Bound charge (${\rho }_{\mathrm{b}}=-\nabla \cdot \mathbf{P}$, ${\sigma }_{\mathrm{b}}=\mathbf{P}\cdot \mathbf{n}$)

The effective electric charge associated with electric polarization is bound charge. For polarization density $\mathbf{P}$, its volume charge density is ${\rho }_{\mathrm{b}}=-\nabla \cdot \mathbf{P}$. At a boundary with unpolarized surroundings, its surface charge density is ${\sigma }_{\mathrm{b}}=\mathbf{P}\cdot \mathbf{n}$, where $\mathbf{n}$ is the outward unit normal vector.