3821:
144:
2392:(orientation polarisation), or can be induced in any molecule in which the asymmetric distortion of the nuclei is possible (distortion polarisation). Orientation polarisation results from a permanent dipole, e.g., that arises from the 104.45° angle between the asymmetric bonds between oxygen and hydrogen atoms in the water molecule, which retains polarisation in the absence of an external electric field. The assembly of these dipoles forms a macroscopic polarisation.
168:
3061:
2217:
5204:
47:
3544:
2868:
1654:
2244:. It is the relationship between the electric field and the dipole moment that gives rise to the behaviour of the dielectric. (Note that the dipole moment points in the same direction as the electric field in the figure. This is not always the case, and is a major simplification, but is true for many materials.)
4030:
Researchers "doped" BST thin films with magnesium, analyzing the "structure, microstructure, surface morphology and film/substrate compositional quality" of the result. The Mg doped BST films showed "improved dielectric properties, low leakage current, and good tunability", meriting potential for use
2407:
of the molecules. Because the rotation is not instantaneous, dipolar polarisations lose the response to electric fields at the highest frequencies. A molecule rotates about 1 radian per picosecond in a fluid, thus this loss occurs at about 10 Hz (in the microwave region). The delay of the response to
2224:
In the classical approach to the dielectric, the material is made up of atoms. Each atom consists of a cloud of negative charge (electrons) bound to and surrounding a positive point charge at its center. In the presence of an electric field, the charge cloud is distorted, as shown in the top right of
4354:
considered from the standpoint of their interaction with electric, magnetic or electromagnetic fields. Thus we are concerned with gases as well as with liquids and solids and with the storage of electric and magnetic energy as well as its dissipation." (p. 1) (Technology Press of MIT and John Wiley,
2443:
If a crystal or molecule consists of atoms of more than one kind, the distribution of charges around an atom in the crystal or molecule leans to positive or negative. As a result, when lattice vibrations or molecular vibrations induce relative displacements of the atoms, the centers of positive and
4023:
The research was part of an effort to provide the Army with highly-tunable, microwave-compatible materials for broadband electric-field tunable devices, which operate consistently in extreme temperatures. This work improved tunability of bulk barium strontium titanate, which is a thin film enabler
2537:
is the dependence of the permittivity of a dielectric material on the frequency of an applied electric field. Because there is a lag between changes in polarisation and changes in the electric field, the permittivity of the dielectric is a complex function of the frequency of the electric field.
4788:
Lee, Che-Hui; Orloff, Nathan D.; Birol, Turan; Zhu, Ye; Goian, Veronica; Rocas, Eduard; Haislmaier, Ryan; Vlahos, Eftihia; Mundy, Julia A.; Kourkoutis, Lena F.; Nie, Yuefeng; Biegalski, Michael D.; Zhang, Jingshu; Bernhagen, Margitta; Benedek, Nicole A.; Kim, Yongsam; Brock, Joel D.; Uecker,
3401:
2419:
frequencies or less, the molecules are bent and stretched by the field and the molecular dipole moment changes. The molecular vibration frequency is roughly the inverse of the time it takes for the molecules to bend, and this distortion polarisation disappears above the infrared.
1793:
3056:{\displaystyle {\begin{aligned}\varepsilon '&=\varepsilon _{\infty }+{\frac {\varepsilon _{s}-\varepsilon _{\infty }}{1+\omega ^{2}\tau ^{2}}}\\\varepsilon ''&={\frac {(\varepsilon _{s}-\varepsilon _{\infty })\omega \tau }{1+\omega ^{2}\tau ^{2}}}\end{aligned}}}
1014:, positive charges are displaced in the direction of the field and negative charges shift in the direction opposite to the field. This creates an internal electric field that reduces the overall field within the dielectric itself. If a dielectric is composed of weakly
4789:
Reinhard; Xi, X. X.; Gopalan, Venkatraman; Nuzhnyy, Dmitry; Kamba, Stanislav; Muller, David A.; Takeuchi, Ichiro; Booth, James C.; Fennie, Craig J.; Schlom, Darrell G. (2013). "Exploiting dimensionality and defect mitigation to create tunable microwave dielectrics".
1518:
4020:(ARL) conducted research on thin film technology. Barium strontium titanate (BST), a ferroelectric thin film, was studied for the fabrication of radio frequency and microwave components, such as voltage-controlled oscillators, tunable filters and phase shifters.
