Maxwell-Faraday Equation - Does It Even Say the Right Thing?

So those who like electric motors and generators look to the Maxwell-Faraday equation to get direction and relative motion of current right. Curling electric fields and changing magnetic fields, described by this equation, give us the logic we use to run millions of machines world-wide. What's more this equation works.

We can do much better. The Maxwell-Faraday equation doesn't capture the complexity of what is really going on with the curl in the currents. This equation instead uses some vector calculus to explain the big picture of what is really going on. The equation tells us that a curling electric field and thus a curling current due to a changing magnetic field. Now why might that be?

The magnetic field is often a tight curl of individual electrons that emanates from one pole of a magnet and terminates in the opposite pole of the magnet with the same total curl to preserve the conservation of angular momentum. The Maxwell-Ampere equation shows us the relative polarities and spin of the electrons and how that relates to an electron current. The curl of a magnetic field is equal to the displacement and volume charge current. The curl of a current field is proportional to a magnetic field at some distance from a coil or a current carrying wire.

Once the polarities have been sorted out we can dive into the Maxwell-Faraday equation. Starting with the right side of the equation we find the changing magnetic field. A changing magnetic field involves a tight spiraling field of electrons. As this tight spiraling field approaches the point under analysis by the equation the field gets tighter and the number of spinning electrons becomes greater. When we observe a point under analysis that is conductive we find that the tight curls accelerate the electrons in the conductive material.

Conservation of angular momentum (some have written conservation of energy) and other electrons in the conductive material find themselves in a larger curl oriented in the opposite direction. For this reason the left side of the Maxwell-Faraday equation shows the large counter-curl of the electrons as a curl of an electric field.

Can Physics Do Better Than the Maxwell-Heaviside Equations

Heaviside's version of Maxwell's Equations are a history lesson. There have to be better ways of describing electric phenomena and magneto attraction. Running through Maxwell's equations tells us the basics of the way electromagnetism works using the concept of fields, flow of fields and the flux of the flow of these fields. Specifically a branch of physics examines the flux of the flow of magnetic fields to describe how magnets will behave and electric flux of the flow describes how charged particles will behave. In addition to Maxwell's equations the Lorentz force equation provides additional information on the behaviour of charge in the presence of the above mentioned 'fields'.

The Gauss-Maxwell electric field equation describes a volume charge can be represented as a diverging electric field. This is a convenient representation of electric phenomena and it seems to hold at a high level. Is this equation accurate at a microscopic or nanoscopic level?

The Gauss-Maxwell magnetic field equation is simply a vector calculus identity. The electrons turbulently fly off any given wire and curl. This is especially true for natural magnets. The normal of this curl is what Maxwell and Heaviside termed the 'magnetic' field in this set of equations.

The Maxwell-Ampere equation states that a magnetic field curls around a volume current density or a changing displacement current. It is important to note that when the electron field curls the magnetic field lines up as well as in the case of an inductive coil electromagnet. These two relationships reflect that when there is turbulence in a field of moving electrons the spinning electrons interact with the laminar flow of current in a manner described by the inductance equations.

The Maxwell-Faraday equation should be rewritten. There is a lot going on when we relate the change in magnetic field to a curl in the surrounding electric field. Specifically Lenz's law shows us that opposing eddy current show up when a magnetic field is presented. The magnetic field sets up and increases in a tight fashion. What this equation is really saying is that conservation of angular momentum of electrons causes a large curl of electrons to set up when a tight curl of electrons in a magnetic field is presented. The whole truth of electromagnetic induction with respect to curls of currents and counter-curls of current are not being told using this equation or any other popular equation.

Finally, Lorentz's equation shows us what direction a particle will travel in the presence of electric and magnetic fields. A moving charge will be deflected by a magnetic field or turbulence in a field of moving or curling electrons. Charge will see a force by other charge and the equation sums this up neatly.

