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In physics, the electric displacement field or electric flux density is a vector-valued field that appears in Maxwell's equations. It generalizes the electric field to account for the effects of bound charges within materials. "D" stands for "displacement," as in the related concept of displacement current. Image File history File links Stop_hand. ... A black hole concept drawing by NASA. Physics (from the Greek, φυσικός (physikos), natural, and φύσις (physis), nature) is the science of the natural world dealing with the fundamental constituents of the universe, the forces they exert on one another, and the results produced by these forces. ... In physics and in vector calculus, a spatial vector is a concept characterized by a magnitude, which is a scalar, and a direction (which can be defined in a 3-dimensional space by the Euler angles). ... Maxwells equations (sometimes called the Maxwell equations) are the set of four equations, attributed to James Clerk Maxwell, that describe the behavior of both the electric and magnetic fields, as well as their interactions with matter. ... In physics, an electric field or E-field is an effect produced by an electric charge (or a time-varying magnetic field) that exerts a force on charged objects in the field. ... 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 interactions. ... 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; it is not a real current (movement of charge), but it has the units of current, and creates a magnetic field, as current does. ...

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. Permittivity is an intensive physical quantity that describes how an electric field affects and is affected by a medium. ...

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 medium. ... 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 a generalized quantity or a certain kind of geometrical entity that includes all the ideas of scalars, vectors, matrices and linear operators. ... In mathematics, a matrix (plural matrices) is a rectangular table of numbers or, more generally, of elements of a ring-like algebraic structure. ...

Interpretation of the displacement field

The electric displacement field is sometimes known as the "macroscopic electric field," in contrast to the electric field E, which is analogously the "microscopic electric field." The difference is that the macroscopic field "averages out" the jumble of electric fields from charged particles that make up otherwise electrically neutral material.

Thus D can be considered the field after taking into account the response of a medium to an external field, for instance by means of charge migration, reorientation of electric dipoles, etc. These responses can be summed into the quantity known as the polarisation of a medium, mentioned above. In electrostatics, the polarization is the vector field that results from permanent or induced electric dipole moments in a dielectric material. ...

Capacitor interpretation

Imagine a microscopic parallel plate capacitor placed across a point in space (or in a medium) with no charges present except on the capacitor. 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 edge of one of the capacitors: A capacitor is a device that stores energy in the electric field created between a pair of conductors on which equal but opposite electric charges have been placed. ... In physics and mathematical analysis, Gausss law gives the relation between the electric flux flowing out a closed surface and the electric charge enclosed in the surface. ...

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). The International System of Units (abbreviated SI from the French language name Système International dUnités) is the modern form of the metric system. ... 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 simpliest forms of the Ampère-Maxwell equation:

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:

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.