The 'Magnetic Field' and Spinning Electrons

The biggest mystery I see in the physics of electromagnetics and electrical engineering concerns Heaviside's four equations representing Maxwell's equations in vector calculus form. The Gauss-Maxwell equations dictate the shape of the fields as they were observed before Bohr's model of the atom took hold. The Ampere-Maxwell equation dictates current flow and it's relationship to the 'magnetic' field. The magnetic field was a construct necessary before we could understand how a lattice of metal ions related to free electrons and bound electrons. Finally the Faraday-Maxwell equation describes the first derivative of the Ampere-Maxwell with respect to time. This is critical for understanding how the electromotive force is generated.

The Ampere-Maxwell and Faraday-Maxwell equations seem to work both ways. That is to say the Ampere-Maxwell equation is often made reference with respect to the magnetic field forming around a conductor. But the curl of the current of an electromagnet also produces the straight portion of the magnetic field. Likewise with the Faraday-Maxwell equation the curl of an electron field produces a change in the magnetic field. The opposite is true. The change in a a magnetic field causes a curl in the electric field. We use this equation to explain electric generators and electric motors.

Many of the applications where we see magnetic fields set up are around conductors. Conductors are the most common place to find free electrons carrying charge. We know from the telegraphers' equations that there are parasitic leaking of charge from the conductor in the form of conductance and I will add capacitance and inductance. In the case of inductance the parasitic electrons eddy out around the dielectric surrounding the conductor. This creates a curl of the electron field surrounding a conductor with a net drift velocity of its electrons.

The curl vector from vector calculus of the electron field is proportional to the magnetic field lines. Magnetism is just electrons moving in a curling manner. Previous blog posts sought to explain how the curl of the electrons leads to attraction and repulsion of magnetic solids or current carrying wires. Explaining magnetic phenomenon any other way may be difficult enough to prove truth to the circulating electrons. Perhaps X-ray imaging of time lapsed magnetic phenomenon can answer questions at the Government Labs in Oakridge, Switzerland or Sandia.