= Solution
Use a cold, unmagnetized, collisionless <electron> plasma with immobile ions. For an oscillating field proportional to $e^{-i\omega t}$, the <electron> <displacement> follows $-m_e\omega^2\mathbf x=-e\mathbf E$. Hence $\mathbf P=-n_ee\mathbf x=-n_ee^2\mathbf E/(m_e\omega^2)$ and
$$
\boxed{\epsilon_r(\omega)=1-\frac{\omega_p^2}{\omega^2},\qquad
\omega_p^2=\frac{n_ee^2}{\epsilon_0m_e}.}
$$
The induced polarization opposes the field because <electron> inertia changes the phase of its <displacement>. <Maxwell's equations> give transverse electromagnetic <dispersion>
$$
\omega^2=\omega_p^2+c^2k^2.
$$
Thus <transverse waves> propagate above the <plasma frequency>, while below it the wavenumber is imaginary and a semi-infinite lossless plasma reflects an incident <wave> with an evanescent interior field. In the cold electrostatic model, a longitudinal <density> oscillation instead has frequency $\omega_p$.
Collisions at rate $\nu$ give $\epsilon_r=1-\omega_p^2/[\omega(\omega+i\nu)]$ for this time convention, introducing absorption. A background <magnetic field> makes the response anisotropic, and thermal motion supplies additional <dispersion> and static screening. The divergent zero-frequency cold collisionless formula should not be mistaken for a complete description of static Debye screening. \b[The simple <dielectric> function is a dynamical electron-inertia response under stated assumptions.]
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