Permittivity

Permittivity ε is the macroscopic property that ties the displacement field D to the electric field E in a linear dielectric: D = εE. It has units of farads per metre, and for most materials ε = ε₀(1 + χ_e), where ε₀ ≈ 8.854 × 10⁻¹² F/m is the permittivity of free space and χ_e is the dimensionless electric susceptibility of the medium. Vacuum has the smallest permittivity (ε = ε₀); every material medium has a larger one, because its bound charges polarize and partially shield any applied field.

The ratio κ = ε/ε₀ is the relative permittivity, also called the dielectric constant — a dimensionless number that tells you how much the medium amplifies a capacitor's storage capacity relative to vacuum. Air is essentially indistinguishable from vacuum (κ ≈ 1.0006). Glass and most ceramics fall in the range 4–10. Pure water is famously high (κ ≈ 80) thanks to its strong permanent molecular dipoles. Specialty ceramics like barium titanate can reach κ in the thousands and are the workhorse material of every miniature ceramic capacitor.

Permittivity is a frequency-dependent quantity in general: the value of ε that a material shows in response to a static field is not the same as its response at radio frequencies, infrared, or visible light. The frequency-dependence of permittivity (its dispersion) is the entire subject of optics, since the speed of light in a medium is c/√(εμ/ε₀μ₀) — and "the refractive index" is essentially the square root of the relative permittivity at optical frequencies for non-magnetic materials.