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In [[electromagnetism]], the '''magnetic susceptibility''' <math>\chi</math> ([[latin]]: ''susceptibilis'' “receptive”) is a dimensionless proportionality constant that indicates the degree of [[magnetization]] of a material in response to an applied [[magnetic field]]. A related term is '''magnetizability''', the proportion between [[magnetic moment]] and [[magnetic field|magnetic flux density]].<ref>{{cite encyclopedia |year=1997 |title =magnetizability, ξ |encyclopedia=IUPAC Compendium of Chemical Terminology—The Gold Book |publisher=[[International Union of Pure and Applied Chemistry]] |edition=2nd |url=http://goldbook.iupac.org/search.py?search_text=magnetizability}}</ref> A closely related parameter is the [[Permeability (electromagnetism)|permeability]], which expresses the total magnetization of material and volume.
This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users.


==Definition of volume susceptibility==
If you would like use the '''MathML''' rendering mode, you need a wikipedia user account that can be registered here [[https://en.wikipedia.org/wiki/Special:UserLogin/signup]]
::''See also '' [[Permeability (electromagnetism)#Relative permeability and magnetic susceptibility|Relative permeability]].
* Only registered users will be able to execute this rendering mode.
The ''volume magnetic susceptibility'', represented by the symbol <math>\chi_v</math> (often simply <math>\chi</math>, sometimes <math>\chi_m</math>&nbsp;– magnetic, to distinguish from the [[electric susceptibility]]), is defined in the [[International System of Units]]&nbsp;— in other systems there may be additional constants — by the following relationship:
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:<math>
Registered users will be able to choose between the following three rendering modes:  
\mathbf{M} = \chi_v \mathbf{H}.
</math>


Here
'''MathML'''
:<math forcemathmode="mathml">E=mc^2</math>


:'''M''' is the [[magnetization]] of the material (the [[magnetic dipole moment]] per unit volume), measured in [[ampere]]s per meter, and
<!--'''PNG''' (currently default in production)
:<math forcemathmode="png">E=mc^2</math>


:'''H''' is the [[Effective magnetic field|magnetic field strength]], also measured in amperes per meter.
'''source'''
:<math forcemathmode="source">E=mc^2</math> -->


<math>\chi_v</math> is therefore a [[dimensionless quantity]].
<span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples].


The [[magnetic field|magnetic induction]] '''B''' is related to '''H''' by the relationship
==Demos==


:<math>
Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]:
\mathbf{B} \ = \ \mu_0(\mathbf{H} + \mathbf{M}) \ = \ \mu_0(1+\chi_v) \mathbf{H} \ = \ \mu \mathbf{H}
</math>


where μ<sub>0</sub> is the [[magnetic constant]] (see table of [[physical constant]]s), and
<math> (1+\chi_v) </math> is the [[Permeability (electromagnetism)#Relative permeability and magnetic susceptibility|relative permeability]] of the material.
Thus the ''volume magnetic susceptibility'' <math>\chi_v</math> and the [[magnetic permeability]] <math>\mu</math> are related by the following formula:
:<math>\mu = \mu_0(1+\chi_v)\,</math> .
Sometimes<ref>{{cite web|author=Richard A. Clarke |url=http://info.ee.surrey.ac.uk/Workshop/advice/coils/mu/#itns |title=Magnetic properties of materials |publisher=Info.ee.surrey.ac.uk |date= |accessdate=2011-11-08}}</ref> an auxiliary quantity called ''intensity of magnetization'' (also referred to as ''magnetic polarisation'' '''J''') and measured in [[Tesla (unit)|teslas]], is defined as
:<math>\mathbf{I} = \mu_0 \mathbf{M} \,</math> .
This allows an alternative description of all magnetization phenomena in terms of the quantities '''I''' and '''B''', as opposed to the commonly used '''M''' and '''H'''.


