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electric susceptibility wikipedia jump to content main menu main menu move to sidebar hide navigation main page contents current events random article about wikipedia contact us contribute help learn to edit community portal recent changes upload file special pages search search appearance donate create account log in personal tools donate create account log in contents move to sidebar hide top 1 definition for linear dielectrics 2 molecular polarizability toggle molecular polarizability subsection 2 1 ambiguity in the definition 3 nonlinear susceptibility 4 dispersion and causality 5 see also 6 references toggle the table of contents electric susceptibility 26 languages العربية беларуская català čeština deutsch español eesti فارسی français עברית हिन्दी hrvatski magyar bahasa indonesia italiano 日本語 한국어 nederlands norsk nynorsk polski português русский slovenščina српски srpski українська 中文 edit links article talk english read edit view history tools tools move to sidebar hide actions read edit view history general what links here related changes upload file permanent link page information cite this page get shortened url switch to legacy parser print export download as pdf printable version in other projects wikidata item appearance move to sidebar hide from wikipedia the free encyclopedia degree of polarization this article needs more citations please help improve this article by adding citations to reliable sources unsourced material may be challenged and removed find sources electric susceptibility news newspapers books scholar jstor november 2010 learn how and when to remove this message in electricity electromagnetism the electric susceptibility χ e displaystyle chi _ text e latin susceptibilis receptive is a dimensionless proportionality constant that indicates the degree of polarization of a dielectric material in response to an applied electric field the greater the electric susceptibility the greater the ability of a material to polarize in response to the field and thereby reduce the total electric field inside the material and store energy it is in this way that the electric susceptibility influences the electric permittivity of the material and thus influences many other phenomena in that medium from the capacitance of capacitors to the speed of light 1 2 definition for linear dielectrics edit if a dielectric material is a linear dielectric then electric susceptibility is defined as the constant of proportionality which may be a tensor relating an electric field e to the induced dielectric polarization density p such that 3 4 p ε 0 χ e e displaystyle mathbf p varepsilon _ 0 chi _ text e mathbf e where p displaystyle mathbf p is the polarization density c m 2 ε 0 displaystyle varepsilon _ 0 is the electric permittivity of free space electric constant f m χ e displaystyle chi _ text e is the electric susceptibility dimensionless e displaystyle mathbf e is the electric field v m in materials where susceptibility is anisotropic different depending on direction susceptibility is represented as a tensor known as the susceptibility tensor many linear dielectrics are isotropic but it is possible nevertheless for a material to display behavior that is both linear and anisotropic or for a material to be non linear but isotropic anisotropic but linear susceptibility is common in many crystals 3 the susceptibility is related to its relative permittivity dielectric constant ε r displaystyle varepsilon _ textrm r by χ e ε r 1 displaystyle chi _ text e varepsilon _ text r 1 so in the case of a vacuum χ e 0 displaystyle chi _ text e 0 at the same time the electric displacement d is related to the polarization density p by the following relation 3 d ε 0 e p ε 0 1 χ e e ε r ε 0 e ε e displaystyle mathbf d varepsilon _ 0 mathbf e mathbf p varepsilon _ 0 1 chi _ text e mathbf e varepsilon _ text r varepsilon _ 0 mathbf e varepsilon mathbf e where ε ε r ε 0 displaystyle varepsilon varepsilon _ text r varepsilon _ 0 ε r 1 χ e displaystyle varepsilon _ text r 1 chi _ text e molecular polarizability edit main article polarizability a similar parameter exists to relate the magnitude of the induced dipole moment p of an individual molecule to the local electric field e that induced the dipole this parameter is the molecular polarizability α and the dipole moment resulting from the local electric field e local is given by p ε 0 α e local displaystyle mathbf p varepsilon _ 0 alpha mathbf e_ text local this introduces a complication however as locally the field can differ significantly from the overall applied field we have p n p n ε 0 α e local displaystyle mathbf p n mathbf p n varepsilon _ 0 alpha mathbf e _ text local where p is the polarization per unit volume and n is the number of molecules per unit volume contributing to the polarization thus if the local electric field is parallel to the ambient electric field we have χ e e n α e local displaystyle chi _ text e mathbf e n alpha mathbf e _ text local thus only if the local field equals the ambient field can we write χ e n α displaystyle chi _ text e n alpha otherwise one should find a relation between the local and the macroscopic field in some materials the clausius mossotti relation holds and reads χ e 3 χ e n α 3 displaystyle frac chi _ text e 3 chi _ text e frac n alpha 3 ambiguity in the definition edit the definition of the molecular polarizability depends on the author in the above definition p ε 0 α e local displaystyle mathbf p varepsilon _ 0 alpha mathbf e_ text local p displaystyle p and e displaystyle e are in si units and the molecular polarizability α displaystyle alpha has the dimension of a volume m 3 another definition 5 would be to keep si units and to integrate ε 0 displaystyle varepsilon _ 0 into α displaystyle alpha p α e local displaystyle mathbf p alpha mathbf e_ text local in this second definition the polarizability