Work of Polarization

A material is said to be polarized if the positive and negative charges within the material become slightly displaced from one another due to an electric field.

Figure 6-1: The effect of polarizing a Cesium Chloride structure--there is displacement of the ions according to their charge due to an applied electric field. The net result is that some charge accumulates on the surface of the material.

For electric work due to polarizing a material:

$$\input{equations/nye-E}$$ (06-5)

The electric displacement, $\vec{D}$, is the total polarization per unit volume. The electric displacement is the sum of two terms: the electric field in free space and the contribution due to the polarization of the material. The electric displacement $\vec{D}$ can be thought of as the net polarization. $\ensuremath{{\kappa}_\circ}$ is the permittivity of free space; it is a conversion between the units of electric field and polarization and its value reflects how an electromagnetic wave travels through the vacuum.³

The polarization work done is:

$$\input{equations/nye-Ework}$$ (06-6)

Linear Isotropic Material Properties

The simplest model for polarizable material is that the induced polarization density $\vec{P}$ is linearly related to the applied field $\vec{E}$:

$$\input{equations/nye-E-iso}$$ (06-7)

$\chi$ is the dielectric susceptibility. $\chi$ is a measure of the extend to which a material to form internal dipoles.

An isotropic material is one that the response of a material does not depend on the direction of the applied field with respect to the orientation of the crystal--that is the polarization direction is parallel to the applied field $\vec{E}$.⁴

In an isotropic material, then, the polarization of the material is in the same direction as the direction of electric field that is trying to polarize it:

$$\input{equations/nye-E-dis}$$ (06-8)

$$\input{equations/nye-E-kapdef}$$ (06-9)

$\kappa$ is called the permittivity of a material.

If $\kappa$ does not depend on $\vec{E}$ and the material generates no heat as it is polarized, then

$$\input{equations/nye-E-workdensity}$$ (06-10)