2766:
3692:
that operates by polarising the paraelectric, allowing it to return to ambient temperature (by dissipating the extra heat), bringing it into contact with the object to be cooled, and finally depolarising it, would result in refrigeration.
2074:
4141:), may retain excess internal charge or "frozen in" polarisation. Electrets have a semi-permanent electric field, and are the electrostatic equivalent to magnets. Electrets have numerous practical applications in the home and industry.
2254:
This is the essence of the model in physics. The behaviour of the dielectric now depends on the situation. The more complicated the situation, the richer the model must be to accurately describe the behaviour. Important questions are:
3391:
3328:
2444:
negative charges are also displaced. The locations of these centers are affected by the symmetry of the displacements. When the centers do not correspond, polarisation arises in molecules or crystals. This polarisation is called
3963:
2631:, and therefore dielectric relaxation is measured relative to the expected linear steady state (equilibrium) dielectric values. The time lag between electrical field and polarisation implies an irreversible degradation of
3839:
The most obvious advantage to using such a dielectric material is that it prevents the conducting plates, on which the charges are stored, from coming into direct electrical contact. More significantly, however, a high
2588:
is the permittivity of the free space. Because permittivity indicates the strength of the relation between an electric field and polarisation, if a polarisation process loses its response, permittivity decreases.
5029:
Cole, M. W.; Hubbard, C.; Ngo, E.; Ervin, M.; Wood, M.; Geyer, R. G. (July 2002). "Structureâproperty relationships in pure and acceptor-doped Ba1âxSrxTiO3 thin films for tunable microwave device applications".
1304:
3902:
3539:{\displaystyle \tan(\delta )={\frac {\varepsilon ''}{\varepsilon '}}={\frac {\left(\varepsilon _{s}-\varepsilon _{\infty }\right)\omega \tau }{\varepsilon _{s}+\varepsilon _{\infty }\omega ^{2}\tau ^{2}}}}
1983:
2685:
2873:
1668:
2345:
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of a material. This is usually caused by the delay in molecular polarisation with respect to a changing electric field in a dielectric medium (e.g., inside capacitors or between two large
3832:
dielectric material with high permittivity as the intervening medium between the stored positive and negative charges. This material is often referred to in technical contexts as the
3265:
2861:
2669:
is the dielectric relaxation response of an ideal, noninteracting population of dipoles to an alternating external electric field. It is usually expressed in the complex permittivity
1006:, because they have no loosely bound, or free, electrons that may drift through the material, but instead they shift, only slightly, from their average equilibrium positions, causing
1649:{\displaystyle \mathbf {D} \ =\ \varepsilon _{0}\mathbf {E} +\mathbf {P} \ =\ \varepsilon _{0}\left(1+\chi _{e}\right)\mathbf {E} \ =\ \varepsilon _{0}\varepsilon _{r}\mathbf {E} .}
725:
4027:
In a 2004 research paper, U.S. ARL researchers explored how small concentrations of acceptor dopants can dramatically modify the properties of ferroelectric materials such as BST.
2455:
as well as dipolar polarisation. The ferroelectric transition, which is caused by the lining up of the orientations of permanent dipoles along a particular direction, is called an
2128:
1999:
1883:
4000:
of the polarisation response for a narrow range of frequencies, generally in the microwave band. It consists of a "puck" of ceramic that has a large dielectric constant and a low
2646:
refers to the relaxation response of a dielectric medium to an external, oscillating electric field. This relaxation is often described in terms of permittivity as a function of
1838:
3240:
2836:
2201:
4848:
Kong, L. B.; Li, S.; Zhang, T. S.; Zhai, J. W.; Boey, F. Y. C.; Ma, J. (2010-11-30). "Electrically tunable dielectric materials and strategies to improve their performances".
3215:
3174:
1367:
1333:
3133:
698:
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3602:
This shows the response of dielectrics to an applied DC field to behave according to a power law, which can be expressed as an integral over weighted exponential functions.
2157:
1912:
1511:
1489:
1249:
1227:
2650:, which can, for ideal systems, be described by the Debye equation. On the other hand, the distortion related to ionic and electronic polarisation shows behaviour of the
2525:
different electrical properties. As a result, some parts of the membrane of a neuron may be excitable (capable of generating action potentials), whereas others are not.