would have the si unit of c m 2 v yet another definition exists 5 where p displaystyle p and e displaystyle e are expressed in the cgs system and α displaystyle alpha is still defined as p α e local displaystyle mathbf p alpha mathbf e_ text local using the cgs units gives α displaystyle alpha the dimension of a volume as in the first definition but with a value that is 4 π displaystyle 4 pi lower nonlinear susceptibility edit in many materials the polarizability starts to saturate at high values of electric field this saturation can be modelled by a nonlinear susceptibility these susceptibilities are important in nonlinear optics and lead to effects such as second harmonic generation such as used to convert infrared light into visible light in green laser pointers the standard definition of nonlinear susceptibilities in si units is via a taylor expansion of the polarization s reaction to electric field 6 p p 0 ε 0 χ 1 e ε 0 χ 2 e 2 ε 0 χ 3 e 3 displaystyle p p_ 0 varepsilon _ 0 chi 1 e varepsilon _ 0 chi 2 e 2 varepsilon _ 0 chi 3 e 3 cdots except in ferroelectric materials the built in polarization is zero p 0 0 displaystyle p_ 0 0 the first susceptibility term χ 1 displaystyle chi 1 corresponds to the linear susceptibility described above while this first term is dimensionless the subsequent nonlinear susceptibilities χ n displaystyle chi n have units of m v n 1 the nonlinear susceptibilities can be generalized to anisotropic materials in which the susceptibility is not uniform in every direction in these materials each susceptibility χ n displaystyle chi n becomes an n 1 degree tensor dispersion and causality edit plot of the dielectric constant as a function of frequency showing several resonances and plateaus which indicate the processes that respond on the time scale of a period this demonstrates that thinking of the susceptibility in terms of its fourier transform is useful in general a material cannot polarize instantaneously in response to an applied field and so the more general formulation as a function of time is p t ε 0 t χ e t t e t d t displaystyle mathbf p t varepsilon _ 0 int _ infty t chi _ text e t t mathbf e t mathrm d t that is the polarization is a convolution of the electric field at previous times with time dependent susceptibility given by χ e δ t displaystyle chi _ text e delta t the upper limit of this integral can be extended to infinity as well if one defines χ e δ t 0 displaystyle chi _ text e delta t 0 for δ t 0 displaystyle delta t 0 an instantaneous response corresponds to dirac delta function susceptibility χ e δ t χ e δ δ t displaystyle chi _ text e delta t chi _ text e delta delta t it is more convenient in a linear system to take the fourier transform and write this relationship as a function of frequency due to the convolution theorem the integral becomes a product p ω ε 0 χ e ω e ω displaystyle mathbf p omega varepsilon _ 0 chi _ text e omega mathbf e omega this has a similar form to the clausius mossotti relation 7 p r ε 0 n α r 1 1 3 n r α r e r ε 0 χ e r e r displaystyle mathbf p mathbf r varepsilon _ 0 frac n alpha mathbf r 1 frac 1 3 n mathbf r alpha mathbf r mathbf e mathbf r varepsilon _ 0 chi _ text e mathbf r mathbf e mathbf r this frequency dependence of the susceptibility leads to frequency dependence of the permittivity the shape of the susceptibility with respect to frequency characterizes the dispersion properties of the material moreover the fact that the polarization can only depend on the electric field at previous times i e χ e δ t 0 displaystyle chi _ text e delta t 0 for δ t 0 displaystyle delta t 0 a consequence of causality imposes kramers kronig constraints on the susceptibility χ e 0 displaystyle chi _ text e 0 see also edit application of tensor theory in physics magnetic susceptibility maxwell s equations clausius mossotti relation linear response function green kubo relations references edit electric susceptibility encyclopædia britannica cardarelli françois 2000 2008 materials handbook a concise desktop reference 2nd ed london springer verlag pp 524 section 8 1 16 doi 10 1007 978 1 84628 669 8 isbn 978 1 84628 668 1 1 2 3 griffiths david j 2017 introduction to electrodynamics 4 ed cambridge university press pp 181 190 freeman richard king james lafyatis gregory 2019 essentials of electricity and magnetism electromagnetic radiation oxford university press doi 10 1093 oso 9780198726500 003 0001 isbn 978 0 19 872650 0 1 2 crc handbook of chemistry and physics pdf 84 ed crc pp 10 163 archived from the original pdf on 2016 10 06 retrieved 2016 08 19 butcher paul n cotter david 1990 the elements of nonlinear optics cambridge university press doi 10 1017 cbo9781139167994 isbn 9781139167994 freeman richard king james lafyatis gregory 2019 essentials of electricity and magnetism electromagnetic radiation oxford oxford university press doi 10 1093 oso 9780198726500 003 0001 isbn 978 0 19 872650 0 retrieved 2022 02 18 authority control databases gnd retrieved from https en wikipedia org w index php title electric_susceptibility oldid 1362749268 categories electric and magnetic fields in matter electrical quantities hidden categories articles with short description short description matches wikidata articles needing additional references from november 2010 all articles needing additional references this page was last edited on 5 july 2026 at 23 55 utc page was rendered with parsoid text is available under the creative commons attribution sharealike 4 0 license additional terms may apply by using this site you agree to the terms of use and privacy policy wikipedia is a registered trademark of the wikimedia foundation inc a non profit organization privacy policy about wikipedia disclaimers contact wikipedia legal safety contacts code of conduct developers statistics cookie statement mobile view search search toggle the table of contents electric susceptibility 26 languages add topic