Editing Permittivity (section)

== Vacuum permittivity ==
{{main|Vacuum permittivity}}

The vacuum permittivity {{mvar|ε}}{{sub|o}} (also called '''permittivity of free space''' or the '''electric constant''') is the ratio {{math|{{sfrac|''D''|''E''}}}} in [[Vacuum|free space]]. It also appears in the [[Coulomb force constant]],

<math display="block">k_\text{e} = \frac{1}{\ 4\pi \varepsilon_0\ }</math>

Its value is{{physconst|eps0|ref=only}}<ref>{{cite web |title = Latest (2018) values of the constants |publisher = U.S. [[National Institute of Standards and Technology]] (NIST) |website = Physics.nist.gov |date = 2019-05-20 |url = http://physics.nist.gov/cuu/Constants/index.html |access-date=2022-02-05}}</ref>

<math display="block">\varepsilon_0 \ \stackrel{\mathrm{def}}{=}\  \frac{1}{c^2\mu_0}  \approx 8.854\,187\,8128(13)\times 10^{-12}\text{ F/m } </math>

where
* {{mvar|c}} is the [[speed of light]] in free space,
* {{mvar|µ}}{{sub|0}} is the [[vacuum permeability]].

The constants {{mvar|c}} and {{mvar|µ}}{{sub|0}} were both defined in SI units to have exact numerical values until the [[2019 revision of the SI]]. Therefore, until that date, {{mvar|ε}}{{sub|0}} could be also stated exactly as a fraction, <math>\ \tfrac{1}{c^2\mu_0} = \tfrac{1}{35\,950\,207\,149.472\,7056\pi}\text{ F/m}\ </math>
even if the result was irrational (because the fraction contained {{mvar|π}}).<ref>{{cite web |title=Latest (2006) values of the constants |publisher=US [[NIST]] |website=Physics.nist.gov |date=2017-07-01|url=http://physics.nist.gov/cuu/Constants/index.html |access-date=2018-11-20}}</ref> In contrast, the ampere was a measured quantity before 2019, but since then the ampere is now exactly defined and it is {{mvar|μ}}{{sub|0}} that is an experimentally measured quantity (with consequent uncertainty) and therefore so is the new 2019 definition of {{mvar|ε}}{{sub|0}} ({{mvar|c}} remains exactly defined before and since 2019).