= Microscopic dielectric polarization
Two routes to <electric polarization> are displacement and reorientation. An <electric field> can shift the centres of positive and negative <electric charge> in a neutral <chemical atom> or <molecule>, inducing an <electric dipole moment>. A <polar molecule> already has an <electric dipole moment>; a field biases its orientation. At finite <temperature>, random molecular motion opposes complete alignment, so a nonzero average need not mean that every <electric dipole> points the same way.<University Physics Volume 2 by Samuel J. Ling and others/8.5 Molecular Model of a Dielectric>[§8.5, Figures 8.19–8.20 and the thermal-fluctuation qualification following Figure 8.20]{ref}
For a single species with number per unit <volume> $n$, the <electric polarization> is
$$
\mathbf P=n\langle\mathbf p\rangle.
$$
The brackets denote the local average <electric dipole moment>, rather than its magnitude. Opposite orientations can cancel while individual <electric dipole moments> remain nonzero.<Classical Electromagnetism: An intermediate level course by Richard Fitzpatrick/Polarization>[equation (803): number density times locally averaged molecular dipole moment]{ref} This averaging explains how an initially unpolarized material can respond strongly without acquiring net <electric charge>.
\Image[/dielectric-microscopic-displacement-and-orientation.png]
{title=Two microscopic routes to <electric polarization>}
{description=Original schematic: upper panels show coincident charge centres becoming separated; lower panels show existing <electric dipoles> changing from cancelling orientations to a biased distribution with incomplete alignment. Arrows run from negative to positive <electric charge>. Positions, displacements and orientations are illustrative, not measurements or a simulation of a particular substance.}
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