==Conversion between SI and CGS units==
* accessibility:
Note that these definitions are according to [[International System of Units|SI]] conventions. However, many tables of magnetic susceptibility give [[Centimetre gram second system of units|CGS]] values (more specifically [[Centimetre gram second system of units#Electromagnetic units (EMU)|emu-cgs]], short for electromagnetic units, or [[Gaussian units|Gaussian-cgs]]; both are the same in this context). These units rely on a different definition of the permeability of free space:<ref name=bennett>{{
** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]]
cite journal
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)]
| author = Bennett, L. H.; Page, C. H.; and Swartzendruber, L. J.
** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)]
| title = Comments on units in magnetism
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)]
| year = 1978
** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]].
| journal = Journal of Research of the National Bureau of Standar
** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]].
| volume = 83
** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode.
| issue = 1
| publisher = [[NIST]], USA
| pages = 9–12
| doi = }}</ref>


:<math>
==Test pages ==
\mathbf{B}^{\text{cgs}} \ = \ \mathbf{H}^{\text{cgs}} + 4\pi\mathbf{M}^{\text{cgs}} \ = \ (1+4\pi\chi_{v}^{\text{cgs}}) \mathbf{H}^{\text{cgs}}
</math>


The [[dimensionless]] CGS value of volume susceptibility is multiplied by 4π to give the dimensionless [[International System of Units|SI]] volume susceptibility value:<ref name=bennett/>
To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages:
*[[Displaystyle]]
*[[MathAxisAlignment]]
*[[Styling]]
*[[Linebreaking]]
*[[Unique Ids]]
*[[Help:Formula]]


:<math>\chi_v^{\text{SI}}=4\pi\chi_v^{\text{cgs}}</math>
*[[Inputtypes|Inputtypes (private Wikis only)]]
 
*[[Url2Image|Url2Image (private Wikis only)]]
For example, the [[Centimetre gram second system of units|CGS]] volume magnetic susceptibility of water at 20°C is −7.19×10<sup>−7</sup> which is −9.04×10<sup>−6</sup> using the [[International System of Units|SI]] convention.
==Bug reporting==
 
If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de .
==Mass susceptibility and molar susceptibility==
There are two other measures of susceptibility, the ''mass magnetic susceptibility'' (χ<sub>mass</sub> or χ<sub>g</sub>, sometimes χ<sub>m</sub>), measured in m<sup>3</sup>·kg<sup>−1</sup> in SI or in cm<sup>3</sup>·g<sup>−1</sup> in CGS  and the ''[[Mole_(unit)|molar]] magnetic susceptibility'' (χ<sub>mol</sub>) measured in m<sup>3</sup>·mol<sup>−1</sup> (SI) or cm<sup>3</sup>·mol<sup>−1</sup> (CGS) that are defined below, where ρ is the [[density]] in kg·m<sup>−3</sup> (SI) or g·cm<sup>−3</sup> (CGS) and M is [[molar mass]] in kg·mol<sup>−1</sup> (SI) or g·mol<sup>−1</sup> (CGS).
 
:<math>\chi_\text{mass} = \chi_v/\rho</math>
 
:<math>\chi_\text{mol} = M\chi_\text{mass} = M\chi_v/\rho</math>
 
==Sign of susceptibility: diamagnetics and other types of magnetism==
If χ is positive, a material can be [[paramagnetic]]. In this case, the magnetic field in the material is strengthened by the induced magnetization. Alternatively, if χ is negative, the material is [[diamagnetic]]. In this case, the magnetic field in the material is weakened by the induced magnetization. Generally, non-magnetic materials are said to be para- or diamagnetic because they do not possess permanent magnetization without external magnetic field. [[Ferromagnetic]], [[ferrimagnetism|ferrimagnetic]], or [[antiferromagnetic]] materials have positive susceptibility and possess permanent magnetization even without external magnetic field.
 
