Original Derivation

From experiment we have four laws, they are:

Coulomb’s Law: ∇⋅D = ρ

Ampere’s Law: ∇×H = J

Faraday’s Law: ∇×E + ∂B-∂t = 0

Absence of free Magnetic Monopoles: ∇⋅B = 0

We also have the continuity equation:

( )∇ ⋅J + ∂ρ-= 0 =⇒ ∇ ⋅ J + ∂D- = 0 ∂t ∂t

which means we replace J in Ampere's Law by its generalization. J → J + ∂D-∂t, then we have Maxwell's Equations:

∇⋅D = ρ

∇×H = J + ∂∂Dt-

∇×E + ∂B-∂t = 0

∇⋅B = 0

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