The Maxwell-Heaviside Equations

This blog has been alive for two years and I wanted to reflect on the basic tenants of electromagnetics. Namely, the four Maxwell-Heaviside equations. These four equations and the Lorentz force equation backbone electromagnetics for all practicing electrical engineers.

Gauss' law of electricity is useful as it shows the direction that a  charge will travel in given the presence of an electric field. The electric field is a useful construct because its magnitude gives us insight into the behaviour of electric phenomena.

Gauss' law of magnetism is somewhat less useful. A magnetic field is the normal vector in the curl of an electron field. Gauss' law of magnetism points out that the divergence of a curl is zero. That is the magnetic field is electrons curling and the divergence of that curling field is zero. This fact is also a vector calculus identity.

The Maxwell-Ampere equation can be read two ways. The curl in a magnetic field gives a current and the curl of electrons gives a magnetic field which is the normal to the field of curling electrons. The curl of a curling field does add up to a current. This is backwards from the way we should be thinking about electricity. The current in a wire generates a magnetic field which surrounds the wire. The current from the wire spins off a type of leakage current which spins. The telegraphers equations dictate this type of behaviour.

The Maxwell-Faraday equation involves Lenz's law and the principle of electromagnetic induction. The equation, in differential form, states that the change in a magnetic field will be a curl in the electric field. Understanding what is really going on takes closer consideration. When a loop of current sees an increase in the curl of an electron field one has to consider the nature of the curl. The curl in the electron field is very tight as it was generated by a permanent or electromagnet. The magnetic domains or curl in the electron field of the coil is random.

Due to particle interactions the coil starts to see a tight curl in its electron fields. The law of conservation of angular momentum causes a Lenz' phenomenon curling in the opposite direction. This phenomenon is harnessed as current to drive a load in an electric generator.

When the Maxwell-Heaviside equations were developed the developers had jar batteries, wires and coils at their disposal. Reconciling their world with a modern electronic world takes understanding and patience.

On Capacitance

How capacitance works is poorly defined. Some texts will point out that a dielectric is polarized such that energy is stored to counter the prevailing electric field. But what are the electrons doing? How are these electrons moving? I have explored this topic previously and will revisit it again because capacitance is complicated and so many texts make it sound simple.

The energy in a capacitor is proportional to the voltage squared. Voltage is the excited energy of an electron. Energy is also proportional to the dielectric constant of the dielectric material. The surface area is also proportional to the energy stored but the surface area is not always equal on both plates of a capacitor but we will get to some of the subtleties of capacitance later. Lastly, the energy stored between two plates of a capacitor is inversely proportional to the distance between the two plates or poles.

So what are the electrons doing in a capacitor to store energy? First they move. Electrons move at a fraction of the speed of light. Estimates of how fast an electron move vary but electrons don't move at the speed of light. Electrons don't move at speeds a regular person could understand. Electrons move at a fraction of the speed of light that is to say a speed that is meaningless in kilometers per hour.

We know that electron take in a large number of electrons before they begin to excite at the voltage levels of the conductor charging the capacitor. Electrons flow in and the voltage or excitement of the electrons in the conductor don't immediately rise. The electrons flow through the dielectric to the return and are immediately back-filled by electrons in the dielectric. As more energized or higher voltage electrons enter the dielectric the dielectric becomes more energetic. The electrons that are back-filling the incoming electrons have a higher and higher voltage until their voltage matches the incoming electrons. The capacitor is fully charged.

When a capacitor is fully charged there is an excitement at both plates. The capacitor has a lot of statistical properties that may well have to do with the exponential distribution or the Poisson distribution. Electrons will move into the dielectric with a high relative energy and they will keep moving towards the return. Eventually the electron will return towards the energized plate. It is the continuous dance between the energetic plate and the return that constitutes capacitance. Electrons moving quickly towards the opposing plate only to be back-filled by electrons seeming to polarize the dielectric.

The statistics of electrons in a capacitor has yet to be fully understood. Understanding that things are not fully understood is the first step in understanding the capacitor and eventually the diode and transistor.

Electron Field Curl and Force

If an electron flies through a dense medium of particles it will be deflected.

If a group of electrons deflects in a circle or an elipse a magnetic field has been created. The field of electrons has a measurable curl.

If enough electrons are moving in a circular pattern they will interact to cause similar movement in nearby electrons. The curl of the electron field can be seen as the magnetic field.

Electrons ejected from a coil or a permanent magnet will wrap back from one pole to the opposing pole.

When electron curls add, such as when a South pole comes near a North pole, mass will be drawn in causing the two poles to attract. When two wires have additive curls they will attract mass between them causing a repulsive force known as Ampere's force.

When electron curl is opposite then the field of curling electrons will bend back to terminate at its opposing pole. Matter will be drawn into the curl causing a repulsive force.

When common mode wires eject electrons the curl of their electrons cancels each other out causing matter to scatter as the atoms have less curl. The scattered matter causes the wires to attract. This is known as Ampere's force law.

A wire will eject electrons as the telegraphers model states. Some of the ejected electrons will travel in a circle or an ellipse and end up back on the wire. This phenomenon will happen all around the wire.

Ejected electrons tend to curl in a tight circle or elipse. When these tight curls interact with a conductive media the tend to induce a larger curl in the opposite direction. This opposing curl is temporarty and caused by a counter-spin of opposing atoms.

When the curl of ejected electrons influences a nearby wire it will temporarily cause eddy current to flow on the near side or the far side of the wire. This is known as the proximity effect.

When the internal curl of electrons turns towards the core of a conductor as it does; the eddy current opposes the current at the center of the conductor. This is known as the skin effect.

On Inductance

Ampere's equation states that the magnetic field wraps around the current in a steady state. This means that electrons might leave a conductor and spin back onto that same conductor around the atoms and molecules in the surrounding media. The normal of the electron spin is represented by magnetic field lines.

Faraday's law will be the focus of this post. Faraday's law states that a changing magnetic field will induce an electric field according to the left hand rule. This is opposite the right hand rule used in Ampere's law. We must explore why this is.

A magnetic field is a tight curl of electrons spinning in the same direction. Electrons that were spinning in the opposite direction because of the movement of the magnetic field or the circuit within the magnetic field will push outwards and cause a momentary electromotive force through a circuit. Electric motors take advantage of this.

In the figure below the circulating electrons counter-clockwise are due to an external magnetic field. Really the electrons are just lining up due to collisions. In between the spinning due to magnetism exists a counter-spin. In this case clockwise. This clockwise spin is not constrained to a small tight spin so it pushes outwards to a larger and larger Faraday current until it can produce an electromotive force in a circuit.

This is how a changing magnetic field induces an electromotive force in a circuit.

The Missing Maxwell's Equation

Heaviside's  version of Maxwell's equations are missing one equation. Either that or the equation has to be inferred.

