Inductance and the Telegrapher's Equations

What is inductance? A circular definition asks us to believe it is the induced magnetic field by a current or a displacement current. But what is it really?

Inductance is the eddy currents experienced when electrons are rushed down a wire as described by Gausses equations described by Maxwell and then Heaviside. The inductance is formed outside a conductor in a dielectric. Eddies within eddies of current rotating around atoms, molecules and groups thereof. This eddy phenomenon that happens around nuclei in a sort of a telegrapher's drift storing energy in angular momentum of electrons and then atomic nuclei themselves. This energy storage ability of a dielectric medium is described by magnetic permeability and electric permeability.

It is interesting to think about how many electrons flow through a wire. One Coulomb is in the order of ten to the eighteen electrons. That is a huge number of charge carriers. The telegrapher's equations point out that some charge bleeds off in the conductance parameter. Mainly the inductance parameter and also the capacitance parameter are important. As the charge heads down the wire certain 'hot carriers' will bleed off into the dielectric and eddy out around a dielectric nucleus. This spin gives the atoms that extra bit of angular momentum which is also known as energy stored in a magnetic field or inductance. It may once have been known as field flux where the field is contained in the dielectric.

Neat to think about how nested these electron eddies can be. More turns in an inductor or electromagnet lead to more feverish eddies or spin. More angular momentum leads to more energy stored in the magnetic field and more inductance.

After a current has been removed from a wire the angular momentum of the electron eddies unwinds. The magnetic field is said to collapse and the spinning electrons have a propensity to collapse into the wire keeping the current going. This is just as the inductor in the telegrapher's equations would have predicted.

There is a reason for those wonky inductance calculations.

Gauss' Laws in Tight

So as any two atoms or molecules come together there has to be a slight attraction. We see this hot side attraction will come about from a divergence. The electrons are so much less massive than the nucleus that they scatter quickly. Some electrons from one nucleus will end up overloading a second nucleus. The result of this electron-proton-proton-electron oscillation is a brief and slight attraction instead of repulsion. The vast majority of the time this attraction does not result in a chemical bond but rather some gravity.

Next it is important to see how these slight 'hot side' attractions build in a structure to form larger objects such as planets or stars. Gauss' laws add up and there is always a propensity for the hot side to reside in closer to the middle of a mass. There is a more dense electron cloud as we approach the center of a sphere of mass.

Relationship Between Chemical Bonds and Gravity

So we have an idea whereby when large numbers of atoms and molecules are in close proximity they tend to stick together. There are a lot of molecules. There may be upwards of ten to the twenty-fifth power molecules in a meter squared. Humans just can't comprehend that type of magnitude.

Gauss' law of electric fields will force electrons in a repulsive manner. These electrons will clear a way towards the nucleus which will attract the electron from the adjacent molecule or atom.

It is interesting to compare a strong Gaussian attraction to a weak one. Notably, a strong diatomic atomic - chemical attraction and a gravitational attraction.

A diatomic molecule has an almost full valence shell. Two atoms together form what looks more like a stable double shell together. Statistically these atoms stay together. We can imagine that the atoms come together the electrons scatter before the nucleus feels any of the push or pull of Maxwell's equations. Because the electrons move so quickly the attractive force of the nucleus is exposed. Electrons from the adjacent atom will be attracted beginning the diatomic attraction. This attraction settles out in a molecule because of the inherent stability of the double shell.

Let's look at the weakest case we can find to see if it fits with our model for the weak force of gravity, helium. We can imagine that the helium atoms come together the electrons scatter before the nucleus feels any of the push or pull of Maxwell's equations. Because the electrons move so quickly the attractive force of the nucleus is exposed. Electrons from the adjacent atom will be briefly attracted before being pushed away. This force is brief and it is statistically valid for only small fractions of time. Larger masses see more statistical attraction building towards the gravitational attraction of large masses.

Small Gravity Large Gravity

It has long been postulated that gravity holds for small masses as it does for large masses.

If two small helium atoms met in the vacuum of space their outer shell would repel exposing their inner nucleus which would also repel. What wouldn't repel is the whole structure which would have a net attraction.

