= Solution
<Polarization density> $\mathbf P$ is <electric dipole moment> per unit volume. Displacing positive and negative <bound charges> leaves the bulk nearly neutral locally but can produce uncompensated charge where polarization varies or terminates. For a <dielectric> occupying a volume with outward unit normal $\mathbf n$,
$$
\boxed{\rho_b=-\nabla\cdot\mathbf P,\qquad \sigma_b=\mathbf P\cdot\mathbf n.}
$$
The <divergence theorem> makes their total sum zero for a body described entirely by bound dipoles. Uniform polarization gives no interior volume charge but generally gives opposite surface charges on different faces.
In a linear isotropic <dielectric>, $\mathbf P=\epsilon_0\chi_e\mathbf E$ and $\mathbf D=\epsilon_0\mathbf E+\mathbf P=\epsilon\mathbf E$. <Gauss's law> becomes $\nabla\cdot\mathbf D=\rho_f$, separating free from <bound charge>. Across a static interface, tangential <electric field> is continuous, while the normal <displacement> jumps by the free surface charge. Polarization charges alter the internal field, as in the <dielectric> cylinder calculation. Molecular distortion and orientation contribute differently, and response can depend on <temperature> and frequency. \b[<Bound charge> is a redistribution of material charge, not an additional free-charge reservoir.]
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