Maxwell's first two equation known as the Gauss equations of electricity and magnetism define static electric and magnetic fields. Ampere and Faraday have equations that follow Gauss' to define magnetic fields and currents and currents in the presence of changing magnetic fields.

The missing equation would be based on the simple electromagnet. A curling electron or current field produces a magnetic field. The curl of the volume current density is equal to the magnetic field vector with a proportionality constant. Now Gauss' equation for magnetism breaks down into the divergence of a curl which by vector calculus identities is just an identity.

Faraday's law ends up being a result of Lenz' law. A tight magnetic field (spin of electrons) will cause a larger counter-spin of electrons due to the conservation of angular momentum.

Sharp Charge vs. Dull Charge in an Atom

On the left side of the periodic table we have atoms with what are termed a positive charge. On the right side of the periodic table we see negative charges. All, in reality, are balanced. Each proton has an associated electron to balance it.

Positive atoms on the left side of the periodic table have an extra electron above the previous filled complement of electrons. This electron peels off easily leading to negatively charged ion. These two configurations can be seen as sharp. When the electrons balance the protons the negative charge can be seen as sharp. Where the electron resided the charge is sharp and very negative. When the electron peels off the result will be a dull positive charge. The imbalance caused by more protons than electrons will be felt through the Maxwell-Gauss electric equation.

Negative atoms on the right side of the periodic table have too few electrons to make up a full complement of electrons for a shell. The extra positive charge that presents itself around the atom will tend to draw electrons from farther away. This positive charge can be seen as sharp. When the atom is successful in drawing in another electron the valence shell will be complete. This atom now has a dull negative charge which is spread around the outside of the electron and not quite balanced by the protons' charge in the nucleus of the atom.

Sharp charge vs dull charge can be important in understanding why chemical reactions happen.

Molecule Attraction in Masses

Masses have an attractive force that pulls large things down. Towards the center of mass and less often towards the periphery of mass electrons will tend to jump. This sharp negative charge will move quickly over a distance between molecules.

Charge balance will seek to reassert itself as the electron moves from the center of mass towards the periphery of mass. Electric dipoles in the larger mass will be dragged negative side down. This drags large mass down while small mass (electrons) often move in the opposite direction.

Electrons don't just move straight out to the periphery of mass. They may move at angles to perfect radial movement. With ten to the twenty molecules in a mass the averaging effect happens quickly.

There is sharp charge and dull charge at play in a gravitational force. The sharp negative charge comes from excess electrons on the inside of any sphere or mass. The dull and moving dipoles in otherwise balanced molecules provides the dull negative charge that makes its way inwards giving us a gravitational force.

Little things, electrons, are always moving up sharply while both big and little things are attracted towards the center of a mass in a process we call gravity. The attraction back towards the center of mass serves a charge balance function as well as replacing the mass that bolted sharply and quickly from within the mass.

Particles Making Up a Large Mass

To understand the London Force or gravity it is important to understand how groups of particle stick together. This stickiness is additive and as an object gets bigger there tends to be a larger force pulling the mass together. I'd like to look at why.

A sphere is going to be more crowded at the center than at the periphery. Secondly, an atom may be modeled as a sphere with electrons on the outside and with an ionic core. The electrons on the outside of atoms will interact at the center of a mass (perhaps a sphere) and produce an elevated negative charge level as one approaches the center of mass. The opposite occurs at the periphery of a sphere of mass becomes more relatively positive than the center. The mass doesn’t have to be a sphere.

At the periphery of mass the atoms and molecules will seem to bend outwards. The negative charge will be relatively sparse compared with the center of mass. An inversion layer will look to occur now between the charge at the center and periphery of the mass. This inversion layer is similar to that of a semiconductor depletion layer except it is a progression throughout the mass rather than a discrete line between different doping profiles in a semiconductor.

Electrons will push outwards from the center of mass to the periphery. Charge balance will pull them back. Electrons and holes will be dragged towards the center of mass. This creates the London force or gravity.

Maxwell's Equations Restated

If I could modify Maxwell's equations to make them more practical I'd take them one by one. First of all the equations we call Maxwell's are Heaviside's restatement, using vector calculus, of Maxwell's nine equations. Maxwell's equations were put together before Bohr put together the model for the atom. Some updates should really be made.

The Maxwell-Gauss equation for electric fields shows electric fields terminating at charge points. This equation defines how electric fields look.

The Maxwell-Gauss equation for magnetic fields may not tell us much. If we take a magnetic field to be the normal vector in the spin of an electron field then there may not be much going on with this equation. The Maxwell-Gauss equation for magnetism says simply that the divergence of a curl is equal to zero. This is a vector calculus identity!

The Maxwell-Ampere equation states that the curl of a magnetic field is equal to the volume current density. This tells us that a current carrying wire will be surrounded by a magnetic field elliptically around the current carrying wire.

What is equally interesting to the Maxwell-Ampere equation is the fact that the curl of electric charge movement through space yields a magnetic field around the current carrier. This can be found directly from the Maxwell-Ampere equation but is worth restating in its own equation. After all, it defines all electro-magnets.

The Maxwell-Faraday equation is the most complicated and nuanced of Maxwell's equations. It seems that a changing magnetic field causes a curl in the electric field. Coils moving through a magnetic field will likely have their spins line up with the spins in the magnetic field. The conservation of angular momentum comes in to play and a reverse circular movement of electrons produces an electromotive force.

So rather than using Heaviside-Maxwell's four equations I'd use Maxwell-Ampere's equation, Maxwell-Ampere's modified equation above and the Maxwell-Faraday's equation to explain electromagnetics.

Inductance and Random Movement of Electrons

Inducing a magnetic field has long been referred to as inductance. When a curling field of electrons is induced in a region of space it is said to have a magnetic field. The more curl to the field the greater the magnetic field intensity. The electrons can really get spinning and if we look closely we can see that the electrons exhibiting curl in the field have a great deal of order to them. The flux of the flow is said to be inductive but it could also be described as curling.

We can also make observations with the opposite phenomenon. When there is no curling to the movement of electrons they tend to move randomly. There is no tight packing of molecules or atoms in the space where this random movement of electrons exists. The matter falls out of these spaces and we have a relative vacuum. This vacuum is nothing like a proper vacuum there is just less flux to the flow of electrons in the region where random motion of electrons exists.

Consider the experiment where two wires are place next to each other with odd mode current running through them. The flux of the flow is additive causing the curl from each wire's ejected electrons to add. This adds order to the system. Extra curl in the electron field draws in more ions and matter to force the two wires apart.

Consider the experiment where two wires are place next to each other with common mode current running through them. The flux of the flow subtracts with the curl from one wire's ejected electrons canceling the curl from the electrons on the other wire. The result is randomness. Electrons moving about a different manner will scatter and make it difficult for matter or ions to exist there. The wires will move closer to each other as a result. 

Capacitance and Electron Movement in the Dielectric

Capacitors store charge on parallel plates. The question I'd like to answer is how are the electrons moving in order to store the charge. Electrons flow into the negative plate of the capacitor during charging. An equal number of electrons flow out of the positive terminal during this charging process.

