Generators Interacting with the Field

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

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

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

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

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

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

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