==Experimental methods to determine susceptibility==
Volume magnetic susceptibility is measured by the force change felt upon a substance when a magnetic field gradient is applied.<ref>{{cite book
| author=L. N. Mulay
| title=Techniques of Chemistry
| editor=A. Weissberger and B. W. Rossiter
| publisher=Wiley-Interscience: New York
| volume=4
| page = 431
| year=1972}}</ref> Early measurements are made using the [[Gouy balance]] where a sample is hung between the poles of an electromagnet. The change in weight when the electromagnet is turned on is proportional to the susceptibility. Today, high-end measurement systems use a [[superconductive]] magnet. An alternative is to measure the force change on a strong compact magnet upon insertion of the sample. This system, widely used today, is called the [[Evans balance]].<ref>{{cite web|url=http://www.sherwood-scientific.com/msb/msbindex.html |title=Magnetic Susceptibility Balances |publisher=Sherwood-scientific.com |date= |accessdate=2011-11-08}}</ref> For liquid samples, the susceptibility can be measured from the dependence of the [[Nuclear magnetic resonance|NMR]] frequency of the sample on its shape or orientation.<ref>{{ SAM_ @dreamlyf10
cite journal
| author=J. R. Zimmerman, and M. R. Foster
| title=Standardization of NMR high resolution spectra
| journal=J. Phys. Chem.
| volume=61
| year=1957
| pages=282–289
| doi=10.1021/j150549a006
| issue=3}}</ref><ref>{{
cite journal
| author=Robert Engel, Donald Halpern, and Susan Bienenfeld
| title=Determination of magnetic moments in solution by nuclear magnetic resonance spectrometry
| journal=Anal. Chem.
| volume=45
| year=1973
| pages=367–369
| doi=10.1021/ac60324a054
| issue=2}}</ref><ref>{{
cite journal
| author=P. W.  Kuchel, B. E. Chapman, W. A. Bubb, P. E. Hansen, C. J. Durrant, and M. P. Hertzberg
| title=Magnetic susceptibility: solutions, emulsions, and cells
| journal=Concepts Magn. Reson.
| volume=A 18
| year=2003
| pages=56–71
| doi=10.1002/cmr.a.10066}}</ref><ref>{{
cite journal
| author=K. Frei and H. J. Bernstein
| title=Method for determining magnetic susceptibilities by NMR
| journal=J. Chem. Phys.
| volume=37
| year=1962
| pages=1891–1892
| doi=10.1063/1.1733393|bibcode = 1962JChPh..37.1891F
| issue=8 }}</ref><ref>{{
cite journal
| author=R. E. Hoffman
| title=Variations on the chemical shift of TMS
| journal=J. Magn. Reson.
| volume=163
| year=2003
| pages=325–331
| doi=10.1016/S1090-7807(03)00142-3
| pmid=12914848
| issue=2|bibcode = 2003JMagR.163..325H }}</ref>
 
==Tensor susceptibility==
The magnetic susceptibility of most [[crystal]]s is not a scalar quantity. Magnetic response '''M''' is dependent upon the orientation of the sample and can occur in directions other than that of the applied field '''H'''. In these cases, volume susceptibility is defined as a [[tensor]]
 
:<math> M_i=\chi_{ij}H_j  </math>
 
where ''i'' and ''j'' refer to the directions (e.g., ''x'' and ''y'' in [[Cartesian coordinates]]) of the applied field and magnetization, respectively. The [[tensor]] is thus rank 2 (second order), dimension (3,3) describing the component of magnetization in the ''i''-th direction from the external field applied in the ''j''-th direction.
 
==Differential susceptibility==
In [[ferromagnetic]] crystals, the relationship between '''M''' and '''H''' is not linear. To accommodate this, a more general definition of ''differential susceptibility'' is used
 
:<math>\chi^{d}_{ij} = \frac{\part M_i}{\part H_j}</math>
 
where <math>\chi^{d}_{ij}</math> is a [[tensor]] derived from [[partial derivative]]s of components of '''M''' with respect to components of '''H'''.
When the [[coercivity]] of the material parallel to an applied field is the smaller of the two, the differential susceptibility is a function of the applied field and self interactions, such as the [[magnetic anisotropy]]. When the material is not [[Saturation_(magnetic)|saturated]], the effect will be nonlinear and dependent upon the [[Domain wall (magnetism)|domain wall]] configuration of the material.
 
==Susceptibility in the frequency domain==
When the magnetic susceptibility is measured in response to an [[Alternating current|AC]] magnetic field (i.e. a magnetic field that varies sinusoidally), this is called ''AC susceptibility''. AC susceptibility (and the closely related "AC permeability") are [[complex number]] quantities, and various phenomena (such as resonances) can be seen in AC susceptibility that cannot in constant-field (DC) susceptibility. In particular, when an AC field is applied perpendicular to the detection direction (called the "transverse susceptibility" regardless of the frequency), the effect has a peak at the [[ferromagnetic resonance]] frequency of the material with a given static applied field. Currently, this effect is called the ''microwave permeability'' or ''network ferromagnetic resonance'' in the literature. These results are sensitive to the [[Domain wall (magnetism)|domain wall]] configuration of the material and [[eddy currents]].
 