Electrons flow into and out of a capacitor. There are also reports that the dielectric region in the middle of the capacitor is polarized when charged. Dipole type molecules form dielectrics whose poles line up against the incident electric field. This description of capacitor action seems static and lifeless. Clearly there is a lot going on in a charging or charged capacitor.

The statistics of electron flow involve multiple interactions with a conducting lattice or a non-conducting dielectric. How fast electrons back-fill incident electrons must also be examined. If an electron travels into a dielectric material with a high amount of potential energy that electron will leave behind a hole. The hole draw an electron from the dielectric. This enables the polarizing electrical engineering profs talk about.

If millions of electrons are observed we begin to notice a pattern of behaviour during charging or in a charged capacitor. We observe electrons entering the dielectric with a Poisson type distribution. A certain number of electrons enter the dielectric and then are replaced with a less energetic electron. This continues until the energy in the electrons in the dielectric is equal to the charging voltage. Then the capacitor is said to be charged.

Electrons dive through the dielectric with relatively high kinetic energy. These particles bump back towards the negative plate. This action pushes electrons away at the positive plate. These electrons return toward the electromotive force where they are pumped with negative voltage towards the negative end of the capacitor or elsewhere in the circuit.

Charge, Capacitance and the Transmission Line

A charged plate of a capacitor causes electrons to jump from the more negative plate towards the positive plate. There is very little conductance so most of the electrons ultimately make a round trip. Understanding the electron dynamics helps to understand how capacitors really work.

Dielectric materials are not conductive. If an electron moves into a dielectric kinetically it will be replaced by an electron from the dielectric. The electrons swap places. When a capacitor begins to charge the energy from the swapped electron is far less than the electron moving into the dielectric with significantly more kinetic energy. As time progresses the electrons in the dielectric contain more and more energy in the form of root mean squared velocity until the capacitor is fully charged. At this point the electrons in the dielectric contain enough energy to keep the electrons on the plate stimulated.

The telegrapher's transmission line model has a shunt capacitance. A small proportion of electrons flowing out the dielectric of a conductor will be replaced by electrons from the dielectric. This constant replacement charges the dielectric around the conducting medium. Capacitance, inductance and conductance all describe how electrons leave a transmission line and interact with the surrounding dielectric.

Electron Movement in a Dielectric

Understanding how electrons move through and interact with a dielectric material is instrumental in understanding capacitance or gravity. When electrons are more plentiful and active voltage is found to be more negative. The more negative voltage area is going to have electrons emanating from it. These electrons will fly relatively fast and straight. A dielectric material will backfill the fast electron with an electron moving in a more erratic manner.

There is a lot of space between atoms in a medium. This allows electrons moving from a more negatively charged region to a less negatively charged medium. The atoms the electron passes along the way may give up electrons to backfill the fast electron that blew past. How fast this backfill process happens depends on the root mean squared speed of electrons at that point in space. 

Electron movement is generally more ordered when an electron moves from negative to positive. This is because there is generally a lot of space between atoms.  Less ordered is the movement when moving from positive to negative. This is because the electrons will wander back at the local root mean squared speed to backfill a fast moving electron going from a more negative environment to a more positive environment. Electrons shoot one way and bubble back to fill the charge balance from the electron that blasted away.

Capacitance and Gravity

Understanding how electrons move through and interact with a dielectric material is instrumental in understanding capacitance or gravity. When electrons are more plentiful and active voltage is found to be more negative. The more negative voltage area is going to have electrons emanating from it. These electrons will fly relatively fast and straight. A dielectric material will back-fill the fast electrons with electrons moving in a more erratic manner in the other direction.

There is a lot of space between atoms in a medium. This allows certain electrons to take off statistically according to the Poisson distribution. The electrons that take off will leave a charge imbalance behind. Electrons move with a speed that is a fraction of the speed of light. That is to say electrons move very quickly. Electrons will move in to replace the electron that took off from the more negative region.

Electron movement is more ordered when an electron moves from negative to positive. Less ordered is the movement when moving from positive to negative. Electrons shoot one way and bubble back to fill the charge balance from the electron that blasted away.

This is true in a capacitor. A planet also acts in this way. Not only do electrons bubble back to fill in for escaped charge but positive ions are pulled in as well creating gravity.

Capacitors have electrons jumping from the more negative plate towards the positive plate. Electrons in the dielectric instantly back-fill the escaped electron from the negative plate. Eventually the back-fill electrons have enough kinetic energy to store Joules of capacitive energy.

Patterns of Electron Movement

There are massive numbers of electrons that move through any system under consideration. It is fair to say that electrons move as a group in a pattern or they move perfectly randomly. A group or a pattern of electrons moves in a predictable way through an electric or electronic circuit. Random movements of electrons around the nuclei of atoms represents heat.

The root mean squared speed of an electron moving randomly is measured as a fraction of the speed of light. Electrons are often used to exchange heat between various parts of a solid, liquid or gas. My BBQ outside is hot but there is no net movements of ions or electrons in the BBQ itself yet the electrons must be moving at a rate of speed that is hard to measure using modern instruments.

Contrast static electrical phenomenon with the movement of electrons in a group. It has been found that the only way to do this is in a circuit. When a large group of electrons move in the same manner they have to find a way towards charge balance. No part of a circuit can escape charge balance. So again, we want to understand how statistically and in large groups how electrons behave.

Start, if you will, with the various types of impedance that have been identified. These impedance take the form of linear differential equations with respect to charge. Do the various impedance; inductive, resistive and capacitive, have any bearing on the statistical movement of electrons in a group? I will submit to you the answer is a resounding yes.

The movement of electrons through any medium with resistance is the subject of any elementary electromagnetic text book. Electrons are accelerated to extreme speeds and then they collide with the lattice and move sideways or backwards.

Inductance is more interesting. Inductance implies inducing a magnetic field. The electron field of an inductive part is a curling vector field - the electron field. This curl interacts with other curling fields or creates other curling fields. This is how magnetic materials attract. Inductive electron fields are turbulent. These fields rotate in a circle. This happens naturally on a transmission line electrons explode from the line and rotate as they pass multiple atoms in the dielectric as a wave does past a stationary object.

How exactly does a capacitor or a transmission line store energy in a capacitave electric field? The form and distribution of electron movement within a capacitor. Electrons will dive into a capacitor but will be quickly back-filled by electrons in the dielectric. As the diving electron moves through the dielectric the back-fill property of the dielectric will continue. Electrons will be diving quickly in one direction and bubbling (back-filling) in the other direction until the kinetic energy of electrons in both directions is equal and the capacitor is fully charged. 

Attraction Gravity and Relative Pressures

Particles seem to attract each other. The particles loose kinetic energy and gain gravitational energy as they collide in a non-elastic manner. When particles are in proximity to each other they have been observed to have the London forces pulling them together. This fundamental force is the result of the electron pressure being higher on the outside of a mass when compared to the inside of a mass.