Maxwell's Equations Revisited

In previous blog posts I've stated the Gauss' law of magnetism is just a vector calculus identity. Ampere - Maxwell equation simply states that electricity moving in a circular or turbulent motion is what we call magnetism. The magnetic field is the normal vector of the circulation or turbulence of the electron flow.

Now I look at the Maxwell - Faraday equation and relate it to Lenz's law. The tight circulation of magnetic field or curling electrons is observed by its counter-rotating motion of other electrons working to conserve angular momentum. It is the counter-rotation that we observe in an electric generator and we normally attribute that to the Maxwell-Faraday equation. In the Maxwell-Faraday equation the change in magnetic field magically creates a curling electric field.

Laminar and Turbulent Flow

The link between fluid dynamics and electron flow is incomplete and a bit on a stretch for most physicists but what better place to explore the topic than a blog? Laminar and Turbulent flow are two fluid concepts. Current and inductance are analogs. A turbulent flow that wraps back on itself stored energy in the same way as an induced curl field in a circuit. The telegraphers' equations specify the current as the series linear circuit elements R and L.

Viscosity is the propensity of the fluid to resist deformation. If an electron is injected into one side of a copper wire does one pop out the other side? Certainly yes though the turbulence of the route the electron takes is questionable. Now if you tried to push a Coulomb of electrons into the wire the capacitance specified by the telegraphers' equations would have to absorb all of the charge save the bleed off due to G.

In effect the ratio of R:G tells us something about how electrons behave in an electronic circuit. What is the ratio of electrons that push through to the load vs those that end up back at the electromotive force source having not delivered energy to the load. The probability that the electron will not deliver energy to the load is R:G.

Magnets and Spin

Every chemist learns about the electron spin and magnetism. The so called magnetic field is just the propensity for electrons to 'curl' to borrow a term from vector calculus. So from the North pole of a magnet to the South pole of another magnet the curl will tend to align. The curl will also tend to make a round trip. The electrons curl on the way into one pole of a magnet and they curl on the way out of the other end of a magnet.

So what of electric generators and motors? We set up a field of curling electrons and we expose a coil to the field.The tight curl of electrons begs for the coil to conserve angular momentum. There are tight swirls due to the magnet and an induced larger swirl that constitutes the current that makes up the voltage presented in a generator.

As a generator turns it exposes itself to more and more of the curled field of electrons. Then as the generator coil moves past pi radians the process reverses itself. This can be characterized by Maxwell-Faraday's law but also invokes Lenz's law. These two laws or relationships can be explained as one idea but I will reserve this explanation for another post.

The reason magnets attract different poles is due to a mess of electrons rotating in opposite directions. At the boundary between electrons moving one way and another (magnetic field lines in opposing directions) there are many collisions. These collisions will at as a relative low pressure zone pulling the magnets towards each other. The sheer pressure of the electrons puts a mechanical force on the rotor of the generator.

Conversely, when two like poles are put next to each other the spin of their electrons does a tight loop to its opposing pole. This looping of electrons draws in matter and causes the two like poles to push away from each other. The same phenomenon is at play in Ampere's laws of attraction.

The Idea of Electron Pressure

Pressure is measured in force per unit area. Do we allow that electrons carrying mass can exert force on a cross section of a wire? Certainly we observe electromigration of mass through wires. The electrons seem to push through resistances without too much interaction. Electrons seem to spring through a lattice of copper like putty through sand.

If the electrons in a mass are dense from the standpoint of small masses travelling at 1% of the speed of light. Then as we bend the medium to make a sphere or a cube the electrodense inside will push electrons outwards. The outwards push will be fast compared with the pull back for charge balancing. All of the negative charge lost is filled with returning mass.

One of the thoughtful mistakes that might be made is assuming that electron pressure is less than it is. Electrons seem to be the light cloud that surrounds the real mass of the nucleus. In fact electrons moving at 1% of the speed of light exert a pressure that adds up to gravity. Internal electron pressure is greater than outer electron pressure causing a charge inversion. The balance of charge and mass is a push inwards towards the center of mass.