Electro-chemistry and Electromagnetism

Fusing the laws of electro-chemistry and electromagnetism seem elusive. We have a lot of tools at our disposal from CERN to the Oakridge colliders. Seeing the relationship and patterns between ions and electrons will certainly be one of the next century's major endavours. Though expensive, statistical research into the interaction between electrons and their more massive and less massive particle friends.

Let's consider the interaction between two helium atoms coming at each other with kinetic energy. Two electrons find themselves somewhere near each nucleus. It is unlikely that the two nuclei will come together first. Instead, more likely, two electrons will interact causing one or both of them to accelerate in what might look, on such a small scale, as a violent way. This interaction will scatter the two electrons more than the two nuclei or the other two electrons.

If the universe contained only these two helium atoms, then the electrons would fly off until they were attracted back to a nucleus through the acceleration due to the electric fields of the imbalanced nuclei. Remember that there are only two atoms in this make-believe universe.

Important to note in this little scenario is that the hot path is the screaming mutual acceleration of the two hot electrons the return path is the less violent return of the electrons to their valence position outside their respective helium atom.

Why, pray-tell, do I present this scenario? It is important to understand this small scenario before exploring how trillions more atoms and molecules behave in a bunch to create gravity using what we most often call electrostatic or electro-statistical attraction.

Generators Interacting with the Field

Conventionally generators inject mechanical work and take electrical energy to a load such as a light bulb or a clothes dryer. A so called 'magnetic' field is gener
ated with permanent magnets or electromagnets.

Maxwell's equations tell us that electrons spiral around magnetic fields. It seems to me that magnetic fields are just the curl of a dense electron field. This being the case, how does a generator work. The Maxwell-Faraday equation lets us know that the spatial curl of the electron field - as it changes in time - is equal to the curl in the electric field or the acceleration of electrons. As the generators rotor spins the coil has a changing view of the curl of electrons. The greater in change of the exposed curl to the coil the greater the electric field or voltage presented to the electrical load. The following diagram attempts to explain.

I've shown the direction of the electrons at the fringe of the electron field but the electrons, in fact, permeate the diagram between the two poles of the magnet. The diagram shows the rotor's coil at zero pi radians were the coil is aligned to minimize coupling from the electron field to the coil. The change in the electron curl exposed to the generator's coil accelerates the electrons causing a voltage at the electrical load.

The diagram above shows the generator's rotor at pi over four radians. The amount of electron angular velocity that the coil is exposed to is actually decreasing compared with the preceding figure.
The angular velocity of the electrons countered by the angular velocity of the rotor creates an acceleration of electrons in a sinusoidal manner.

Now what if we were to look at things in a more traditional manner. Lets look at the two diagrams above with the 'magnetic' field instead.

In the diagram above the rotor is at zero radians and there is said to be no flux linkages or coupling between the magnetic field and the rotor coil.

In the diagram above the rotor coil is at pi over four radians and the flux linkages of the 'magnetic' field are coupling with the coil of the rotor. The Maxwell-Faraday equation tells us that as the flux linkages change so does the voltage at the load end of the coil.

Gravity Models Starting with Electrostatics

Gravity exerts a force on an object towards the center of the largest mass in the vicinity of that object. Gravity is usually, in our experience, exerted by the Earth, the Moon and the Sun. The masses under observation will tend to act somewhat like the small charges they are made of.

Important to note the similarities between the universal gravity equation between two masses and the charge equation detailing the force between two charges. These similarities have been seen for a very long time but they have yet to be explained. We can chalk these similarities down to clues to how our universe might behave.

If gravity were like a game of Jenga then a block from the bottom would be put on top. Holes would be left in the bottom. In the case of gravity the holes are filled in Jenga the building eventually collapses. Negative charges are more likely to be in the vicinity of other negative charges towards the center of a mass due to simple geometry. Electrons will be ejected from the tight core of the center of mass with an excess of kinetic energy.

Electrons with excess kinetic energy are like the Jenga blocks from the bottom that are taken out to be put on top. This kinetic electron eventually interacts with other atoms and molecules and eventually slows down and joins with an atom or molecule. The slow down and joining to an atom or molecule is like the Jenga block being put on the top of the Jenga structure.

This is where gravity differs from a Jenga game. The electrons near to the ejected electrons are going to move in to back-fill the ejected electron with excess kinetic energy. So there is a circuit. The low voltage side is the high kinetic electron moving away from the center of mass. The return path is the electrons that back-fill that highly kinetic electron by moving in to charge balance the system. This happens continuously creating the widely observed gravity effect.