In terms of [[ferromagnetic resonance]], the effect of an ac-field applied along the direction of the magnetization is called ''parallel pumping''.
 
For a tutorial with more information on AC susceptibility measurements, see [http://www.qdusa.com/resources/pdf/1078-201.pdf here (external link)].
 
==Examples==
{| class="wikitable"  style="margin:auto; text-align:center;"
|+ Magnetic susceptibility of some materials
! Material  !![[Temperature]]!![[Pressure]] !!colspan="2" | <math>\chi_{\text{mol}}</math> (molar susc.)!! colspan="2" | <math>\chi_{\text{mass}}</math>  (mass susc.) !! colspan="2" | <math>\chi_{v}</math> (volume susc.)  !! ''M'' ([[molar mass]]) !!<math>\rho</math> ([[density]])
|-
| style="text-align:right;"| [[Units of measurement|Units]] || style="text-align:center;"|([[Celsius|°C]])|| style="text-align:center;"|([[Atmosphere (unit)|atm]])|| style="text-align:center;"|SI<br/>([[cubic meter|m<sup>3</sup>]]·[[Mole (unit)|mol]]<sup>−1</sup>)|| style="text-align:center;"|CGS<br/>([[cubic centimeter|cm<sup>3</sup>]]·[[Mole (unit)|mol]]<sup>−1</sup>)|| style="text-align:center;"|SI<br/>([[cubic meter|m<sup>3</sup>]]·[[kg]]<sup>−1</sup>)|| style="text-align:center;"|CGS<br/>([[cubic centimeter|cm<sup>3</sup>]]·[[gram|g]]<sup>−1</sup>)|| style="text-align:center;"|SI<br/>|| style="text-align:center;"|CGS<br/> (''[[electromagnetic unit|emu]]'')|| style="text-align:center;"|(10<sup>−3</sup> [[kg]]/[[Mole (unit)|mol]])<br/>or ([[gram|g]]/[[Mole (unit)|mol]])|| style="text-align:center;"|(10<sup>3</sup> [[kg]]/[[cubic meter|m<sup>3</sup>]])<br/>or ([[gram|g]]/[[cubic centimeter|cm<sup>3</sup>]])
|-
|align="left" | [[Water (data page)|water]] <ref>{{
cite journal
| author=G. P. Arrighini, M. Maestro, and R. Moccia
| title=Magnetic Properties of Polyatomic Molecules: Magnetic Susceptibility of H<sub>2</sub>O, NH<sub>3</sub>, CH<sub>4</sub>, H<sub>2</sub>O<sub>2</sub>
| journal=J. Chem. Phys.
| volume=49
| year=1968
| pages=882–889
| doi=10.1063/1.1670155|bibcode = 1968JChPh..49..882A
| issue=2 }}</ref> ||20||1 ||−1.631×10<sup>−10</sup>||−1.298×10<sup>−5</sup> ||−9.051×10<sup>−9</sup> ||−7.203×10<sup>−7</sup> ||−9.035×10<sup>−6</sup> ||−7.190×10<sup>−7</sup> ||18.015 ||0.9982
|-
|align="left" | [[bismuth]] <ref>{{
cite journal
| author = S. Otake, M. Momiuchi and N. Matsuno
| title = Temperature Dependence of the Magnetic Susceptibility of Bismuth
| year = 1980
| journal = J. Phys. Soc. Jap.
| volume = 49
| issue = 5
| pages = 1824–1828
| doi = 10.1143/JPSJ.49.1824|bibcode = 1980JPSJ...49.1824O }}
The tensor needs to be averaged over all orientations: <math>\chi=(1/3)\chi_{||}+(2/3)\chi_{\perp}</math> .</ref>|| 20 ||1||−3.55×10<sup>−9</sup> ||−2.82×10<sup>−4</sup>||−1.70×10<sup>−8</sup> ||−1.35×10<sup>−6</sup> ||−1.66×10<sup>−4</sup> ||−1.32×10<sup>−5</sup>|| 208.98
||9.78
|-
|align="left" | [[Carbon|Diamond]] <ref>{{
cite journal
| author = J. Heremans, C. H. Olk and D. T. Morelli
| title = Magnetic Susceptibility of Carbon Structures
| year = 1994
| journal = Phys. Rev. B
| volume = 49
| issue = 21
| pages = 15122–15125
| doi = 10.1103/PhysRevB.49.15122|bibcode = 1994PhRvB..4915122H }}</ref>  || [[Room temperature|R.T.]]||1 ||−7.4×10<sup>−11</sup> ||−5.9×10<sup>−6</sup>|| −6.2×10<sup>−9</sup>||−4.9×10<sup>−7</sup> || −2.2×10<sup>−5</sup> ||−1.7×10<sup>−6</sup>  || 12.01|| 3.513
