What is the meaning of Maxwell's equations

Maxwell's equations

Maxwell's equations, the basic equations of classical electrodynamics, which contain all phenomena of the Electromagnetism and the optics include. The equations are partial, linear, coupled first order differential equations; they were made by J.C. Maxwell as part of his ›dynamic theory of the electromagnetic field‹. This is essentially based on the field concept of M. Faradays, who formulated electromagnetism as a theory of close-up effects.

The Maxwell equations are



Describe the field sizes E. (electric field strength), D. (dielectric displacement), B. (magnetic flux density) and H (magnetic field strength) the electric and magnetic fields. The material equations mediate between themεE. = D. or. B. = μH. ρ is the electrical charge density, j the current density, in conductive media the extended Ohm's law applies j = σE. (σ: electric conductivity). The term

will also be Maxwell's displacement current called; it was introduced by Maxwell to make the system of equations consistent and means that only the change in an electrical field (e.g. when a capacitor is charged and discharged) produces a magnetic field.

The physical content of the equations states the following: (1): The electrical charges represent sources and sinks of the electrical field. (2): The magnetic field is source-free, there are no isolated ones magneticMonopoles. (3): Changes in the magnetic flux over time generate eddies in the electric field (FaradayschesInduction law). (4): Conduction and displacement currents generate eddies in the magnetic field, they are often (somewhat imprecisely) referred to as sources of the magnetic field (Ampère's laws).

In a vacuum (ρ = 0, j = 0, ε = ε0, μ = μ0) the Maxwell equations simplify to div E. = div B. = 0, red E. = -∂B. / ∂t and red B. / μ0 = ε0E. / ∂t. From this immediately follow the Wave equations in a vacuum