The electrons on the inside of a mass have a higher propensity than the ions to push outwards with higher kinetic energy. This energy dissipates as the electron moves to the outside of the mass. Electrons and ions back-fill the escaping electrons causing the gravitational effect including the London force.

The relative pressure of the electrons is higher as one moves towards the periphery of a mass. This high relative pressure forces the nucleus of various atoms towards the center of mass. Lower energy electrons move towards the center of mass as well.

The Movement of Ions and Electrons and Gravity

Capacitance stores voltage between plates or charge on the plates. Energy is said to be stored between the plates of a capacitor in an electric field. The electric field exists in a dielectric. A dielectric is a material that does not conduct electricity. Contrasting good conductors and dielectrics may be a worth while exercise. How do the electrons move in both cases?

If a negative voltage is presented at one end of a good conductor the surplus electrons with relatively high root-mean-squared speed is injected into the wire. The high root-mean-squared speed will dissipate over the more free electrons in the conducting lattice of copper or aluminium. Furthermore, the excess electrons will exert significant pressure in an attempt to reach an equilibrium number of electrons relative to the number of electrons the element prefers to keep in its outer shells. If a positive voltage is presented at the conductor then electrical tension not pressure will ensue.

If a negative voltage is presented at one end of a capacitor the charge will dive into the dielectric towards the opposing plate. The root mean squared speed of the electron will dissipate as the electron moves through the dielectric. Another really important thing will happen. In a dielectric, electrons will quickly back-fill the charged electron that has moved through the dielectric. This back-fill property is important because it serves to mitigate the charge at the active plate of the capacitor. The energy in a capacitor is thus stored in an electron dance and back-fill property where electrons slow down and continue to move within the dielectric of the capacitor.

Eventually, when a capacitor is charged, the back-fill electrons are moving with the same root-mean-squared charge as the charging electron group. The dielectric is alive with kinetic electrons carrying as much energy back to the charging plate as the charging plate is attempting to dissipate to the return plate.

The electrons in a capacitor or a large mass may be seen to have two groups of velocities. The charged electrons move at a faster root-mean-squared velocity and have more kinetic energy. This kinetic energy dissipates as the electron moves through space. In a charged capacitor the two groups of velocities are the same.

Gravity and capacitance are similar phenomenon. Both have the kinetic charge and back-fill return of the electron. What becomes evident is that the back-fill return applies not just to electrons. Ions may be swept in the back-fill process. The kinetic electrons move from the center of the Earth outwards and then the back-filled ions and electrons move towards the center of mass. This is what pulls an apple to the Earth or what defines the orbit of the International Space Station.

Wave Nature of the Electron and Inductance

There have been reports of a Fourier spectrum of elementary particles. Light has a wave nature and so too do the elementary particles the electron, the neutron and the proton. All energy behaves in a wave/particle duality. If waves and vortexes are natural phenomena then how do we construct one from the other.

It is important to understand how the flux of electrons' flow around conductors and dielectrics. The telegraphers equations show us that the medium around a conducting wire causes capacitance, inductance and conductance in the wire. Resistance is caused by the electrons interacting with the conducting metal lattice.

Capacitance stores energy in kinetic electrons jumping off and then returning to the wire in a rather linear path. Inductance stores energy in electron turbulence or the curl of an movement of electrons after they jump off the wire. Conductance is composed of electrons that jump off the signal or power wire while other electrons makes their way to the return wire.

If ten to the power of ten electrons are moving down a wire some of the electrons will spill out or radiate from the wire. The electrons will move around a matrix of ions in the dielectric. As with any wave the wave will refract off of ions until the attenuated wave has moved in a circle. Could this be where we get inductance? A small percentage of electrons behaving as waves store inductive energy in the curl of the electron field flow.

The telegraphers equations show us the relative values of inductance, capacitance, conductance and resistance. A small percentage of conducted electrons end up moving like a wave in a circle just as we see that the relative inductance of a transmission line is extremely small compared with the conducting electrons component.

Electron Movement Causing Capacitance

What happens when we see electron movement without net electron movement? Charge balance and electron speed are such that if an electron moves and another electron replaces the moving electron in a very short time frame then there will have been no net displacement current.

Large numbers of electrons can become excited and move to a nearby ground plane or return connection. This means that large numbers of electrons in a dielectric will move counter to the charged electrons causing capacitance. The very statistics that make up the to and fro of electron movement in a capacitor are the electric field that stores energy in a Farad of capacitance.

Highly charged electrons move down a conductor. As they approach a dielectric they find a quick path to ground through the well know relationships displayed in the capacitance equation. Electrons statistically shoot down to the return conductor and are at once replaced by less energetic electrons in the dielectric. This statistical electron dance is said to store energy in the electric field. A vacuum of high energy electrons appears on the less energetic side of the capacitor as the electrons in the dielectric are sucked away to replace the high energy electrons moving quickly on the adjacent capacitor's plate.

Electron Flow

The flux of the electron field flow has stimulated scientific inquiry since before electrons had properly been discovered. A large enough mass will contain countless numbers of electrons. These electrons must be studied statistically and through field theory. In fact, all electrical theory is explained through vector fields.

Flows that flux in a turbulent manner or one that wraps back on itself in a circle are said to be inductive. That is to say a magnetic field is induced.

Flows that flux in a stochastic manner returning to the point of origin are said to be capacitive. There is a capacity to store energy in a fluxed field that does not exhibit continuous change.

Electron Pressure and Gravity

Electrons make up a part of all spherical shaped masses in the solar system. All of these electrostatic entities exhibit gravity. The more massive the mass the higher the intensity of the observed gravity. I would like to focus on the electrons in the mass. As these electrons push out mass is drawn in to take its place. For every action there is an equal and opposite reaction force.

At the center of the mass there are more interacting electrons which have charge and will repel each other in a stronger way they the oppositely charged ions. As electrons move from the center of mass to the periphery of the mass they accelerate and the number of electrons exhibiting this behaviour increase. Gravity increases as the outward pushing electrons are replace by positive ions and electrons.

There is - effectively - a rain of electrons that pours upwards at all times sucking everything else downwards towards the center of mass.

The Magnetic Earth

If we were able to look down on the Earth from Polaris we would see the North Pole out towards the equator. We would not see the magnetic field surrounding the Earth.

As we watch the Earth spin counter clockwise from Polaris we would note that particles are interacting with the Earth and being accelerated off of the planet. The particles, including electrons, eddie off of the Earth and spin clockwise all around the planet. This clockwise spin or curl in the electron field is observed by our magnetic compass to point North.

All of the particles surrounding the Earth interact and their curls begin to line up with time. At the poles the curl bends back and heads through the Earth's core in the opposite direction. Drawing lines through the mathematical normal to all of these electron curls yields the magnetic field lines.

