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<onlyinclude>The '''permittivity of free space''', '''ε<sub>0</sub>''', is a physical constant used often in [[electromagnetic force|electromagnetism]], and is the capability of a [[vacuum]] to permit [[electric field]]s. It is also connected to the [[energy]] stored within an electric field and [[capacitance]].</onlyinclude>  
<onlyinclude>The '''permittivity of free space''', '''ε<sub>0</sub>''', is a physical constant used often in [[electromagnetic force|electromagnetism]]. It represents the capability of a [[vacuum]] to permit [[electric field]]s. 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.</onlyinclude> The permittivity of free space, '''ε<sub>0</sub>''', is defined as:<Ref name=hyp>Hyperphysics. (August 27, 2015). ''Electric and Magnetic Constants'' [Online], Available: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elefie.html</ref>  


It has a value of 8.8542 x 10<sup>-12</sup> F/m ([[farad]]s per [[meter]]),<ref>WolframResearch. (August 27, 2015). ''Permittivity of Free Space'' [Online], Available: http://scienceworld.wolfram.com/physics/PermittivityofFreeSpace.html</ref> and is defined as:<Ref name=hyp>Hyperphysics. (August 27, 2015). ''Electric and Magnetic Constants'' [Online], Available: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elefie.html</ref>  
<center><math>\epsilon_0 = \frac{1}{\mu_0 c^2}\approx8.8542 \times 10^{-12} </math> F/m ([[farad]]s per [[meter]])</center>


<center><m>\epsilon_0 = \frac{1}{\mu_0 c^2}</m></center>
where
 
*<math>\mu_0</math> is the [[permeability of free space]] and
*<math>c</math> is the [[speed of light]].
 
An electric field, <math>E</math>, in a region of space has field energy associated with it, that [[energy density]] is:<ref>Jackson, John David (1998). Classical Electrodynamics (3rd ed.). New York: Wiley. p. 213</ref>
<center> <math>\frac{Energy}{volume}= \frac{\epsilon_0 E^2}{2 } </math></center>
 
The energy stored in a [[capacitor]] (with no [[dielectric]]) is:
 
<center>Energy <math> = \frac{\epsilon_0 A}{2d} V^2</math></center>
 
where


where
*<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.


*<m>\mu_0</m> is the [[permeability of free space]] and
*<m>c</m> is the [[speed of light]].


It is used to relate two [[charge]]s separated by a distance to the [[force]] between them, simply known as the [[Coulomb force]]. It does so in the following way:<ref name=hyp/>
The permittivity of free space can also be used to find the [[Coulomb force]]. The constant gives how strong the [[force]] is between two [[charge]]s separated by a distance:<ref name=hyp/>


<center><m>F = \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r^2}</m></center>
<center><math>F = \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r^2}</math></center>


where
where


*<m>F</m> is the Coulomb force,
*<math>F</math> is the Coulomb force,
*<m>q_1</m> and <m>q_2</m> are two charges, and
*<math>q_1</math> and <math>q_2</math> are two charges, and
*<m>r</m> is the separation between the charges.
*<math>r</math> is the separation between the charges.
 
== For Further Reading ==
For further information please see the related pages below:
*[[Permeability of free space]]
*[[Electric field]]
*[[Photon]]
*[[Capacitor]]
*Or explore a [[Special:Random|random page]]
 


==References==
==References==
{{Reflist}}
{{reflist}}

Revision as of 23:08, 31 May 2018

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)

where

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]

where

  • [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]

where

  • [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:


References

  1. ↑ 1.0 1.1 Hyperphysics. (August 27, 2015). Electric and Magnetic Constants [Online], Available: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elefie.html
  2. ↑ Jackson, John David (1998). Classical Electrodynamics (3rd ed.). New York: Wiley. p. 213
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