Lecture 8 Part 2 Discovering Maxwell's Equations

By boosting Gauss' Law we discover Ampere-Maxwell's equation. The displacement current is thus derived from first principles. Electric current conservation follows from Ampere-Maxwell's equation. Faraday's law is obtained by boosting Gauss' law for the magnetic field which states that magnetic monopoles do not exist.The eight Maxwell's equations, two quartets, one homogeneous and the other with a source, the four vector electric current density, are thus obtained from two local differential equations, Gauss' Law for electric and magnetic charge densities.