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What is the Vacuum Permittivity (Electric Constant)?

Answer #1

Level 2 (without higher mathematics)
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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.

    Electric positive / negative charge - attraction and repulsion
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    The attractive and repulsive force between electric charges.
  • 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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