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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,


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


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

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