Editing Relative permittivity (section)

== Definition ==
Relative permittivity is typically denoted as {{math|''ε''<sub>r</sub>(''ω'')}} (sometimes {{math|''κ''}}, lowercase [[kappa]]) and is defined as
: <math>\varepsilon_\text{r}(\omega) = \frac{\varepsilon(\omega)}{\varepsilon_{0}},</math>
where ''ε''(''ω'') is the [[complex number|complex]] frequency-dependent [[permittivity]] of the material, and ''ε''<sub>0</sub> is the [[vacuum permittivity]].

Relative permittivity is a [[dimensionless quantity|dimensionless]] number that is in general [[complex number|complex-valued]]; its real and imaginary parts are denoted as:<ref name=ChenVaradan2004>{{cite book|author1=Linfeng Chen |author2=Vijay K. Varadan |name-list-style=amp |year=2004|title=Microwave electronics: measurement and materials characterization |url=https://books.google.com/books?id=2oA3po4coUoC&pg=PA8 |publisher=John Wiley and Sons |isbn=978-0-470-84492-2 |doi=10.1002/0470020466 |page=8, eq.(1.15)}}</ref>
:<math> \varepsilon_\text{r}(\omega) = \varepsilon_\text{r}'(\omega) - i \varepsilon_\text{r}''(\omega). </math>

The relative permittivity of a medium is related to its [[electric susceptibility]], {{math|''χ''<sub>e</sub>}}, as {{math|1=''ε''<sub>r</sub>(''ω'') = 1 + ''χ''<sub>e</sub>}}.

In anisotropic media (such as non cubic crystals) the relative permittivity is a second rank [[tensor]].

The relative permittivity of a material for a [[frequency]] of zero is known as its '''static relative permittivity'''.

=== Terminology ===
The historical term for the relative permittivity is ''dielectric constant''. It is still commonly used, but has been deprecated by standards organizations,<ref name=IEEE1997>{{cite journal |author=[[IEEE]] Standards Board|url=https://ieeexplore.ieee.org/document/8638365|title=IEEE Standard Definitions of Terms for Radio Wave Propagation | journal=IEEE STD 211-1997 |year=1997 |page=6}}</ref><ref name="IUPAC">{{cite journal |last=Braslavsky |first=S.E.|url=http://iupac.org/publications/pac/2007/pdf/7903x0293.pdf |title=Glossary of terms used in photochemistry (IUPAC recommendations 2006)|journal=Pure and Applied Chemistry|volume=79 |issue=3 |year=2007 |pages=293–465|doi=10.1351/pac200779030293|s2cid=96601716}}</ref> because of its ambiguity, as some older reports used it for the absolute permittivity ''ε''.<ref name=IEEE1997/><ref>{{cite book
|last = King
|first = Ronold W. P.
|author-link = Ronold W. P. King
|title = Fundamental Electromagnetic Theory
|publisher = Dover
|year = 1963
|location = New York
|page = 139}}</ref><ref name=Jackson/> The permittivity may be quoted either as a static property or as a frequency-dependent variant, in which case it is also known as the ''dielectric function''. It has also been used to refer to only the real component ''ε''′<sub>r</sub> of the complex-valued relative permittivity.{{citation needed|date=September 2013}}

=== Physics ===
In the causal theory of waves, permittivity is a complex quantity. The imaginary part corresponds to a phase shift of the polarization {{math|'''P'''}} relative to {{math|'''E'''}} and leads to the attenuation of electromagnetic waves passing through the medium.  By definition, the linear relative [[vacuum permittivity|permittivity of vacuum]] is equal to 1,<ref name=Jackson>
{{cite book 
|author=John David Jackson
|title=Classical Electrodynamics
|url=https://archive.org/details/classicalelectro00jack_697
|url-access=limited
|edition=Third
|publisher= Wiley
|location=New York
|year=1998
|isbn=978-0-471-30932-1
|page=[https://archive.org/details/classicalelectro00jack_697/page/n177 154]
}}</ref> that is {{nowrap|1=''ε'' = ''ε''<sub>0</sub>}}, although there are theoretical [[Quantum vacuum state#Non-linear permittivity|nonlinear quantum effects in vacuum]] that become non-negligible at high field strengths.<ref name=Mourou>{{cite journal|doi=10.1103/RevModPhys.78.309|title=Optics in the relativistic regime|year=2006|last1=Mourou|first1=Gerard A.|journal=Reviews of Modern Physics|volume=78|issue=2|page=309|bibcode=2006RvMP...78..309M}}</ref>

The following table gives some typical values.
{|class="wikitable"
|+ Low-frequency relative permittivity of some common solvents
|-
! colspan="2" |Solvent
! Relative permittivity
! Temperature
|-
|C<sub>6</sub>H<sub>6</sub>
| [[benzene]] || 2.3 || 298 K  (25&nbsp;°C)
|-
|Et<sub>2</sub>O
| [[diethyl ether]] || 4.3 || 293 K  (20&nbsp;°C)
|-
|(CH<sub>2</sub>)<sub>4</sub>O
| [[tetrahydrofuran]] (THF) || 7.6 || 298 K  (25&nbsp;°C)
|-
|CH<sub>2</sub>Cl<sub>2</sub>
| [[dichloromethane]] || 9.1 || 293 K  (20&nbsp;°C)
|-
|NH<sub>3</sub>(''liq'')
| [[ammonia|liquid ammonia]] || 17 || 273 K  (0&nbsp;°C)
|-
|C<sub>2</sub>H<sub>5</sub>OH
| [[ethanol]] || 24.3 || 298 K  (25&nbsp;°C)
|-
|CH<sub>3</sub>OH
| [[methanol]] || 32.7 || 298 K  (25&nbsp;°C)
|-
|CH<sub>3</sub>NO<sub>2</sub>
| [[nitromethane]] || 35.9 || 303 K  (30&nbsp;°C)
|-
|HCONMe<sub>2</sub>
| [[dimethyl formamide]] (DMF) || 36.7 || 298 K  (25&nbsp;°C)
|-
|CH<sub>3</sub>CN
| [[acetonitrile]] || 37.5 || 293 K  (20&nbsp;°C)
|-
|H<sub>2</sub>O
| [[water]] || 78.4|| 298 K  (25&nbsp;°C)
|-
|HCONH<sub>2</sub>
| [[formamide]] || 109 || 293 K  (20&nbsp;°C)
|}

The relative low frequency permittivity of [[ice]] is ~96 at −10.8&nbsp;°C, falling to 3.15 at high frequency, which is independent of temperature.<ref>{{cite journal |doi=10.3189/S0022143000018840|title=Dielectric Properties of Ice and Snow–a Review |year=1965 |last1=Evans |first1=S. |journal=Journal of Glaciology |volume=5 |issue=42 |pages=773–792 |s2cid=227325642 |doi-access=free }}</ref>  It remains in the range 3.12–3.19 for frequencies between about 1&nbsp;MHz and the far infrared region.<ref>{{citation |title=A summary of the complex dielectric permittivity of ice in the megahertz range and its applications for radar sounding of polar ice sheets |author1=Fujita, Shuji |author2=Matsuoka, Takeshi |author3=Ishida, Toshihiro |author4=Matsuoka, Kenichi |author5=Mae, Shinji |url=https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/32469/1/P185-212.pdf }}</ref>