Maxwell’s Equations

Four equations, known as Maxwell’s equations, are regarded as the basis of all electrical and magnetic phenomena. These equations are as fundamental to electromagnetic phenomena as Newton’s laws are to mechanical phenomena. The theory developed by Maxwell turned out to be in agreement with Einstein’s theory of relativity. The equations predicted the existence of electromagnetic waves (traveling patterns of electric and magnetic fields), which travel at a speed of

Maxwell’s Equations

Time Sequence of E and B

Maxwell’s Equations

Gauss’s law (electrical): The total electric flux, Φ E =, through any closed surface equals the net charge inside that surface divided by  o This relates an electric field to the charge distribution that creates it

Gauss’s law (magnetism): The total magnetic flux through any closed surface is zero The number of field lines that enter a closed volume must equal the number that leave that volume The magnetic field lines cannot begin or end at any point Isolated magnetic monopoles have not been observed in nature

Faraday’s law of Induction: An electric field is created by a changing magnetic flux Induced voltage Emf=- around any closed path, equals the rate of change of the magnetic flux through any surface bounded by that path Example: A current is induced in a conducting loop placed in a time- varying B

Ampere-Maxwell Law A generalization of Ampere’s law Creation of a magnetic field by a changing electric field and electric currents The line integral of the magnetic field around any closed path is the given sum

The Lorentz Force Law F = qE + qv x B Maxwell’s equations, together with this force law, completely describe all classical electromagnetic interactions