Permittivity

Also called Vacuum permittivity, epsilon naught, Electric constant

The constant describing how an electric field is established in a material or in free space. The vacuum value, epsilon naught, is 8.85 times 10 to the minus 12 in coulombs squared per newton square metre.

\varepsilon_0 = 8.85 \times 10^{-12} \ \mathrm{C}^2/(\mathrm{N}\cdot\mathrm{m}^2)

Printed in the Constants group of both the AP Physics 2 and the AP Physics C: Electricity and Magnetism sheets. It is the electric member of a pair; the magnetic one is permeability.

Its relationship to the Coulomb constant is worth memorising as an identity, not two facts. The sheets print

k = \frac{1}{4\pi\varepsilon_0} = 9.0 \times 10^9 \ \mathrm{N}\cdot\mathrm{m}^2/\mathrm{C}^2

so $\varepsilon_0$ and $k$ are the same constant wearing different clothes. A larger permittivity means a smaller $k$ , which means weaker forces between the same charges at the same separation. Note the AP value is 9.0e9 as printed, not the 8.99e9 many textbooks carry.

Where it shows up: Coulomb's law and the field of a point charge in either form, Gauss's law as $q_{\text{enc}}/\varepsilon_0$ , and the parallel-plate capacitance $C = \kappa \varepsilon_0 A / d$ , where the dielectric constant $\kappa$ is itself the ratio of the material's permittivity to the vacuum value.

A dielectric slid between capacitor plates raises the permittivity, weakens the field for the same stored charge, and so raises the capacitance. That is permittivity doing its job: describing how readily a medium permits an electric field to be set up in it.

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