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.