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Polarization is P = ε₀χₑE, where χₑ is electric susceptibility. The relative permittivity εᵣ = 1 + χₑ gives total field E = E₀/εᵣ inside dielectric. Capacitance with dielectric: C = εᵣε₀A/d.
Compare capacitance with and without dielectric. Measure field reduction and relate to susceptibility values in reference tables.
When you studied dielectric polarization, you learned that an electric field applied to an insulating material causes microscopic dipoles — either permanent molecular dipoles that align, or induced charge displacements — to line up with the field. The result is a net bound surface charge on the dielectric that partially cancels the free charges on the capacitor plates. Electric susceptibility χₑ (chi-sub-e) is the number that quantifies how strongly a material polarizes: the polarization field P is related to the applied field E by P = ε₀χₑE. A large χₑ means the material polarizes easily and creates a large opposing field; a small χₑ means the material barely responds.
The connection to the total field inside the material is direct. The bound surface charge creates a field that opposes the applied field, reducing the net field inside the dielectric. Accounting for both the free charge field and the opposing bound charge field gives a total field E = E₀/(1 + χₑ). The combination (1 + χₑ) appears so frequently that we give it a name: the relative permittivity εᵣ = 1 + χₑ, sometimes called the dielectric constant. Vacuum has χₑ = 0 and εᵣ = 1. Water has χₑ ≈ 79 and εᵣ ≈ 80, meaning water's dipoles polarize so strongly that the field inside water is reduced to about 1/80 of its free-space value — which is why water is such an effective solvent for ionic compounds.
The practical payoff for capacitors is immediate. A parallel-plate capacitor with no dielectric has C₀ = ε₀A/d. Insert a dielectric filling the gap and the field inside drops by a factor of εᵣ, which means the voltage V = Ed drops by the same factor for the same stored charge Q. Since C = Q/V, the capacitance increases to C = εᵣε₀A/d = εᵣC₀. The dielectric effectively allows more charge to be stored at the same voltage — it multiplies the capacitance by the dielectric constant. This is precisely why real capacitors are packed with ceramic, polymer, or electrolytic dielectric materials: a few grams of high-εᵣ material can replace what would otherwise require a much larger physical structure, and the field energy stored in the electric field U = ½CV² scales up accordingly.