Permittivity of free space

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The permittivity of free space, ε0, is a physical constant used often in electromagnetism. It represents the capability of a vacuum to permit electric fields. It is also connected to the energy stored within an electric field and capacitance. Perhaps more surprisingly, it's fundamentally related to the speed of light. The permittivity of free space, ε0, is defined as:[1]

[math]\epsilon_0 = \frac{1}{\mu_0 c^2}\approx8.8542 \times 10^{-12} [/math] F/m (farads per meter)


An electric field, [math]E[/math], in a region of space has field energy associated with it, that energy density is:[2]

[math]\frac{Energy}{volume}= \frac{\epsilon_0 E^2}{2 } [/math]

The energy stored in a capacitor (with no dielectric) is:

Energy [math] = \frac{\epsilon_0 A}{2d} V^2[/math]


  • [math]A[/math] is the area of the plates,
  • [math]d[/math] is the distance between the plates
  • [math]V[/math] is the voltage between the plates.

The permittivity of free space can also be used to find the Coulomb force. The constant gives how strong the force is between two charges separated by a distance:[1]

[math]F = \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r^2}[/math]


  • [math]F[/math] is the Coulomb force,
  • [math]q_1[/math] and [math]q_2[/math] are two charges, and
  • [math]r[/math] is the separation between the charges.

For Further Reading

For further information please see the related pages below:


  1. 1.0 1.1 Hyperphysics. (August 27, 2015). Electric and Magnetic Constants [Online], Available:
  2. Jackson, John David (1998). Classical Electrodynamics (3rd ed.). New York: Wiley. p. 213

Authors and Editors

Bethel Afework, Gokul Dharan, Jordan Hanania, Kailyn Stenhouse, Jason Donev
Last updated: June 4, 2018
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