# 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

\[\chi_e = \epsilon_r -1.\label{5.17.4}\]