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| In [[physics]], the '''Planck charge''', denoted by <math>q_\text{P}</math>, is one of the base units in the system of [[natural units]] called [[Planck units]]. It is a quantity of [[electric charge]] defined in terms of [[fundamental physical constants]].
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| The Planck charge is defined as:<ref>{{cite journal
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| |first1=Michael |last1=Stock
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| |first2=Thomas J |last2=Witt
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| |title=CPEM 2006 round table discussion 'Proposed changes to the SI'
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| |journal=Metrologia
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| |volume=43
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| |number=6
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| |pages=583
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| |year=2006
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| |doi=10.1088/0026-1394/43/6/014
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| |bibcode = 2006Metro..43..583S }}</ref>
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| <ref>{{cite book|last=Pavšič|first=Matej|title=The Landscape of Theoretical Physics: A Global View|year=2001|publisher=Kluwer Academic|location=Dordrecht|isbn=0-7923-7006-6|pages=347–352|url=http://www.springer.com/physics/theoretical%2C+mathematical+%26+computational+physics/book/978-0-7923-7006-2?otherVersion=978-1-4020-0351-6}}</ref>
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| :<math>q_\text{P} = \sqrt{4 \pi\epsilon_0 \hbar c} = \sqrt{2 c h \epsilon_0} = \frac{e}{\sqrt{\alpha}} = 1.875\;5459 \times 10^{-18}</math> [[coulomb]]s,
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| where:
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| :<math> c \ </math> is the [[speed of light]] in the [[vacuum]],
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| :<math> h \ </math> is [[Planck's constant]],
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| :<math> \hbar \equiv \frac{h}{2 \pi} \ </math> is the [[reduced Planck constant]],
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| :<math> \epsilon_0 \ </math> is the [[permittivity of free space]]
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| :<math> e \ </math> is the [[elementary charge]]
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| :<math> \alpha \ </math> = (137.03599911)<sup>−1</sup> is the [[fine structure constant]].
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| The Planck charge is <math>\alpha^{-1/2} \approx 11.706</math> times greater than the [[elementary charge]] ''e'' carried by an [[electron]].
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| The [[Gaussian units|Gaussian cgs units]] are defined so that <math>4 \pi\epsilon_0 = 1</math>, in which case <math>q_\text{P}</math> has the following simple form:
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| :<math>q_\text{P} = \sqrt{ \hbar c}.</math> | |
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| It is customary in theoretical physics to adopt the [[Lorentz–Heaviside units]] (also known as rationalized cgs). When made natural (<math>c=1</math>) they are like the SI system with <math>\epsilon_0 = \mu_0 = 1</math>. Therefore it is more appropriate to define the Planck charge as
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| :<math>q'_\text{P} = \sqrt{\epsilon_0 \hbar c} = \frac{e}{\sqrt{4\pi\alpha}} = 5.291 \times 10^{-19}</math> [[coulomb]]s, | |
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| When charges are measured in units of <math>q'_\text{P}</math>, i.e., when <math>q'_\text{P}</math> is set equal to 1, we obtain <math>\alpha = e^2/(4\pi)</math>, which is commonly used in theoretical physics. In contrast, in (non-rationalized) natural cgs units where <math>q_\text{P}=1</math> we have <math>\alpha = e^2</math>.
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| ==See also==
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| *[[Orders of magnitude (charge)]]
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| == Notes and references==
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| {{Reflist|2}}
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| {{Planck's natural units}}
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| {{Portal bar|Physics}}
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| {{DEFAULTSORT:Planck Charge}}
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| [[Category:Natural units|charge]]
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| [[Category:Electromagnetism]]
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| [[Category:Units of electrical charge]]
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