The permittivity of free space (sometimes called the vacuum permittivity) is a constant of nature that specifies how strong the electric force between electric charges is in vacuum, or put another way it tells us how strongly the electric field reacts to the presence of charges in empty space. This quantity is normally represented with the symbol ε_{0} (read "epsilon zero" or "epsilon naught"). In SI units, the vacuum permittivity is defined to have an exact value of

ε_{0} = 1/(μ_{0}c^{2}),

where μ_{0} is the magnetic permeability of free space and `c` stands for the speed of light in vacuum. This has the approximate numerical value

ε_{0} ≅ (8.854 187 817)*10^{-12} F/m.

In more familiar units, F/m = C^{2}/(N m^{2}).

The permittivity of free space tells us how strong the electric force is, because it determines the constant that appears in Coulomb's law:

k = 1/(4πε _{0})

More generally, ε_{0} appears in Maxwell's equations (specifically in Gauss' law), which is how it determines how strong an electric field results from a particular distribution of charges and many other properties of electromagnetism.

Inside of a material (usually referred to as the "medium" in this context), atoms may become electrically polarized, leading to a different effective value for the electrical permittivity inside the material^{*}, which changes the properties of electromagnetism in the material, and the new permittivity is often written simply as ε. Among the effects of the change in permittivity is that in a capacitor the capacitance is increased by a factor of ε/ε_{0}, known as the dielectric constant of the material. A different electrical permittivity also changes the propagation of electromagnetic waves, such as light, by changing the index of refraction. The permittivity node should contain more details on those topics.

I said that the value of the permittivity of free space is *defined* to have a certain value, which may seem odd, since you'd normally think of a property about nature as being something that's *measured*, not defined. The situation here is very similar to the situation with the speed of light. The laws of electromagnetism predict a relationship between ε_{0}, μ_{0}, and c. The best measurements we can make find agreement with this relationship, and so long as that's true, we may define the value of ε_{0} through this relationship if this gives us the most precise known value. If this still seems a bit strange, I suggest you first try to understand why `c` is *defined* to have an exact value, since the logic is essentially the same but the situation is a bit more familiar.

* This is simply a number if the response to the electromagnetic field is linear and isotropic (true for weak enough fields in any material that is not ferroelectric). Otherwise things get more complicated.

Sources:

- J. D. Jackson. Classical Electrodynamics. New York: John Wiley & Sons, Inc., 1999
- 2002 CODATA recommended values, published in Rev. Mod. Phys.
**77**, 1 (2005) and available from NIST at http://physics.nist.gov/cgi-bin/cuu/Value?eqep0|search_for=permittivity

This write-up brought to you by request of Gorgonzola.