Original Derivation
From experiment we have four laws, they are:
Coulomb’s Law: ∇⋅D = ρ
Ampere’s Law: ∇×H = J
Faraday’s Law: ∇×E + = 0
Absence of free Magnetic Monopoles: ∇⋅B = 0
We also have the continuity equation:
which means we replace J in Ampere's Law by its generalization. J → J + , then we have Maxwell's Equations:
∇⋅D = ρ
∇×H = J +
∇×E + = 0
∇⋅B = 0