5.17: Polarization and Susceptibility

When an insulating material is placed in an electric field, it becomes polarized, either by rotation of molecules with pre-existing dipole moments or by induction of dipole moments in the individual molecules. Inside the material, $D$ is then greater than $\epsilon_0 E$. Indeed,

$$D=\epsilon_0E+P\label{5.17.1}$$

The excess, $P$, of $D$ over $\epsilon_0 E$ is called the polarization of the medium. It is dimensionally similar to, and expressed in the same units as, $D$; that is to say $\text{C m}^{-2}$. Another way of looking at the polarization of a medium is that it is the dipole moment per unit volume.

In vector form, the relation is

$$\textbf{D}=\epsilon_0\textbf{E}+\textbf{P}.\label{5.17.2}$$

If the medium is isotropic, all three vectors are parallel.

Some media are more susceptible to becoming polarized in a polarizing field than others, and the ratio of $P$to $\epsilon_0 E$ is called the electric susceptibility $\chi_e$ of the medium:

$$P=\chi_e \epsilon_0E.\label{5.17.3}$$

This implies that $P$ is linearly proportional to $E$ but only if $\chi_e$ is independent of $E$, which is by no means always the case, but is good for small polarizations.

When we combine Equations $\ref{5.17.1}$ and $\ref{5.17.3}$ with $D = \epsilon E$ and with $\epsilon_r = \epsilon / \epsilon_0$, the relative permittivity or dielectric constant, we obtain

$$\chi_e = \epsilon_r -1.\label{5.17.4}$$