Electric - Magnetic Eddy Currents

In electromagnetics it is so important to understand the Maxwell-Ampere equation and the Maxwell-Faraday equation. What better way to understand these equations then an example. The magnetic brake that generates electric eddy currents is a fun example.

A conducting copper disc is spun with the North pole of a magnet above and the South pole of a magnet beneath. The disc is hard to turn due to the magnets and it generates heat. The question is, of course, why?

The disc in the figure above spins counter clockwise when viewed from above. Eddy currents develop near the magnets. The diagram above shows the direction of electron travel rather than the direction of current travel. The magnets are releasing spinning electrons that are spinning quite tightly in the counter-clockwise direction. This generates a tight spinning set of electrons around the copper nuclei on the left side of the diagram. Angular momentum must be preserved so larger curls of current develop in the copper disk.

The eddy current flows within the conductor and outside the conductor. Even though these electron flows are shown in the diagram to be in a few radial positions with one radius, they occur at all radial positions and with a statistically varying radius. The eddy currents circulate end to end throughout the conductor to some extent. The eddy currents circulate outside the conductor most vigorously near to the conductor and less so as one extends away from the conductor. As in the conductor these eddy currents occur at all radial positions and they circulate throughout the dielectric surrounding the conductor until they are too small to be measured.

Under the magnets the electrons in the copper disc spin with the spin induced by the magnets' ejected electrons. As an area of the disc spins away from the magnets the angular momentum continues thought the tight spins get wider as the spinning electrons dissipate and the spin becomes random again.

The disc warms up due to the excess change in angular momentum first to match the magnets and then to preserve angular momentum. All of these non-random re-arrangements of electrons cause interactions with the copper lattice. This causes heat.

Another way to see the eddy brake is to consider the Maxwell Faraday equation with respect to the change in magnetic field and the effect that will have on the electric field in the disc. The Maxwell Ampere equation applies to the circulating current due to the magnetic field.

Maxwell's Equations Collapase

Maxwell's equation that is Gauss' equation for electricity tells us that negative particles tend to accelerate away for negative particles and towards positive charges.

Assuming that the the magnetic field is just the curl of loose electrons then Gauss’ law of magnetism breaks down into a vector calculus identity.

Ampere's law describes the working of an electromagnet or a non-accelerating electron-nucleus dynamic. If the curl of the loose electrons is substituted for the magnetic field then we have the curl of the curl of the loose electrons is equal to the sum of currents. This is just true as it describes how I see the idea of 'magnetism'.

Often called Faraday’s law this relationship describes a changing magnetic field and its effect on a coil of wire. This relation allows electric generators to work. Making the same substitution as we made in the previous two equations and we have a simple relation that the change in circular charge is proportional to the acceleration of these charges.

Even Mode Ampere's Law Using Circulating Current

Maxwell's equations describe electromagnetic fields as far as an electrical engineering student would understand them. Gauss, Ampere, Faraday and Heaviside are all said to be linked to these equations through a history of development of electricity, magnetism and the vector calculus.

The Maxwell-Faraday equation states that the curl of the electric field is equal to the first derivative of the magnetic flux density with respect to time. Deconstructing this relationship shows us that the spacial change in the electric field will affect the acceleration of electrons. The electrons may jerk in a curled field, they may accelerate or they may curl with a group drift velocity. The other side of the equation points to a 'magnetic' field that changes with time. The changing magnetic field is an important component for the rest of this post.

If a 'magnetic' field really points to a drift or acceleration of electrons in a curling motion then we have to relate that to the equation at hand. The Maxwell-Faraday equation indicates, at a very minimum, an acceleration of electrons in a circular motion. The electrons may, in fact, jerk in a circular direction. This jerk and acceleration is an important part of the ejection of electrons so to influence the flux of the electron flow outside the conductor. The parameters of the telegrapher's equations describe all of these electron-dielectric interactions and they have been discussed on previous posts.

I've posted about the proximity effect and the skin effect before. The proximity effect describes the interaction between one conductor and another when electrons are accelerating in a circular way. The skin effect deals with the interaction of similarly accelerating eddy currents only the skin effect is one conductor's eddy currents acting on itself. The eddy currents can be looked at as a result of the parameter's described by the telegrapher's equations. Alternatively, we can use the fictitious 'magnetic' field to explore the interactions between the two conductors.

