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=== Capacitor charge compensation model === [[File:Capacitor schematic with dielectric.svg|thumb|Capacitor schematic with dielectric]] An explanation that has appeared in different forms is analogous to charge on a capacitor. If there is a potential difference between two materials due to the difference in their work functions (contact potential), this can be thought of as equivalent to the potential difference across a capacitor. The charge to compensate this is that which cancels the electric field. If an insulating dielectric is in between the two materials, then this will lead to a [[polarization density]] <math>\mathbf P</math> and a [[Maxwell's equations#Bound charge and current|bound surface charge]] of <math>\mathbf P \cdot \mathbf n</math>, where <math>\mathbf n</math> is the surface normal.<ref>{{Cite journal |last=Fisher |first=L. H. |date=1951 |title=On the Representation of the Static Polarization of Rigid Dielectrics by Equivalent Charge Distributions |url= https://pubs.aip.org/aapt/ajp/article/19/2/73-78/1034513 |journal=American Journal of Physics |volume=19 |issue=2 |pages=73–78 |doi=10.1119/1.1932714 |bibcode=1951AmJPh..19...73F |issn=0002-9505}}</ref><ref>{{Cite book |last=Griffiths |first=David |title=Introduction to Electrodynamics |date=29 June 2017 |publisher=Cambridge University Press |isbn=978-1-108-33351-1 |pages=296–354 |doi=10.1017/9781108333511.008}}</ref> The total charge in the capacitor is then the combination of the bound surface charge from the polarization and that from the potential. The triboelectric charge from this compensation model has been frequently considered as a key component.<ref>{{Cite journal |last=Ireland |first=Peter M. |date=2010 |title=Triboelectrification of particulate flows on surfaces: Part II — Mechanisms and models |url= https://linkinghub.elsevier.com/retrieve/pii/S0032591009006081 |journal=Powder Technology |volume=198 |issue=2 |pages=199–210 |doi=10.1016/j.powtec.2009.11.008}}</ref><ref>{{Cite journal |last1=Matsusaka |first1=S. |last2=Maruyama |first2=H. |last3=Matsuyama |first3=T. |last4=Ghadiri |first4=M. |date=2010 |title=Triboelectric charging of powders: A review |url= https://linkinghub.elsevier.com/retrieve/pii/S0009250910004239 |journal=Chemical Engineering Science |volume=65 |issue=22 |pages=5781–5807 |doi=10.1016/j.ces.2010.07.005|bibcode=2010ChEnS..65.5781M |hdl=2433/130693 |hdl-access=free }}</ref><ref>{{Cite journal |last1=Xie |first1=Li |last2=Li |first2=Junjie |last3=Liu |first3=Yakui |date=2020 |title=Review on charging model of sand particles due to collisions |journal=Theoretical and Applied Mechanics Letters |volume=10 |issue=4 |pages=276–285 |doi=10.1016/j.taml.2020.01.047 |s2cid=225960006 |issn=2095-0349|doi-access=free |bibcode=2020TAML...10..276X }}</ref><ref>{{Cite journal |last1=Han |first1=Chun |last2=Zhou |first2=Qun |last3=Hu |first3=Jiawei |last4=Liang |first4=Cai |last5=Chen |first5=Xiaoping |last6=Ma |first6=Jiliang |date=2021 |title=The charging characteristics of particle–particle contact |url= https://linkinghub.elsevier.com/retrieve/pii/S0304388621000322 |journal=Journal of Electrostatics |volume=112 |page=103582 |doi=10.1016/j.elstat.2021.103582|s2cid=235513618 }}</ref> If the additional polarization due to strain ([[piezoelectricity]]) or bending of samples ([[flexoelectricity]]) is included<ref name=":5" /><ref name=":26" /> this can explain observations such as the effect of curvature<ref name=":8" /> or inhomogeneous charging.<ref name=":25" />
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