Heaviside interpreted Maxwell's equations as four equations. Let's consider what these four equations really mean.
Maxwell's Gauss equation for electricity states that the charge contained in a volume is equal to the electric field from that volume. Electrons moving at a fraction of the speed of light move far faster than protons and neutrons moving at a fraction of this speed. This root mean squared speed differential leads to Gauss' equation for electricity.
Maxwell Gauss' equation for magnetism states that the net magnetic flux from a volume will always equal zero. This mean that magnetic fields will look elliptical at all times. A magnetic field is a curling field of electrons. If we put a curling electron or current field into the Gauss magnetism equation we get the divergence of a curl is equal to zero. This is a vector calculus identity.
The Maxwell Ampere equation has the curl of a curl. The magnetic field is a curling field of electrons. Those electrons curl from a current of electrons due to the electron's tendency to orbit surrounding nuclei. The magnetic field is the curl vector from the field of rotating electrons. These magnetic fields bend elliptically around currents.
The Maxwell Faraday equation states the change in magnetic field causes a curl in the electric field. Understanding how electrons curl is instrumental to understanding this equation. When a conductive curled wire enters or turns in a magnetic field the field induces tight curls of electrons in the wire. At a higher level the electrons oppose the tight curls due to conservation of angular momentum. As the curls of the electrons change there is a brief counter curl at the macroscopic level in the curled conductor.