Now if three small atoms met in a vacuum their outer shells would experience a definite repulsion. Electrons which travel at a fraction of the speed of light would quickly move out of the way exposing a line on the nucleus. This balance may precipitate a momentary exchange of electrons even if a proper chemical bond is not formed.

When many atoms and larger molecules get together in a bunch the middle molecules will have a net crowd of electrons which will experience a natural repulsion. The electrons will move towards the outside of the total mass but the nuclei will pull back. This total gravitational attraction is hard to ignore.

Electrostatics and Gravity

There are definite tendencies that exert themselves on a mass that is clumped in a bundle of molecules or atoms. We find gravity which may well be electrostatic. There will be an outward pressure pushing lighter negatively charged electrons out and heavier ions in. The pressure is due to an ever so slight abundance of negative charge which finds itself on the inside of the bundle of molecules or atoms. Some lighter electrons will escape and be drawn outwards at an accelerated pace. This electron will tend outwards until it is accelerated inwards by the imbalanced, remaining, positive charge. The electron will be accelerated inwards until it collides with the heavier ions. Eventually if there is no collision the electron will be drawn out again at an accelerated pace restarting the cycle.

The charge imbalances are so slight and the number of electrons and ions are so great gravity ends up being quite fluid. A type of reverse buoyancy.

Imagine an ion at each face of a cube. Pretending that electrons don’t repel each other then, statistically, we would expect there to be a higher electron density inside the cube when compared with the outside of the cube. Because electrons do repel each other we would expect an accelerating divergence from inside the cube.

At a certain point the electron will be attracted back towards the cube. The inward-most electrons will tend to scatter while the outward-most electrons will exert a pressure towards the center of a large mass.

It is important to remember that the electrons are far lighter and faster than the ions. These little things will go to work around the main mass causing movement. The electron will dictate gravity through an outwards and inwards oscillation described above.

Flux and Electromagnetism

The concept of flux in Elecromagnetics may be more than 150 years old. What does it mean really. The use of electric flux and magnetic flux is pervasive. Has the meaning changed over the last century. It could be that the founders of electrostatics were thinking a lot more about the particulars of what was going on then we do today. Maybe today we take certain sets of equations for granted and plow through formulas with multi-processor computers using method of moments to gather a solved 3D field.

When the idea of vector field flux was applied to electromagnetics chemistry was still nascent. I'm not certain our fore-bearers had a solid concept of the lattice structure of many metals or a statistical model of the electron voltage vs the positron voltage. Maybe these people were doing what they had to to get published. Regardless the concept of flux remains with respect to electric fields and magnetic fields.

Electric fields - magnetic fields? But fields of what. Well we know there are an abundance of elementary particles out there. Electrons just have to dance in the right way and we will see field like effects because there are so many of them and they move so fast.

The fast movement of electrons in a conductor seem to have effects that stretch far from the conductor itself. The dielectric region beyond the conductor exhibits or contains the flux as it changes in the presence of a surplus or deficit of electrons.

In the case of an antenna this alternating surplus or deficit of electrons that propagates kilometers or mega-meters from the antennas location. There are trillions of electrons located in small bits of atmosphere. It's a hard to conceive of just how may electrons surround an antenna. The chemistry of antenna's could be said to be a statistical marvel.

Electrons at boundaries behave in particular manner. Electrons deep inside a conductor behave in another way all together. Perhaps that is a topic best described in another post.

Magnetics and Vacuums

This topic may seem both trivial or deep depending on how one looks at it.

So earlier I posted that magnetism might just be a result of the vector field flux associated with fast moving particles interacting, every once in a while, with particles that are located far from the point of origin of the electric or electron source of the magnetism according to Maxwell's equations. It is hard to conceive of how much faster electrons move when compared with neutrons and protons.

If in a vacuum a solid magnet exists it breaks the vacuum by definition. That fact aside, lets consider the speed of the electrons in the magnet. They are going at a solid fraction of the speed of light depending on temperature. The solid magnet must be leaking electrons like crazy. Consider the magnetic field lines. A spiral along the magnetic field lines is where you will find a trail of electrons in this near vacuum.

A North pole will then attract a South pole, in a vacuum, in a slightly different way then it would in an environment where the air is thick and the air must 'flux'.