In physics, the electric displacement field or electric flux density or electric induction is a vector field that appears in Maxwell's equations. It accounts for the effects of bound charges within materials. "D" stands for "displacement," as in the related concept of displacement current in dielectrics. A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ... Vector field given by vectors of the form (-y, x) In mathematics a vector field is a construction in vector calculus which associates a vector to every point in a Euclidean space. ... In electromagnetism, Maxwells equations are a set of equations first presented as a distinct group in the later half of the nineteenth century by James Clerk Maxwell. ... In physics, a bound state is a composite of two or more building blocks (particles or bodies) that behaves as a single object. ... Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. ... material is the substance or matter from which something is or can be made, or also items needed for doing or creating something. ... Displacement current is a quantity related to a changing electric field. ...

Definition

In general, D is defined by the relation

where E is the electric field, is the vacuum permittivity, and P is the polarization density of the material. In physics, the space surrounding an electric charge or in the presence of a time-varying magnetic field has a property called an electric field. ... Permittivity is an intensive physical quantity that describes how an electric field affects and is affected by a medium. ... In classical electromagnetism, the polarization density (or electric polarization, or simply polarization) is the vector field that expresses the density of permanent or induced electric dipole moments in a dielectric material. ...

In most ordinary materials, however, D may be calculated with the simpler formula

where is the permittivity of the material; in linear isotropic media this will be a constant, and in linear anisotropic media it will be a rank 2 tensor (a matrix) Permittivity is a physical quantity that describes how an electric field affects and is affected by a dielectric medium and is determined by the ability of a material to polarize in response to an applied electric field, and thereby to cancel, partially, the field inside the material. ... The word linear comes from the Latin word linearis, which means created by lines. ... Isotropic means independent of direction. Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented. ... The word linear comes from the Latin word linearis, which means created by lines. ... This article is being considered for deletion in accordance with Wikipedias deletion policy. ... In mathematics, a tensor is (in an informal sense) a generalized linear quantity or geometrical entity that can be expressed as a multi-dimensional array relative to a choice of basis; however, as an object in and of itself, a tensor is independent of any chosen frame of reference. ... In mathematics, a matrix (plural matrices) is a rectangular table of numbers or, more generally, a table consisting of abstract quantities that can be added and multiplied. ...

Displacement field in a capacitor

Consider an infinite parallel plate capacitor placed in space (or in a medium) with no free charges present except on the capacitor. In SI units, the charge density on the plates is equal to the value of the D field between the plates. This follows directly from Gauss's law, by integrating over a small rectangular box straddling the plate of the capacitor: Capacitors: SMD ceramic at top left; SMD tantalum at bottom left; through-hole tantalum at top right; through-hole electrolytic at bottom right. ... Look up si, Si, SI in Wiktionary, the free dictionary. ... In physics and mathematical analysis, Gausss law is the electrostatic application of the generalized Gausss theorem giving the equivalence relation between any flux, e. ...

The part of the box inside the capacitor plate has no field, so that part of the integral is zero. On the sides of the box, is perpendicular to the field, so that part of the integral is also zero, leaving:

which is the charge density on the plate.

Units

In the standard SI system of units D is measured in coulombs per square meter (C/m²). Look up si, Si, SI in Wiktionary, the free dictionary. ... The coulomb (symbol: C) is the SI unit of electric charge. ... The metre, or meter (symbol: m) is the SI base unit of length. ...

This choice of units results in one of the simplest forms of the Ampère-Maxwell equation: An electric current produces a magnetic field. ...

If one chooses both B and H to be measured in teslas, and E and D to be measured in newtons per coulomb, then the formula is modified to be: The tesla (symbol T) is the SI derived unit of magnetic flux density (or magnetic induction). ...

Therefore it is seen as being preferential to express B & H, and D & E in different sets of units.

Choice of units has differed in history, for instance in the electromagnetic system of scientific units, in which the unit of charge is defined such that (dimensionless), D and E are expressed in the same units.