|-
|align="left" | [[Carbon|Graphite]] <ref name=graphite1>{{
cite journal
| author = N. Ganguli and K.S. Krishnan
| title = The Magnetic and Other Properties of the Free Electrons in Graphite
| year = 1941
| journal = Proceedings of the Royal Society
| volume = 177
| issue = 969
| pages = 168–182
| doi = 10.1098/rspa.1941.0002|bibcode = 1941RSPSA.177..168G
}}</ref>  <math>\chi_{\perp}</math>(to c-axis) || [[Room temperature|R.T.]]||1 ||−7.5×10<sup>−11</sup> ||−6.0×10<sup>−6</sup>|| −6.3×10<sup>−9</sup>||−5.0×10<sup>−7</sup> || −1.4×10<sup>−5</sup> ||−1.1×10<sup>−6</sup>  || 12.01|| 2.267
|-
|align="left" | [[Carbon|Graphite]] <ref name=graphite1/> <math>\chi_{||}</math> || [[Room temperature|R.T.]]||1 ||−3.2×10<sup>−9</sup> ||−2.6×10<sup>−4</sup>|| −2.7×10<sup>−7</sup> ||−2.2×10<sup>−5</sup> || −6.1×10<sup>−4</sup> ||−4.9×10<sup>−5</sup>  || 12.01|| 2.267
|-
|align="left" | [[Carbon|Graphite]] <ref name=graphite1/>  <math>\chi_{||}</math> || -173||1 ||−4.4×10<sup>−9</sup> ||−3.5×10<sup>−4</sup>|| −3.6×10<sup>−7</sup>||−2.9×10<sup>−5</sup> || −8.3×10<sup>−4</sup> ||−6.6×10<sup>−5</sup>  || 12.01|| 2.267
|-
|align="left" | [[Helium|He]] <ref name=gases1>{{
cite journal
| author = R. E. Glick
| title = On the Diamagnetic Susceptibility of Gases
| year = 1961
| journal = J. Phys. Chem.
| volume = 65
| issue = 9
| pages = 1552–1555
| doi = 10.1021/j100905a020}}</ref> ||20 ||1
||−2.38×10<sup>−11</sup>||−1.89×10<sup>−6</sup>||−5.93×10<sup>−9</sup> ||−4.72×10<sup>−7</sup> ||−9.85×10<sup>−10</sup>  || −7.84×10<sup>−11</sup> ||4.0026 || 0.000166
|-
|align="left" | [[Xenon|Xe]] <ref name=gases1/>  ||20 ||1 ||−5.71×10<sup>−10</sup>||−4.54×10<sup>−5</sup>|| −4.35×10<sup>−9</sup>||−3.46×10<sup>−7</sup> ||−2.37×10<sup>−8</sup>  ||−1.89×10<sup>−9</sup>  || 131.29||0.00546
|-
|align="left" | [[Oxygen|O<sub>2</sub>]] <ref name=gases1/> || 20|| 0.209 ||4.3×10<sup>−8</sup>||3.42×10<sup>−3</sup>||1.34×10<sup>−6</sup> ||1.07×10<sup>−4</sup> || 3.73×10<sup>−7</sup>||2.97×10<sup>−8</sup> || 31.99||0.000278
|-
|align="left" | [[Nitrogen|N<sub>2</sub>]] <ref name=gases1/> || 20|| 0.781 ||−1.56×10<sup>−10</sup>||−1.24×10<sup>−5</sup>||−5.56×10<sup>−9</sup> ||−4.43×10<sup>−7</sup> || −5.06×10<sup>−9</sup>||−4.03×10<sup>−10</sup> || 28.01 ||0.000910
|-
|align="left" | [[Aluminium|Al]] <ref name="magneticValues">{{Cite web|url=http://hyperphysics.phy-astr.gsu.edu/Hbase/tables/magprop.html|title=Magnetic Properties of Solids|last=Nave|first=Carl L|work=HyperPhysics|accessdate=2008-11-09}}</ref>  || ||1 || 2.2×10<sup>−10</sup> ||1.7×10<sup>−5</sup>||7.9×10<sup>−9</sup> ||6.3×10<sup>−7</sup> ||2.2×10<sup>−5</sup> ||1.75×10<sup>−6</sup> ||26.98 ||2.70
|-
|align="left" | [[Silver|Ag]] <ref>{{
cite journal
| author = R. Dupree and C. J. Ford
| title = Magnetic susceptibility of the noble metals around their melting points
| year = 1973
| journal = Phys. Rev. B
| volume = 8
| issue = 4
| pages = 1780–1782
| doi = 10.1103/PhysRevB.8.1780|bibcode = 1973PhRvB...8.1780D }}</ref> || 961 ||1||  ||  ||  || ||−2.31×10<sup>−5</sup>||−1.84×10<sup>−6</sup> || 107.87||
|}
 