The Maxwell-Ampere equation confirms the eddie current explanation for the magnetic field. The magnetic field lines are well known to point up from the geographic South pole to the geographic North pole. Using the Maxwell-Ampere equation and the right hand rule and we determine that current flows counter-clockwise when observed from Polaris. Of course electrons travel in the opposite direction to current therefore the eddie current explanation for the magnetic field checks out.

Electromagnetics

1. The curl in the electron velocity field is the magnetic field. Specifically, the normal or curl of the electron field is the magnetic field.
2. Maxwell-Gauss magnetic equation is just a vector calculus identity. The divergence of a curl is always zero. If we consider that the magnetic field lines are just the vector calculus curl of the electron movement field then the identity causes the equation to collapse.
3. Attraction and repulsion of magnetic fields is due to the angular momentum of the electron fields around magnets. Fields support matter which cause repulsion.

Electron Field Curl and Magnetic Effects

In the last post I explained how the electron turbulence has been interpreted for a long time as magnetism. When a field of electrons has curl magnetism is witnessed.

Ampere showed that when two wires had a common mode current they attracted each other. To understand why this happens we have to look at the telegraphers' equations. The inductive component of these equations means that some of the electrons that leave the wire curl. The curl of the even mode wires cancels out leading to dead curl or zero curl. There will be a random type motion to the electrons and they will scatter. There will be no support for more matter and this lack of matter will draw the wires together.

Ampere further showed that odd mode currents caused wires to move away from each other. When currents move in two different wires to oppose each other they generate an induced curl that adds. That is to say the curl is additive. With additive curl and more spinning in the electron field there is more support for positively charged ions. More matter in between the wires forces them apart.

Magnets with North and South poles have to be explained as well in terms of the forces they exert on one another. When a North pole meets a South pole both poles force the electron field to spin in the same manner. Although the poles are opposite the orientation is upside-down. The spins of the electron fields is the same. The tight spin of electrons ultimately attracts the bulk mass of the opposing magnetic pole leading to a force of attraction.

When a North pole meets another North pole or a South pole meets a South pole something different goes on. Each pole has an opposing pole and the spinning electron field will seek out the opposing pole as a sort of terminating point. When a North pole meets a North pole both poles will seek out a South pole for their electron curls to terminate in. The spinning electron field between the two North or South poles of the magnets will draw in matter (positive ions) causing the magnetic poles to repel.

The Ampere wires as well as permanent magnets attract each other and repel each other due to the spins or curls in the electron fields that surround the magnets.

Spinning Electron Curl and Magnetism

When electrons spin in a curling electron field they influence other electrons through collisions and possibly wave related interactions. When electrons spin together in large numbers they create a magnetic effect. In vector calculus the spinning of a field of electrons is known as curl. The curl of the electron field is magnetism.

Electrons can curl because a ferromagnetic material aligns the spinning of the electron field or a field of electrons can align in spin due to a coiled conductor that similarly aligns the curl of the electron field around the coil. The conductor exhibits radiation as shown by the telegrapher's model of the conductor. There is a series inductance, series resistance, shunt capacitance and shunt admittance. It is the series inductance that represents the electrons leaving the coil to cause a curl in the flux of the flow of the electron field.

The curl in the electron field draws in more massive positive ions to form the nuclei of atoms. Precisely, the spinning electrons creates an environment conducive to supporting matter. More mass between two solids will result in the solids seeming to repel. The additional curl can come from two wires with opposite currents on each. Also when two like poles of magnets are put next to each other the curls of both poles wrap back allowing a cushion of air to develop. The cushion of air arises because of the spinning electrons and the ions those electrons draw in.

The pressure that electrons and ions are under near the Earth's surface is great. The electrons and ions are forcing one another together and they will be forced to interact. A square meter of matter may contain more than ten to the twenty seventh power electrons. There is a lot of interaction going on.

A curl in the electron field supports matter in that field. Near the surface of the Earth there is an incredible amount of electron pressure that supports electrons or ions to interact in a close manner.

Tesla and Gravity

Tesla was a great inventor who had opinions on a great many things. Past blog posts, of this blog, have showed some similarity to Tesla's work.

Tesla believed that gravity with an equal and opposite reaction to light escaping from the Earth. This blog thought that radiation was more in the way of Beta particles due to interactions due to the geometry of the mass.

For every action there is an equal and opposite reaction. Both Tesla and this blog agree on that. This blog thinks that electrons and their charge pressure present a constant mass propagating away from the center of mass. Tesla indicated that it was light that posed the equal and opposite reaction to gravity.

The Skin Effect

As current makes it's way down a wire we know there are collisions and parasitic effects. The parasitic effects are defined by the telegrapher's model. When considering the skin effect one has to look at the series inductance in the telegrapher's model. Electrons undergoing conduction are going to find themselves in the middle of the conductor, at the periphery of the conductor or somewhere in-between.

Electrons will push outwards from the center of the conductor and they spin. The spin of electrons creates the 'magnetic' field outside the wire. The same effect goes on inside the wire creating tight spins of electrons.

Lenz's law deals with the conservation of angular momentum as tight spinning electrons cause a bigger more broad current eddy in the surrounding conductor. These eddy currents set up in a current carrying conductor.

The eddy currents set up within a cylindrical shaped conductor. The eddy currents push downwards and backwards counter to the main conducting current. The eddy currents add up to oppose the main conducting current.

Eddy currents are only an issue for alternating current. As the frequency of the alternating current rises so too do the skin effects. The skin depth of alternating current on a conductor decreases as conducting current frequency increases.

Electromagnetic-Chemistry

This is a look at what might be going on at the atomic level of an atom from an electromagnetic vantage point. I haven't chosen any atom in particular to look at. I just want to look at the structure of the periodic table as it relates to some very basic and theoretical electromagnetic theory that goes well beyond the writings of J. Maxwell or O. Heaviside.

It is first interesting to consider the Q-factor for an atom. Q is energy stored divided by energy dissipated. This is usually easiest to measure within the context of one cycle or orbit. Q, for an atom, looks to be nearly infinite as the electrons orbiting an atom don't seem to lose significant amounts of kinetic or photonic energy. We know that electrons dissipate energy through a dissipation of photons or through transmitting energy to the nucleus synthesizing heat.

The statistical distributions and rate parameters of an atom exchanging electrons with other atoms or the vacuum of space don't seem to be well known. One way or another there must be a method of modeling electrons colliding with other matter vs an electron moving away to another atom. In a given atom (any element) with a given number of covalent, ionic or Van Der Walls type bonds, an electron, will leave the atom at a particular rate. This rate is conveniently modeled in statistics using the related Poisson and exponential distributions. The electron departing the atom may be involved in a bond or it may just be a statistical departure due to a collision or charge related effects.

