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Electric Displacement Field




In Physics , the electric displacement field or '''electric flux density''' is a Vector -valued field \mathbf{D} 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 .


DEFINITION


In general, D is defined by the relation

:\mathbf{D} \ = arepsilon_{0} \ \mathbf{E} \ + \ \mathbf{P}

where E is the electric field, arepsilon_{0} is the Vacuum Permittivity , and '''P''' is the Polarization Density of the material.

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

:\mathbf{D} = arepsilon \mathbf{E}

where arepsilon 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 )


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.


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:

: \oint_A \mathbf{D} \cdot d\mathbf{A} = Q

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, d\mathbf{A} is perpendicular to the field, so that part of the integral is also zero, leaving:



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:


abla imes \mathbf{H} = \mu_0 \mathbf{J} + rac{1}{c^2} rac{\partial \mathbf{D}}{\partial t}

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 1 / 4\pi arepsilon_0 = 1 (dimensionless), D and '''E''' are expressed in the same units.