Electric polarization (source code)

= Electric polarization
{title2=$\mathbf P$}
{wiki=Polarization_density}

Electric polarization is electric dipole moment per unit volume. It produces bound volume and surface charge
$$
\rho_{\rm b}=-\nabla\cdot\mathbf P,
\qquad
\sigma_{\rm b}=\mathbf P\cdot\mathbf n.
$$
Across an interface, the net bound sheet charge is $(\mathbf P_1-\mathbf P_2)\cdot\mathbf n$, where $\mathbf n$ points from medium one to medium two.