It is best to use the exponential and Poisson distributions to characterize the random departure of electrons from the vicinity of a nucleus. There doesn't seem to be good data sets to try to develop rate or shape parameters for exponential or related distributions. What we can infer from what we know about atoms is that the electrons move at speeds that can only be characterized through relativity. At these speeds the electron appears to be in more than one place or to have more than the mass of one electron.

From the periodic table we can try and lay out the shape of an ideal stable atom. This is a misnomer as the electrons are traveling very fast and the configuration of an atom will be in constant flux. When looking at the atom we must switch our thinking from the flux of field theory to the discrete nature of natural numbers where there is a discrete number of electrons, protons and neutrons.

Conventionally we have to understand that the elements we observe near a large mass are under a high amount of 'pressure'. A large amount of pressure translates to a lot of electrons that are exchanged between a great number of atoms. In the upper atmosphere there is a lot of plasma interacting with a lot of particle rays from the sun (alpha, beta, gamma et al.). The pressure of a large mass with significant gravity shows atoms in a different manner than the atoms we find in the vacuum of outer space which take the form of plasma rather than the well formed atoms on larger forms of mass and in the periodic table of the elements.

So how do we visualize an atom from any column of the periodic table of the elements. I spend my time looking at columns III, IV and V of the table but any column or row is worth thinking about. Electrical engineers are often concerned with semiconductors, conductors and dielectrics.

Octahedrons are the best shape to consider when envisioning the periodic table and its elements. Octahedrons involve a lot of triangles. Eight to be exact. Octaherons have three squares, for example, one for each dimension in space. Civil engineers love triangles because trusses tend not to collapse when a truss is involved. Octahedrons also stack well so that they can be combined to form a lattice. The Octahedron has eight faces as the periodic table has eight columns and models of electrons have eight statistical positions.

Cubes have eight points allowing that form to show some usefulness whilst considering the periodic table. The trouble is that the cube is made of all square faces and without the triangles a civil engineer likes so much.

Electrons move fast and constantly. There is no reason to believe that electrons always move at speeds less than light speed. When electrons move this fast around a much more massive nucleus we can expect some interesting effects. The spin of both the electron and nucleus will mean that most collisions between the electron and her nucleus will result in a bounce and not a new neutron. This is similar to the effect of a top bouncing off an object as in collides with great spin. Also, the high speeds of the electron mean that the very shape of the atom will be low pass filtered. Rather that a perfect octaheron or cube we end up with a sphere shaped atom if we could look at any type of time lapsed photograph of this particle.

I'll circle back now to the Q factor as it relates to one or more atoms. Single atoms seem to have an extremely high Q factor due to the fact that they don't seem to dissipate energy over short periods of time. Putting ten to the power of forty atoms in close proximity adds a low pass filter effect to the Q factor of the new system. Energy stored vs. energy dissipated goes down greatly because of the energy stored in the form of capacitance and inductance and the energy dissipated rises due to interactions between the electrons and the lattice or nuclear complex. It is important to consider the transmission line equations as they relate to large masses. The transmission line equations as they relate to large masses displaying obvious gravity may be the subject of a future blog post.

Hypothesis on Electromagnetics

Electromagnetics has long been an area where Maxwell's equations have broken down into a set of differential equations describing a wave. Since the Michelson–Morley experiment was performed it has been assumed that an electromagnetic wave propagated without a medium. Previous to the Michelson-Morley experiment there had been an assumption that Ether was the medium electromagnetic energy propagated in.

I would hypothesize that perhaps our medium for electromagnetic power - Ether - is lumpy. So lumpy is the Ether that it may be looked at as electrons, Beta particles or even photons. Electrons jump massive distances in very short periods of time as they travel at a real fraction of the speed of light. Secondly, Diract determined that the electron had a certain duality to it. Perhaps the electron can be seen to be in multiple different places. Due to their incalculable speed, electrons almost appear to be in two places at once yet they may exist only at one point in space.

Electron characteristics might lead one to believe that electrons normally constitute both the signal and the medium for most electromagnetic wave propagation.

It may be required that protons and neutrons are required to produce a plausible medium for the propagation of any significant amount of electromagnetic power. Without a dense medium the power will disperse.

Also note that to receive any signal, current technology requires protons and neutrons to detect a power level derived from photons or, more likely, electrons.

It may be possible that if electrons and photons do not make up a suitable medium for a complete theory then it is at least a good place to start figuring out practical applications for a lumpy or discrete medium. Protons, neutrons and more exotic particles can be factored in later. Getting into drift velocity while at the same time contemplating near light-speed electromagnetic wave propagation seems like a disjointed fact set.

I'm sorry that I'm rambling now. The electron has been shown to show up in aprox. two places at once (Dieract). It makes more sense to me that the electron only measures to be in two places at one as an average in the present. In reality the electron can look to be in infinite places or in the ultimate reality of t+1 the electron is in one place. I'll either post more on this later or erase this text if I feel this is a dumb theory later.

Archimedes' Principle and Gravity

This blog has represented gravity as a type of electron buoyancy. Of course the effect of all of the electrons on the nucleus-es is considered. Assuming Archimedes' principle to be formulated as Wikipedia has as follows: observed weight = mass - displaced mass.

Is it possible to develop a similar relationship for the gravitational relationship between large mass and the electrons escaping a mass the size of a planet. There is a propensity for electrons to escape the center of mass due to the excess negative charge found there in any mass. Permeating the mass is the propensity for negative charge to want to move out from the center of mass. Charge balance brings electrons and with it mass back towards the center of mass in what we call gravity.

Observed weight = pressure due to charge balance return to the center of mass - pressure of electrons moving towards the periphery of mass. There are differences between gravity and Archimedes' buoyancy however they are analogous. Buoyancy involves atoms of different sizes displacing each other while gravity involves different parts of the atomic structure displacing each other to cause movement of a mass.

Electron Statics and Gravity

Electrostatics-wise, gravity can be seen in figure 1 as more proximate negative charges towards the center of a mass. The small and fast charges will accelerate from the center of mass to the periphery of the mass with a mean drift velocity as in any electric circuit. Electrons will jump like a grasshopper towards the periphery of the mass. Figure 1 makes sense if you imagine more mass with the center of mass at the focus of the diagram. Figure 1 is meant to illustrate the crowding of the innermost electrons juxtaposed against the sparse peripheral electrons in any mass.

Due to the charge balance theorem for every electron that accelerates towards the periphery of the mass there will be an electron or ion that take its place. There is an illustration of the effect in figure 2.

The gravitational effect comes from all of the ions that get pulled inwards to counter the electrons moving outwards at a fraction of the speed of light. 

Poisson Distribution and Momentum as they Relate to Capacitance and Gravity

I apologize for the disparate nature of this post. I am going to try to relate some topics that aren't often related. The Poisson distribution for a given area in space may well model how electrons are accelerated. Conservation of momentum will give us a hint as to how electrons behave such that they give us capacitive or gravitational properties.