First, let's look at the proximity effect using eddy currents alone. Electrons eddy out behind the ions of the atoms they are passing causing a curl. The fastest electrons are moving through the lattice near the surface of the conductor where they can 'leap frog' for a faster speed and less impeded acceleration. Electrons eddy out of the conductor causing a flux in the flow of electrons surrounding the conductor. In this case, the electrons curl.

The diagram below shows the proximity effect with curl in the electron flow in addition to the drift of electrons against the traditional current.

There may be more to the diagram above than meets the eye. The field of curling electrons has the opposite curl as the electrons ejected by the other conductor. These electrons spin against each other interacting in the middle of the two conductors. A gentle matter stream begins to develop. Th matter flowing out from between the two conductors forces the wires together. This is ampere's force described using Ampere's circulating currents.

The eddy current flows within the conductor and outside the conductor. Even though these electron flows are shown in the diagram to be in a few radial positions with one radius, they occur at all radial positions and with a statistically varying radius. The eddy currents circulate end to end throughout the conductor to some extent. The eddy currents circulate outside the conductor most vigorously near to the conductor and less so as one extends away from the conductor. As in the conductor these eddy currents occur at all radial positions and they circulate throughout the dielectric surrounding the conductor until they are too small to be measured.

Now lets describe the same phenomenon, the proximity effect, using the fictitious 'magnetic' field. The diagram below illustrates the same electromagnetic effect as the diagram above only with 'magnetic' field lines drawn in in the traditional fashion.

Using this model we see the current in the left hand conductor producing a 'magnetic' field that cancels the 'magnetic' field from the right hand conductor. The right hand rule the magnetic field originating from the conductors with opposing current the field lines point the same way between the conductors. Sorting out the directions of the 'magnetic' field can be done using Maxwell-Ampere's 'law'.

Either model amounts to the same effect. The concentration of current due to the proximity effect can be a real menace at high frequencies.


Material Referenced from: Johnson and Graham, High Speed Signal Propagation, 2003.

Permanent Magnets

Magnetic fields can come from magnetic materials or electromagnets. It seems more than certain that electrons pop out the North or the South end of the magnet and, in a circular or helical path, travel with a drift along the 'magnetic' field lines. Electromagnets eject electrons from the edge of the conductors that are twisted around an air core or a ferrite type of material. These electrons travel the path of the magnetic field lines in a helical path doing more spinning than traveling to end up, statistically, where they began.

When the North end of a magnet comes close to the South end of a magnet the spin of the electrons cause a spin flux in between the two bars. The curl in the vector fields add and the matter in between the two bar magnets spins out creating a relative vacuum. The positive ions follow the electrons as they spin out from in between the two magnets. The relative vacuum forces the solid magnets together. The net drift of electrons can sometimes be against the 'magnetic' field lines or with the field lines. The fact that either scenario is possible has likely caused more confusion in the area of 'magnetic' than Maxwell's complicated set of equations.

When the South end of a bar magnet comes close to another South end the curling electrons cancel each other's curl at the center. There is a lot of curling in the field of curling electrons that precipitates the canceled curl at the center. There would seem to be a pad of circulating electrons at each South pole. The two pads exchange electrons in a torrid type form in a circle at the top of a round bar magnet. The angular momentum of the negative charges circulating so viciously drawing in positively charged matter keeping the two ends of the magnets apart. Again, we know the direction of electron curl but we don't know the direction of electron drift. In this case the drift is from or to the South ends of the magnet to or from the North ends of the magnet which are much further apart. Ultimately the linear drift matters less as the spin of electrons matters a great deal in the formation of the force fields we call magnetism.

Electrodynamic Gravity

An imbalance or excess negative charge forces a minority of electrons to push outwards from within the core of a mass. There will be a surplus of negative charge towards the center of a mass due to the geometry of the sphere or any other large mass.

More stable or less kinetic electrons will back-fill the electrons ejected from within the mass.

Back-fill electrons moving towards the center of mass will pull positive charge inwards.

For example, a ball sitting on the surface of the planet will have electrons sucked downward due to the back-filling effect. The nuclei, from the ball, will also be sucked downwards towards the negative electron.

Inner electrons will repel each other. Less kinetic electrons will slide in towards where the initial electron left. The nucleus associated with the less kinetic electron will follow. Eventually the more kinetic electron will will settle 'at the top of the pile' or somewhere further out from the center of mass.

An analogy for the excess electrons is they will pop up towards the surface of a mass like popcorn.

