A group of four partial differential equations that describe all classical phenomena, involving electric and magnetic fields. James Clerk Maxwell (1831 to 1879), a British physicist, first wrote out this complete set of equations:

(1.) ∇·D = ρ

(2.) ∇×H = J + (∂D/∂t)

(3.) ∇·B = 0

(4.) ∇×E = −(∂B/∂t),

where D = electric displacement
ρ = electric charge density H = magnetic field strength J = electric current density B = magnetic flux density E = electric field strength.

Equation (1) is equivalent to Coulomb's law, the inverse square attraction of static electric charges. Equation (2) is Ampere's law relating magnetic fields and currents, which was extended by Maxwell to include induction of a magnetic field by a time-varying electric displacement. Equation (3) is Coulomb's law for magnetic flux, expressing the absence of isolated magnetic charges. Equation (4) is Faraday's law of induction, relating an electric field to a time-varying magnetic flux. Maxwell's equations are the starting point for all calculations involving surface or borehole EM methods.