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# 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

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