Chemistry - Electric displacement field

In physics, the electric displacement field is a vector-valued field

$\vec D$

that appears in Maxwell's equations and that generalizes the electric field. In fact, "D" stands for "displacement".

In most ordinary materials, $\vec D$ may be calculated as

$\vec D = \varepsilon \vec E$

where $\varepsilon$ is the permittivity of the material, which in linear, non isotropic media 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 analagously 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 to field after account is taken of 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 a quantity known as the polarisation of a medium, given the symbol P.

Capacitor interpretation

Imagine one wishes to create an electric field of E at a given point in space. One could achieve this by placing a microscopic capacitor across the point, oriented perpendicular to the required direction of field at that point. The required charge density on the capacitor in order to create the field E is equal to the value of the D field.

Units

In the standard SI system of units D is measured in coulombs per square meter (C/m²).

This choice of units results in one of the simpliest forms of Maxwell's vorticity equations:

$\nabla \times \vec H = \vec j + \partial \vec D / \partial t$

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:

$\nabla \times \vec H = \mu_0 \vec j + 1/c^2 \partial \vec D / \partial t$

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 $1 / 4\pi\varepsilon_0 = 1$ (dimensionless), D and E are expressed in the same units.

Categories: Electromagnetism