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.