One more point you may want to internalize: If you integrate the Faraday / Ampere equations, the divergence of the Magnetic field will never change, and the di

One more point you may want to internalize: If you integrate the Faraday / Ampere equations, the divergence of the Magnetic field will never change, and the divergence of the Electric field ("charge") will obey a continuity equation with the current. So the two Gauss Laws don't really have any Dynamic content, they're just requirements on the initial conditions of the Fields.