Maxwell's Equations Restated

If I could modify Maxwell's equations to make them more practical I'd take them one by one. First of all the equations we call Maxwell's are Heaviside's restatement, using vector calculus, of Maxwell's nine equations. Maxwell's equations were put together before Bohr put together the model for the atom. Some updates should really be made.

The Maxwell-Gauss equation for electric fields shows electric fields terminating at charge points. This equation defines how electric fields look.

The Maxwell-Gauss equation for magnetic fields may not tell us much. If we take a magnetic field to be the normal vector in the spin of an electron field then there may not be much going on with this equation. The Maxwell-Gauss equation for magnetism says simply that the divergence of a curl is equal to zero. This is a vector calculus identity!

The Maxwell-Ampere equation states that the curl of a magnetic field is equal to the volume current density. This tells us that a current carrying wire will be surrounded by a magnetic field elliptically around the current carrying wire.

What is equally interesting to the Maxwell-Ampere equation is the fact that the curl of electric charge movement through space yields a magnetic field around the current carrier. This can be found directly from the Maxwell-Ampere equation but is worth restating in its own equation. After all, it defines all electro-magnets.

The Maxwell-Faraday equation is the most complicated and nuanced of Maxwell's equations. It seems that a changing magnetic field causes a curl in the electric field. Coils moving through a magnetic field will likely have their spins line up with the spins in the magnetic field. The conservation of angular momentum comes in to play and a reverse circular movement of electrons produces an electromotive force.

So rather than using Heaviside-Maxwell's four equations I'd use Maxwell-Ampere's equation, Maxwell-Ampere's modified equation above and the Maxwell-Faraday's equation to explain electromagnetics.