# What is the Vacuum Permittivity (Electric Constant)?

Level 2 (suitable for students)

The electric constant (or vacuum permittivity) is a physical constant and is notated as $$\varepsilon_0$$ (pronounced: "epsilon zero"). It has the following value:

Value of the vacuum permittivity
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• The unit of $$\varepsilon_0$$ is for example ampere-second per voltmeter or farad per meter:

Unit of the vacuum permittivity
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• The vacuum permittivity appears in equations that have to do with electric fields. For example, in Coulomb's law or in the wave equation for electromagnetic waves.

• In our universe, the vacuum permittivity determines how strongly electric charges are allowed to attract or repel each other.

• The vacuum permittivity, together with the vacuum permeability $$\mu_0$$ (magnetic constant), determines how large the speed of light $$c$$ should be in vacuum:

Vacuum permittivity is the reciprocal of the vacuum permeability and speed of light squared
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• Vacuum permittivity $$\varepsilon_0$$ specifies how easy / hard it is for electric fields to penetrate the vacuum. Permittivity $$\varepsilon$$ of water, for example, is about eighty times the permittivity of vacuum: $$\varepsilon = 80 \cdot \varepsilon_0$$. Here the factor $$\varepsilon_{\text r} = 80$$ is called relative permittivity.

How can the vacuum permittivity be determined experimentally?:
The vacuum permittivity $$\varepsilon_0$$ can be determined experimentally, for example, with a so-called Coulomb's torsion balance. Similar to the Eötvös gravitational balance, it exploits the torque exerted on each other by two known charges $$q_1$$ and $$q_2$$.

From the experimentally determined electric force $$F_{\text e}$$ between the two charges, the value of the vacuum permittivity can be found using Coulomb's law:

Coulomb's law rearranged for vacuum permittivity
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