“Maxwell’s equations”的概念、定义、翻译、参考文献-科学参考

Maxwell’s equations

Physics

A set of differential equations describing the space and time dependence of the electromagnetic field and forming the basis of classical electrodynamics. They were proposed in 1864 by James Clerk Maxwell. In SI units the equations are:

$\begin{array}{l} (1) div D = ρ \\ (2) curl E = - ∂ B / ∂ t \\ (3) div B = 0 \\ (4) curl H = ∂ D / ∂ t + J \end{array}$

where D is the electric displacement, E is the electric field strength, B is the magnetic flux density, H is the magnetic field strength, ρ‎ is the volume charge density, and J is the electric current density. Note that in relativity and particle physics it is common to use Gaussian units or Heaviside–Lorentz units, in which case Maxwell’s equations include 4π‎ and the speed of light c. Maxwell’s equations have the following interpretation. Equation (1) represents Coulomb’s law; equation (2) represents Faraday’s laws of electromagnetic induction; equation (3) represents the absence of magnetic monopoles; equation (4) represents a generalization of Ampère’s law.

Mathematics

A set of partial differential equations summarizing the relationships between electricity and magnetism:

$div E = \frac{ρ}{ε_{0}}$
(Gauss’ flux theorem)
$div B = 0$
(Gauss’ law for magnetism)
$curl B - \frac{1}{c^{2}} \frac{\partial E}{\partial t} = μ_{0} J$
(Maxwell-Ampère circuital law)
$curl E + \frac{\partial B}{\partial t} = 0$
(Faraday’s Law of Induction)

Here B is the magnetic field, E is the electric field, J is the current density, ρ‎ is the charge density, ε‎₀ denotes vacuum permittivity, μ‎₀ denotes vaccuum permeability, c is the speed of light, and t is time. Maxwell’s equations unified theories of magnetism, electricity, light, and radiation. Also, importantly, they are not invariant under Galilean relativity but are invariant under Lorentz transformations.

Electronics and Electrical Engineering

A set of classical equations relating the vector quantities applying at any point in a varying electric or magnetic field. The four basic equations are:
$curl H = \frac{\partial D}{\partial t} + j$
$d i v B = 0$
$c u r l E = - \frac{\partial B}{\partial t}$
$d i v D = ρ$
H is the magnetic field strength, D the electric displacement, t is time, j is the current density, B the magnetic flux density, E the electric field strength, and ρ the volume charge density.
From these equations Maxwell deduced that each field vector obeys a wave equation; he also showed that in free space, where j = 0 and ρ = 0, the solutions represent a transverse wave travelling through space with the speed of light, c. These waves are known as electromagnetic waves (see electromagnetic radiation). Further work showed that certain properties of these waves, i.e. reflection, refraction, and diffraction, are identical to the properties of light waves and that light waves are a form of electromagnetic radiation.
Maxwell’s theory deals only with macroscopic phenomena and does not offer an explanation of phenomena arising from interactions on an atomic scale, such as dispersion and the photoelectric effect. On an atomic scale it has been found necessary to introduce the quantum mechanical theory of electromagnetic radiation.
From Maxwell’s equations it is possible to deduce the wave velocity in a medium as
$v = \frac{1}{\sqrt (μ ε)}$
where ε is the permittivity of the medium and μ is its permeability, μ = B/H. In a vacuum the wave velocity is given by
$c = \frac{1}{\sqrt (μ_{0} ε_{0})}$
Thus in a nondispersive medium of refractive index n, where n = c/v,
$n^{2} = μ_{r} ε_{r}$
or in a nonferromagnetic material where μ_r ≊ 1,
$n^{2} = ε_{r}$
where ε_r is the relative permittivity of the medium and μ_r the relative permeability. This is known as Maxwell’s formula. In a dispersive medium the above formula applies provided that all measurements are carried out at the same frequency.