial and scientific wrangling, but the big money investors won out over the scientists and so we have electricity flowing in wires taught to every school child.
But worse still, every electrical engineer was fed on a confusing diet of the science! They I'd not really have to know how it worked just how to fixit, which mainly was a plumbing problem.
It was the generators and the sparks that required gifted and " maverick" that is unsullied scientists and engineers to get it right. Heroes are Tesla, Steinmetz, Dollard, Heaviside. Everyone else opted for the quiet life!
Now Faraday and Maxwell had collaborated on an alternative concept to charge. Faraday had developed the notion of a sphere of influence, in which electric and magnetic tension was induced into objects. This induction was action at a distance, a scientific puzzle since Newton. Faraday observed the tension in this field and described it as electric tension or magnetic tension depending on the experimental source.
Maxwell gives detailed insight into his own experiments with electric induction. He clearly lays ot some methods and rules for what has become known as charge induction or conduction. It has this association with charge, the invisible fluid, because at this elementary level, this was how Maxwell best understood it. He imagined the fluids parting in the middle rather like the waters of the Red Sea in the story of Moses. Charge, or the fluid, depleted from one end and concentrated at the other end/ side of sn object, ostensibly the fluid flowed round the surface.
But how could the fluid be induced to move without contact?
This is where he had to resort to charge having a field of influence entirely other to the fluid itself!
Faraday wanted to remove charge as a fluid and just have a field, Maxwell argued you neede both. This sounds like and is a compromise solution which we still hold onto today.
A field could not be visualised, but maxwell attempted to visualise it as a field of vortices in the fluid. But this would mean that the fluid actually had to fill the universe, so how did that relate to a small object in the laboratory?
He came up with Equipotential lines around a conductor. These lines were inspired by the magnetic lines of " Equipotential" . In fact thy are lines of induction, but because Maxwell kept the charge fluid idea he had to invest the fluid with potential!
Using calculus he split the fluid into small fluid elements and explained that the potential lines showed where the fluid elements would move to if placed on those positions. The movement was t right angles to the line.
These considerations led to fluid being invested with a potential relative to a flow of fluid along the conductor, or later in the conductor.
Maxwell had lost sight of the induction caused by the external body! That is he excluded the inducing faraday field and concentrated on the resultant field induced by flow along the conductor!.
Where did this second field come from? Well Oersted had shown that a magnetic field was induced around a current carrying conductor, that is to say the magnetic substance description of Gilbert was suddenly dropped in favour of the idea of an invisible Faraday field for magnetism emanating around a conductor. But what about Faradays field for the electric fluid/ charge ? In addition this fluid was flowing so did the field move with it?
Maxwell combined the field for a magnet observed around a wire wth that of a field observed around charge/ fluid and posited the whole construct to be in dynamic motion. The combined Equipotential lines he drew , supposedly in solution to a differential equation, are explored at length. However the inducing field that causes the motion of the charge fluid, per se, is now replaced by a Voltaic cell. The first inducing field is cleverly dropped! The undefined battery as source replaces it.
The image of equipotentials is thus misleading. They show only a posited combined field for a fluid flowing on the surface of a conductor and a posited magnetic field caused by this flowing motion of the fluid.
Underpinning these equipotentials is an extension of the fluid medium called charge into all space, but little discussion about how the flow on the conductor relates to this charge extension, nor what substance is extended into space to be the field for magnetism.
However, supposing we have these mediums or a media capable of carrying both behaviours, Maxwell then sets up and solves strain equations for the transmission of strain energy through this medium.
Strain energy inside a solid body or a liquid is capable of resolving into local action! That is action at a distance is in fact resolved strain in some surrounding medium.
Of course none of this was accepted until Hertz waves were demonstrated.
This was indirect proof of some medium which had been called an aether since recurs of Alhrmy began. This invisible aether was scientifically " discredited " by the Michelson Morely experiments, and yet clearly a fundamental part of Maxwells theory.
Einstein who brokered a consensus in a divided physics Also made an impassioned plea for the Aether concept.
We see that later Heaviide pointed out, that the flow of charge was problematic. That removing charge and current and just using Faradys sphere of influence concept was all that was necessary.
How could the induction phenomenon now be explained?
Ivor Catt has put together several fundamental explanations in Theory c, but still much needs to be worked out. In particular, the magnetic induction field, the electric induction field , the motion of the fields around and near a conductor, and. Similarly an insulator. "Charge" induction and "charge" conduction, magnetic charge / flux induction and magnetic charge/ flux conduction. The battery as a source of induction fields, and field storage through capacitance.
In addition Faradays law needs to be reinvestigated in the light of Lenz's law, the Wilmhurst machine for continuous electric field motion, and how the movement of an electric field in a solenoid differs if indeed it does to the movement of a magnetic field in a solenoid.
It is in fact easier to accept that I alter the sound wave patterns that inhabit a body by as much as the lightest touch, creating sound pattern reverberations that are sometimes even audible, than it is to realise that I alter the electromagnetic wave patterns inhabiting objects by a similar touch! But this is precisely what the triboelectric and tribomagnetic scales are telling us. No substance or form is unaffected by the electric or magnetic variation caused by applying force, because ultimately charge is a force.