Permittivity of free space: Difference between revisions
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<onlyinclude>The '''permittivity of free space''', '''ε<sub>0</sub>''', is a physical constant used often in [[electromagnetic force|electromagnetism]] | <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> | ||
<center><math>\epsilon_0 = \frac{1}{\mu_0 c^2}\approx8.8542 \times 10^{-12} </math> F/m ([[farad]]s per [[meter]])</center> | |||
<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 | |||
*<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 [[charge]]s separated by a distance:<ref name=hyp/> | |||
<center>< | <center><math>F = \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r^2}</math></center> | ||
where | 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: | |||
*[[Permeability of free space]] | |||
*[[Electric field]] | |||
*[[Photon]] | |||
*[[Capacitor]] | |||
*Or explore a [[Special:Random|random page]] | |||
==References== | ==References== | ||
{{ | {{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]
where
- permeability of free space and is the
- speed of light. is the
An electric field, energy density is:[2]
, in a region of space has field energy associated with it, thatThe energy stored in a capacitor (with no dielectric) is:
where
- is the area of the plates,
- is the distance between the plates
- voltage between the plates. is the
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]
where
- is the Coulomb force,
- and are two charges, and
- 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 random page
References
- ↑ 1.0 1.1 Hyperphysics. (August 27, 2015). Electric and Magnetic Constants [Online], Available: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elefie.html
- ↑ Jackson, John David (1998). Classical Electrodynamics (3rd ed.). New York: Wiley. p. 213