There is a fundamental property of a volume. If we move out from the center of mass of the volume the charge pressure will decrease. The volume that the inner most charges can occupy will be less and less as we move out from the center of mass. The charge pressure or voltage differential is what moves an energetic electron out from the center of mass and a less energetic electron in to take its place and balance the missing charge.

This phenomenon can be illustrated with a spherical mass. The sphere will have more electron crowding at the center. The volume integral around a small sphere at the center of a large spherical mass will show an electric potential. The sphere slices outwards from the inner sphere have a ratio that is such that the inner sphere slice is slightly smaller assuming the radius remains a multiple of the inner sphere.

Skin Effect and the Maxwell-Faraday Equation

The skin effect is an issue for alternating current where the higher the frequency of the alternating current the more pronounced the skin effect. The material of the conductor also affects the skin effect.

The skin effect on AC transmission lines involves all of the parameters of the telegrapher’s equations. The most important of the parameters involves the electron eddy currents associated with, L, Although most of the inductance, L, will be found outside the conductor some of the inductance or angular momentum. 

Most of the fastest moving electrons will be found at the boundary between the conductor and the dielectric. Fast moving electrons will eddy into the dielectric starting in the direction of current movement and then curling. There will be opposing eddies, the current will eddy into the conductor where it will have a tendency spin and will have the property of angular momentum. 

The eddy currents when viewed from around the conductor and along the length of the conductor will add up constructively towards the surface of the conductor. There will be destructive interference where the eddy currents oppose the direction of normal electron current.

The electrons will have the easiest time accelerating near the cladding of the conductor as they leap-frog their way to an electrical load or away from this load. Some electrons will escape the cladding boundary into the dielectric creating easier acceleration for subsequent electrons in the flow at the cladding.

The acceleration and faster relative velocities near the conductor-dielectric boundary can be seen as a type of easier acceleration because the density of atoms is less outside the conductive lattice when compared with the inside of the lattice. The electrons of an AC current are eddying in both directions and the non-eddy electron shoots down the middle efficiently. As well, with AC, there is a change of direction necessary and this change in direction is facilitated by the capacitance specified by the telegraphers equations.

The velocity or inertia of electrons eddying out around a given nucleus can knock other electrons out of their orbitals and into the curl of the flux of the electron flow. Again with more than 10²⁰ electrons traveling in a very small space the electron density means this may be fairly common. It will be less common for an electron to collide with a nucleus.

The skin effect phenomenon can also be explained using magnetic fields. To see how take a look at the diagram below.

The current will produce a curling magnetic field by the Maxwell-Ampere equation. In turn the changing magnetic field due to the AC current will produce eddy currents within the conductor. At the surface of the conductor the eddy currents will be additive with the prevailing currents. Towards the center of the conductor the eddy currents from around the circumference of the conductor will add up against the conduction current preventing current flow in the middle of the conductor.

Material Referenced from: Johnson and Graham, High Speed Signal Propagation, 2003.

Rings Around Planets

The rings around Saturn have been well known for a long time. Rings likely form around planets due to an interaction between the magnetic field of a planet, that planet's gravity and the planetary spin. Dust and other particles will be kicked around the far reaches of a planet's gravitational influence and not immediately fall to the planet.

The magnetic field of a planet shows that electrons are spinning around the planet and exhibiting a curl in a plane that slices the planet in half along the equator. The spins at the poles will be wonky going from in a plane with the equator to tilted at pi over eight radians from the planet's axis.

As the rings of net current approach the equator the rings flatten out. At the equator the rings are flat and the flux of the flow of electrons is said to curl. In vector calculus the curl does not refer to a simple circular motion. There can be many circular spins on a plane, overlapping circular curls and nested spins. Curl is a measurable quantity and at the equator the curl is in a plane with the rings of a planet.

Inside a ring of current it is likely that positive particles would find themselves. The spinning electrons would have a certain angular momentum but would attract net positive ions or slightly positive atoms and molecules.

These particles, as well as the electrons, have a high root mean squared speed. The bob and buck to some degree in a Brownian manner. Far from the equator the current curls are tilted and it is likely that the particles would be bucked into the gravitational pull of the planet to rain down towards its center.That or the particles would just speed past the equator in a non-geosynchronous orbit.

At the equator of a planet it is likely to have electrons orbiting int a more organized manner. The electrons are going to eddy and curl in the presence of matter and we will find the ring effect around certain planets.