==Sources of confusion in published data==
There are tables of magnetic susceptibility values published on-line that seem to have been uploaded from a substandard source,<ref>{{cite web|url=http://www.reade.com/Particle_Briefings/magnetic_susceptibilities.html |title=Magnetic Properties Susceptibilities Chart from |publisher=READE |date=2006-01-11 |accessdate=2011-11-08}}</ref>
which itself has probably borrowed heavily from the [[CRC Press|CRC Handbook of Chemistry and Physics]]. Some of the data (e.g. for Al, Bi, and diamond) are apparently in CGS '''Molar Susceptibility''' units, whereas that for water is in '''Mass Susceptibility''' units (see discussion above).  The susceptibility table in the CRC Handbook is known to suffer from similar errors, and even to contain sign errors. Effort should be made to trace the data in such tables to the original sources, and to double-check the proper usage of units.
 
==See also==
* [[Curie constant]]
* [[Electric susceptibility]]
* [[Iron]]
* [[Magnetic constant]]
* [[Magnetic flux density]]
* [[Magnetism]]
*[[Magnetochemistry]]
* [[Magnetometer]]
* [[Maxwell's equations]]
* [[Paleomagnetism]]
* [[Permeability (electromagnetism)]]
* [[Quantitative susceptibility mapping]]
* [[Susceptibility weighted imaging]]
 
==References and notes==
{{Reflist}}
==External Links==
*[http://www.cond-mat.de/events/correl14/manuscripts/pavarini.pdf Linear Response Functions ] in Eva Pavarini, Erik Koch, Dieter Vollhardt, and Alexander Lichtenstein (eds.): DMFT at 25: Infinite Dimensions,  Verlag des Forschungszentrum Jülich, 2014 ISBN 978-3-89336-953-9
 
{{DEFAULTSORT:Magnetic Susceptibility}}
[[Category:Physical quantities]]
[[Category:Magnetism]]
[[Category:Electric and magnetic fields in matter]]
[[Category:Scientific techniques]]

Latest revision as of 22:52, 15 September 2019

This is a preview for the new MathML rendering mode (with SVG fallback), which is availble in production for registered users.

If you would like use the MathML rendering mode, you need a wikipedia user account that can be registered here [[1]]

  • Only registered users will be able to execute this rendering mode.
  • Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.

Registered users will be able to choose between the following three rendering modes:

MathML

E=mc2


Follow this link to change your Math rendering settings. You can also add a Custom CSS to force the MathML/SVG rendering or select different font families. See these examples.

Demos

Here are some demos:


Test pages

To test the MathML, PNG, and source rendering modes, please go to one of the following test pages:

Bug reporting

If you find any bugs, please report them at Bugzilla, or write an email to math_bugs (at) ckurs (dot) de .

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