Electrons in a capacitor will behave in a certain fashion according to certain statistical distributions and in line with the material properties of the dielectric. Where gravity is concerned, previous posts have discussed, the tendency for the innermost portions of the mass to have a net negative charge causes accelerations within a mass.

If a plate of a capacitor is brought to a negative voltage the capacitor is know to take in a certain amount of charge. Where this charge goes and how it behaves most likely has to do with the Poisson distribution. Electrons will be ejected from the negative plate at a rate, lambda. The excited electrons will be ejected from the plate quickly but they will be replaced due to the charge-balance theorem right away by nearby electrons in the dielectric.

The electrons fly off the negative plate and, with a statistical regularity, approach the positive side of the capacitor. Eventually if capacitance is not to become conductance the electron will double back. The double-back will happen right away in the form of another electron moving in to take the place of the faster moving electron. This process will happen again and again according to the Poisson distribution due to the more energetic electrons on the negative plate.

If a fast moving electron is going to eject itself from a negative plate both charge balance theorem. The fast moving electron will be supplanted by multiple electrons within a particular point in space. Fast moving electrons move one way and many electrons back-fill going in the opposite direction.  In fact, larger ions can get hauled in the opposing direction to the fast moving electron.

Gravity uses the same fast movement and back-fill principles for electrons only for different reasons. A mass will tend to have more negative charge congregating at the middle of the mass. Fast moving electrons will shoot towards the periphery of mass. Gravity is the effect of having the larger ions hauled towards the center of mass.

Maxwell's Equations Broken Down

Heaviside modified Maxwell's equations to provide a set of equations that define much of electromagnetism as we know it today.

The Maxwell-Gauss' equation for electric fields defines electric fields as a vector field pointing from positive to negative.

The Maxwell-Gauss' equation for magnetism is nothing but a vector calculus identity. If the magnetic field is just a curling electron field then the divergence of a curl will always be zero.

Defining the magnetic field is done through the Maxwell-Ampere equation. The current is the curl on the magnetic field. Stated more simply a localized electron flow will create local and more distant electron turbulence. Due to constructive or destructive electron turbulence conductors will either attract each other or repel each other.

The Maxwell-Ampere equation apply with the curl of a magnetic field is proportional to the currents. If a current field is curled then a proportional magnetic field will be the result. This allows us to build a coil and observe a magnetic field. Really all that is observed is a curling electron field. The additive electron field created by the coil maximizes magnetic effects.

The last effect that Maxwell and Heaviside observed is known as the Maxwell-Faraday equation. This equation largely describes conservation of angular momentum using vector calculus. When a group of electrons enters a region where there is tight spin of electrons the introduced electrons spin tightly. Due to the conservation of angular momentum a very broad spin of electrons sets up in opposition to the tight spinning electron field.

Coils take advantage of the broad spin with each end of the coil catching a momentum effect from a moving coil. We call the Faraday momentum of electrons the electromotive force.

Feeling Gravity

To get a feel for why particles tend to attract one another one can start with a few simple particles and move towards what looks like an infinite number of particles in a large mass. When there are few particles involved the phenomenon is known as the London force. The London force shows that seemingly inert or non-bonding atoms will still attract one another.

The London forces have been simulated. Electrons moving at one percent the speed of light repel each other much faster than their nucleus repel each other. Electrons neutrons and protons fill in where the electron was ejected. This forces the neutrons and protons together with the electrons circulating.

The same phenomenon repeats itself in a linear manner as a mass of particles grows. It never hurts to underline just how many particles a mass has. One kilogram of a given material may have more than ten to the twenty atoms in it. The vast number of particles with a linear growth in attractive forces due to the asymmetry between electrons and their ionic nucleus make for a 'weak attraction' known as gravity.

The tendency towards the center of mass will be for the electrons to interact and be ejected towards the periphery of the mass. Meanwhile the charge balance theorem and the missing mass from the ejected electron will force electrons, neutrons and protons towards the center of mass in what is known as the 'weak force'.

Buoyancy and Particle Size as it Relates to Gravity

An old birthday trick has us filling a balloon with Helium. The Helium displaces a large volume of space with a light mass causing a low density. Relatively speaking there exists a vacuum where we find a concentration of Helium inside the balloon. Pressure is exerted on all boundaries of the relative vacuum known as our birthday balloon. There is more pressure at the bottom of the balloon and the low density balloon rises.

In the case of a helium balloons the inside of the balloon is filled with less dense single helium ions that associate themselves with two electrons. Outside the balloon we find Nitrogen diatomic molecules which are much more dense. Due to the large root mean squared speed of all of these molecules they find a buoyant balance very quickly. The balloon rises. This is the contrast between Helium and diatomic Nitrogen.

Electrons and ions of Silicon and iron exist in a veritable mesh in the Earth's mantle. The speed at which the electrons move with respect to the speed of the ions is fantastic. Ions stay still with a Brownian motion component whilst electrons dart about at one percent of the speed of light - root mean squared speed. The electron portion of the molecules that make up the Earth have a lower density. Electron charge pushes outwards from the center of mass while more massive ions or slower electrons will be pulled towards the center of mass.

Gravity and the Electron Distribution and how it is Additive

It has been observed under many circumstances that substances stick together. The nucleus of an atom, the plastic floating in the ocean and matter as a part of a planet or star tends to stick together. These different types of stick-together-edness may or may not be related.

Gravity and the semiconductor pn-diode may have something in common. If the n-doped portion of the diode is oriented towards the center of mass the p-doped portion might well model the relative expanse towards the outside or periphery of a mass. The electrons get squeezed and they form a depletion effect which means that the electrons are out of position in the mass structure with respect to the charge balance needed for the perfect equilibrium we all learned about in grade eleven chemistry class.

Slower moving protons, neutrons and electrons are drawn towards the center of mass through charge balance neutralization. This geometrically induced electromagnetic effect gives us what we see as gravity.

The electron depletion effect mentioned in the second paragraph is most pronounced towards the center of mass. Towards the outside of a large mass such as the Earth or the Sun we get a cumulative or additive effect of more and more electromagnetic pull that adds to the pressure felt at the surface of the center of mass.

The proportion of force that is exerted on an object can be seen by studying the volume and surface areas of a sphere or a cube. Surface integrals and volume integrals will give answers on the dynamics of the gravity force as it pertains to a mass such as the Earth.

Adding the products of the volume integrals from the center of a mass to the periphery of a mass gives us the answers we need to understand the pressures and densities observed in our solar system. These analyses can get quite complicated fast. Is the surface of a mass liquid or solid? What about the atmosphere? How does this affect gravity? Model this as buoyancy. Move forward with models considering liquids at the surface of an object the size of the sun.

The Magnet, Gravity and a Paper Clip

A popular publication asks the question; How is it possible for a magnet to pick up a paper clip against the force of gravity exerted by an entire planet?

