= Solution
A <dielectric> responds to an <electric field> mainly by displacing or orienting bound charges, rather than by sustaining a steady conduction current. The <polarization density> $\mathbf P$ is <electric dipole moment> per unit <volume (thermodynamics)>. It creates bound charge
$$
\rho_b=-\nabla\cdot\mathbf P,\qquad\sigma_b=\mathbf P\cdot\mathbf n.
$$
Separating these charges from free charge motivates
$$
\mathbf D=\epsilon_0\mathbf E+\mathbf P,\qquad\nabla\cdot\mathbf D=\rho_f.
$$
For an isotropic linear <dielectric>, $\mathbf P=\epsilon_0\chi_e\mathbf E$, so
$$
\boxed{\mathbf D=\epsilon\mathbf E,\qquad\epsilon=\epsilon_0(1+\chi_e)=\epsilon_0\epsilon_r.}
$$
The <electric susceptibility> $\chi_e$ describes material polarization and is not the <magnetic susceptibility>. More generally it is a <tensor> and can depend on <frequency>, field strength and <temperature>.
Electronic polarization displaces an <Electron> cloud relative to its nucleus; ionic polarization displaces positive and negative ions; orientational polarization partially aligns permanent molecular dipoles against thermal disorder. For independent permanent moments of magnitude $p$, weak-field orientational response gives $\chi_e\simeq np^2/(3\epsilon_0k_BT)$ when local-field corrections and interactions are negligible. This explains a common inverse-temperature contribution without asserting that every <dielectric> follows that law.
At a static interface, $\mathbf n\cdot(\mathbf D_2-\mathbf D_1)=\sigma_f$ and the tangential <electric field> is continuous. Bound surface charge is already included through $\mathbf P$. For a homogeneous filled <capacitor>, $C=\epsilon A/d$, and a reversible linear <dielectric> stores <energy density> $u=\mathbf E\cdot\mathbf D/2$. At fixed voltage, insertion raises the stored field <energy> but the voltage source also supplies <energy>; <force> arguments must include that source. At fixed charge the <capacitor energy> instead decreases on insertion.
At <frequencies> too high for a polarization mechanism to follow the field, its contribution weakens. A complex <permittivity> represents dissipative <dielectric loss> as well as phase lag; the sign of its imaginary part depends on the time convention. Strong fields can cause nonlinear response or <dielectric breakdown>, beyond the reversible linear model.
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