Maxwell's equations (redirected from Maxwell's field equations)

Maxwell's equations

Four equations, formulated by James Clerk Maxwell, that together form a complete description of the production and interrelation of electric and magnetic fields. The statements of these four equations are (1) electric field diverges from electric charge, (2) there are no isolated magnetic poles, (3) electric fields are produced by changing magnetic fields, and (4) circulating magnetic fields are produced by changing electric fields and by electric currents. Maxwell based his description of electromagnetic fields on these four statements.

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Maxwell's equations

Four differential equations proposed by James Clerk Maxwell in 1864 as the basis of the theory of electromagnetic waves. They may be written, in vector notation, as Eqs. (1)–(4), where D is the electric

(1) 

(2) 

(3) 

(4) 

displacement, B the magnetic flux density, E the electric field strength or intensity, H the magnetic field strength or intensity, ρ the charge density, and i the current density.

The first equation states that electric flux lines, if they end at all, will do so on electric charges. The second states that magnetic flux lines never terminate. The third is a form of Faraday's law of induction, which states that the rate of change of the magnetic flux threading a circuit equals the electromotive force or line integral of E around the circuit. The fourth integral is based partially on A. M. Ampère's experiments on steady currents which show that the line integral of the magnetic intensity H (or B /μ, where μ is the permeability) around a closed curve equals the current encircled. See Displacement current