This publication has trouble with large numbers and the interactions between the large numbers of fundamental particles involved. Magnetism and gravity work very differently and have been the subject of many of my blog posts. In previous posts I normally prefer to use Maxwell's equations with Heaviside's telegrapher's equations to make points about the real nature of electromagnetic interactions.

Ampere worked to give us a model for magnetism. If we spin electrons in the right way we will create a field of spinning electrons due to the interactions between electrons and the nucleus. The telegrapher's equations point to the mechanism by-which the electrons create spinning fields (L) and more linear electron fields (G and C). The spinning fields beget more positive ions that come in to charge balance the spinning electrons. Ampere's wires are thus forced apart.

Static magnets work in a very elegant manner. The magnet's ejected electrons are what some call the magnetic field. Really electrons are just moving in a circular manner determined by the magnet's electro-molecular geometry. When a magnet is flipped pi radians it's electrons have the opposite spin and the magnet is pointed in the opposite direction. Therefore, the magnet will attract the opposite pole of another magnet. The spinning electron field will line up atoms and molecules and the biggest and dense molecules of the opposing magnet will be attracted to charge-balance spinning electrons in a gas (or vacuum).

Gravity attracting matter has a more subtle explanation than the mechanical explanation as to how magnets attract. Gravity attracts slower moving matter and is an effective back-fill to electrons moving upwards. As matter attracts more matter to itself a positive feedback cycle is produced. Negative charged electrons will repel each other closer to the core of any mass. The escape route for this charge will always be towards the outer shell of the mass. There will be an acceleration of charge towards the outer shell of the mass. The electron ejected from the mass will need to be charge-balanced. This charge balance as ions of all sorts fall back towards the center of mass is what we feel as the force of gravity.

True understanding of the nature of the force of gravity rests on the understanding of how many molecules are involved. While a small number of molecules will exhibit the London Force ten to the twenty-fifth power number of molecules presents a stronger attraction depending on the specific electro-chemical interactions of the constituent molecules. Astro-physicists seem to write a lot about iron.

If paper-clips are the great mystery of physics perhaps we can put to rest the mechanism by-which a paper clip is attracted to a magnet against the force of gravity. Because the mechanisms of these two forces are so different the organized force around a magnet can overcome a very disorganized but statistically relevant force around an entire planet.

Gravity and Maxwell's Equations

Previous blog posts have looked at gravity as a combination of electromagnetism and geometry. Maxwell's equations are the vector calculus description of electromagnetism so it might occur to a physicist that Maxwell's equations can explain gravity. This is only partly true.

The two Maxwell-Gauss equations explain static fields and can get us part of the way towards explaining gravity. Maxwell's equations don't explain the fast moving root mean square speeds observed in electrons and nuclei.

Maxwell-Gauss' electricity equation explains how the fictional electric field works. The field lines in an exaggerated sphere will tend to diverge as the observer moves from the center of mass.

Maxwell-Gauss' magnetism equation explains how the fictional magnetic field works. In reality the magnetic field simply represents the spinning of electrons as they travel through space. The field lines in an exaggerated sphere will tend to have a density that is lower as the observer moves from the center of mass.

Where electric fields converge we find a complicated mix of alternating positive and negative fields. Electrons in close proximity will tend to flee the relative convergence of a dense portion of matter near the center of a mass. Towards the periphery of a mass the opposite is true. Mass tends to seek charge balance and gravity takes the form of particles spinning back towards the center of mass. It is highly likely that the return to the center of mass happens more slowly and with more bumps than the ejection of particles; most notably beta particles.

Magnetic fields are orthogonal to electric fields. Where the magnetic field lines are found to be more dense we find an environment that is ready to impart potential energy to particles. This will happen, most readily, to the small and fast electrons rather than the ions in the nucleus. The ejected beta particles will eventually collide with other electrons or, less likely, with the nucleus of a particle.

The electrons will travel away from the center of mass. The resultant pull due to the charge balance of the mass will yank particles of both 'charges' back towards the center of mass. It is this constant pull that constitutes the gravitational pull that we experience every day on Earth.

Depletion Layer and an Air Gap

It is interesting to consider the differences and similarities between the depletion layer or transition layer in a semiconductor and an air gap. This is important because for decades the mechanical relay used an air gap to produce an 'open circuit' output that would break the circuit and inhibit current flow. Now semiconductors can do the same thing using the depletion layer but exploring this part of a semiconductor takes a bit more imagination.

Imagination is needed because there aren't great descriptions of how the depletion layer works beyond a smoothing of the charge balances between 'positive' and 'negative' doped semiconductor regions. How do those charges jump around? Like the charge discussed in my posts on gravity, the depletion layer may see spark-like charge jumps and fuzzy-Gaussian charge movement akin to the boil seen in a kettle.

The spark-like carriers I write about are often termed hot carriers and although the Poisson - Gaussian statistical movements are not termed cool carriers, The term shot is often used in noise theory and has also been related to the Poisson arrivals in mathematics. Thinking hard about what electrons are doing statistically leads quickly to words like fuzzy vs. spiky.

Let us consider, more closely, the depletion layer of a standard Si diode that does not have Schottkey properties. The standard theory states that there is charge smoothing through the depletion layer. Doped Si on either side of of the p-n junction swaps sides causing the depletion layer to exhibit a neutral or opposing charge.

I'd like to see more research in this area of Poisson vs. Gauss statistics in the p-n junction. How does 1/f noise factor into the analysis? The p-n junction may have a kettle boil of charge that traverses the junction with a statistical equilibrium that causes the diode action. The incoming charge comes in hot and crosses the diode to the junction where it either piles on to the depletion layer or in fires right through relatively hot (though nothing like the Schottkey diode). Diodes behave differently depending on whether or not they are forward or reverse biased.

A full comparison to the air gap in a relay will have to wait for a future blog post. It is enough to say, right now, that when the incoming carriers pile into the diode they are under what people our size might term - incredible pressure. At the electron feature size particles behave differently. The growth of the depletion layer due to incoming carriers leads to what I would estimate is a Gaussian or fuzzy electron distribution. This kettle boil keeps the reversed biased diode 'gaped from conduction'. The depletion layer is not an air gap where arcs are prevented. The depletion layer provides a push back that mimics the air gap of an electro-mechanical relay.

Turbulence and Electron Flow

As stated on a previous post, turbulence and laminar flow are terms usually reserved for aerodynamics. Electrons flowing through a circuit might be said to exhibit turbulent or more graceful flow. During the graceful flow of molecules or electrons density can go up as the electrons are very well ordered. A turbulent flow of electrons consumes more space and draws in positive ions. This is the magnetic push observed between like poles of a magnet.

Question of the day: Can a proper Poisson related (shot pattern of multiple Poisson arrivals) cause light gravity to shift if the right number of electrons are moving with respect the the mass ratio of the electron to nucleus ratio? Light gravity could move shift and swirl without affecting heavy gravity. This would result in two different gravity constants for the same point of space close to a large mass such as a planet. Gravity could then not be said to be simply 9.8 m/s^2.