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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Electric displacement field ： ウィキペディア英語版 Electric displacement field In physics, the electric displacement field, denoted by D, is a vector field that appears in Maxwell's equations. It accounts for the effects of free and bound charge within materials. "D" stands for "displacement", as in the related concept of displacement current in dielectrics. In free space, the electric displacement field is equivalent to flux density, a concept that lends understanding to Gauss's law. It has the SI units of coulomb per squared metre (C m−2). == Definition == In a dielectric material the presence of an electric field E causes the bound charges in the material (atomic nuclei and their electrons) to slightly separate, inducing a local electric dipole moment. The electric displacement field D is defined as :$\backslash mathbf\; \backslash equiv\; \backslash varepsilon\_\; \backslash mathbf\; +\; \backslash mathbf,$ where $\backslash varepsilon\_$ is the vacuum permittivity (also called permittivity of free space), and P is the (macroscopic) density of the permanent and induced electric dipole moments in the material, called the polarization density. Separating the total volume charge density into free and bound charges: :$\backslash rho\; =\; \backslash rho\_\backslash text\; +\; \backslash rho\_\backslash text$ the density can be rewritten as a function of the polarization P: :$\backslash rho\; =\; \backslash rho\_\backslash text\; -\backslash nabla\backslash cdot\backslash mathbf.$ The polarization P is defined to be a vector field whose divergence yields the density of bound charges ''ρ''b in the material. The electric field satisfies the equation: :$\backslash nabla\backslash cdot\backslash mathbf\; =\; \backslash frac\; \backslash rho\; =\; \backslash frac(\backslash rho\_\backslash text\; -\backslash nabla\backslash cdot\backslash mathbf)$ and hence :$\backslash nabla\backslash cdot\; (\backslash varepsilon\_0\backslash mathbf\; +\; \backslash mathbf)\; =\; \backslash rho\_\backslash text$. The displacement field therefore satisfies Gauss's law in a dielectric: :$\backslash nabla\backslash cdot\backslash mathbf\; =\; \backslash rho\; -\backslash rho\_\backslash text\; =\; \backslash rho\_\backslash text$ . However, electrostatic forces on ions or electrons in the material are still governed by the electric field E in the material via the Lorentz Force. It should also be remembered that D is not determined exclusively by the free charge. Consider the relationship: :$\backslash nabla\; \backslash times\; \backslash mathbf\; =\; \backslash varepsilon\_\; \backslash nabla\; \backslash times\; \backslash mathbf\; +\; \backslash nabla\; \backslash times\; \backslash mathbf,$ which, by the fact that E has a curl of zero in electrostatic situations, evaluates to: :$\backslash nabla\; \backslash times\; \backslash mathbf\; =\; \backslash nabla\; \backslash times\; \backslash mathbf$ The effect of this equation can be seen in the case of an object with a "frozen in" polarization like a bar electret, the electric analogue to a bar magnet. There is no free charge in such a material, but the inherent polarization gives rise to an electric field. If the wayward student were to assume that the D field were entirely determined by the free charge, he or she would conclude that the electric field were zero outside such a material, but this is patently not true. The electric field can be properly determined by using the above relation along with other boundary conditions on the polarization density to yield the bound charges, which will, in turn, yield the electric field. In a linear, homogeneous, isotropic dielectric with instantaneous response to changes in the electric field, P depends linearly on the electric field, :$\backslash mathbf\; =\; \backslash varepsilon\_\; \backslash chi\; \backslash mathbf,$ where the constant of proportionality $\backslash chi$ is called the electric susceptibility of the material. Thus :$\backslash mathbf\; =\; \backslash varepsilon\_\; (1+\backslash chi)\; \backslash mathbf\; =\; \backslash varepsilon\; \backslash mathbf$ where ''ε'' = ''ε''0 ''ε''r is the permittivity, and ''ε''r = 1 + ''χ'' the relative permittivity of the material. In linear, homogeneous, isotropic media, ''ε'' is a constant. However, in linear anisotropic media it is a tensor, and in nonhomogeneous media it is a function of position inside the medium. It may also depend upon the electric field (nonlinear materials) and have a time dependent response. Explicit time dependence can arise if the materials are physically moving or changing in time (e.g. reflections off a moving interface give rise to Doppler shifts). A different form of time dependence can arise in a time-invariant medium, in that there can be a time delay between the imposition of the electric field and the resulting polarization of the material. In this case, P is a convolution of the impulse response susceptibility ''χ'' and the electric field E. Such a convolution takes on a simpler form in the frequency domain—by Fourier transforming the relationship and applying the convolution theorem, one obtains the following relation for a linear time-invariant medium: :$\backslash mathbf\; =\; \backslash varepsilon\; (\backslash omega)\; \backslash mathbf(\backslash omega)\; ,$ where $\backslash omega$ is the frequency of the applied field. The constraint of causality leads to the Kramers–Kronig relations, which place limitations upon the form of the frequency dependence. The phenomenon of a frequency-dependent permittivity is an example of material dispersion. In fact, all physical materials have some material dispersion because they cannot respond instantaneously to applied fields, but for many problems (those concerned with a narrow enough bandwidth) the frequency-dependence of ''ε'' can be neglected. At a boundary, $(\backslash mathbf\; -\; \backslash mathbf)\backslash cdot\; \backslash hat\; -\; D\_\; =\; \backslash sigma\_\backslash text$, where ''σ''f is the free charge density and the unit normal $\backslash mathbf\{\backslash hat\{n\}\}$ points in the direction from medium 2 to medium 1. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Electric displacement field」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.