710:
1182:
1087:
storing capacity of the material (by means of polarisation). A common example of a dielectric is the electrically insulating material between the metallic plates of a
4978:
Developments in
Dielectric Materials and Electronic Devices: Proceedings of the 106th Annual Meeting of The American Ceramic Society, Indianapolis, Indiana, USA 2004
4326:
Dielectric, insulating material or a very poor conductor of electric current. When dielectrics are placed in an electric field, practically no current flows in them.
3915:
5330:
4885:
Giere, A.; Zheng, Y.; Maune, H.; Sazegar, M.; Paul, F.; Zhou, X.; Binder, J. R.; Muller, S.; Jakoby, R. (2008). "Tunable dielectrics for microwave applications".
5264:
3629:
causes polarisation and/or alignment of dipoles only parallel to the applied electric field. Contrary to the analogy with a paramagnetic material, no permanent
4171:
behave within an externally applied magnetic field. Ferroelectric materials often have very high dielectric constants, making them quite useful for capacitors.
2399:, remains constant in orientation polarisation; however, the direction of polarisation itself rotates. This rotation occurs on a timescale that depends on the
3801:
have a paraelectricâferroelectric transition just below ambient temperature, providing high tunability. Films suffer significant losses arising from defects.
4050:
Solid dielectrics are perhaps the most commonly used dielectrics in electrical engineering, and many solids are very good insulators. Some examples include
5232:
4935:
published 2003-11-06, issued 2004-10-18, assigned to IHP GmbH- Innovations for High
Performance Microelectronics/Institute Fur Innovative Mikroelektronik
3824:
Charge separation in a parallel-plate capacitor causes an internal electric field. A dielectric (orange) reduces the field and increases the capacitance.
1256:
961:
730:
5003:
3864:
2078:
The susceptibility (or equivalently the permittivity) is frequency dependent. The change of susceptibility with respect to frequency characterises the
4976:
3625:
Paraelectricity is the nominal behaviour of dielectrics when the dielectric permittivity tensor is proportional to the unit matrix, i.e., an applied
3135:
in the denominator due to an ongoing sign convention ambiguity whereby many sources represent the time dependence of the complex electric field with
740:
3633:
needs to exist in a paraelectric material. Removal of the fields results in the dipolar polarisation returning to zero. The mechanisms that causes
1091:. The polarisation of the dielectric by the applied electric field increases the capacitor's surface charge for the given electric field strength.
3333:
3270:
1060:
5212:
4004:. Such resonators are often used to provide a frequency reference in an oscillator circuit. An unshielded dielectric resonator can be used as a
5188:
565:
2306:
1663:
In general, a material cannot polarise instantaneously in response to an applied field. The more general formulation as a function of time is
5167:
5131:
4902:
4689:
4608:
4163:
dielectrics exhibit a spontaneous dipole moment, which can be reversed by an externally applied electric field. This behaviour is called the
580:
202:
5227:
3978:. This allows the capacitor to operate at higher voltages before the insulating dielectric ionises and begins to allow undesirable current.
3768:. The two have mismatched crystal spacing that produces strain within the strontium titanate layer that makes it less stable and tunable.
3757:) substitutes for room temperature devices. Other potential materials include microwave dielectrics and carbon nanotube (CNT) composites.
3684:
Paraelectricity has been explored as a possible refrigeration mechanism; polarising a paraelectric by applying an electric field under
1374:
460:
5257:
5013:
4986:
4646:
1921:
192:
130:
2494:
All cells in animal body tissues are electrically polarised â in other words, they maintain a voltage difference across the cell's
4719:
Debye, P. (1913), Ver. Deut. Phys. Gesell. 15, 777; reprinted 1954 in collected papers of Peter J.W. Debye. Interscience, New York
3844:
allows a greater stored charge at a given voltage. This can be seen by treating the case of a linear dielectric with permittivity
4309:
3577:
2538:
Dielectric dispersion is very important for the applications of dielectric materials and the analysis of polarisation systems.
375:
4291:
5113:
4095:
as a fluid dielectric and to assist in cooling. Dielectric fluids with higher dielectric constants, such as electrical grade
3591:
954:
720:
197:
68:
4948:
Cole, M. W.; Geyer, R. G. (2004). "Novel tunable acceptor doped BST thin films for high quality tunable microwave devices".
2395:
When an external electric field is applied, the distance between charges within each permanent dipole, which is related to
5194:
Dissemination of IT for the
Promotion of Materials Science (DoITPoMS) Teaching and Learning Package "Dielectric Materials"
4625:
3655:
Most dielectric materials are paraelectrics. A specific example of a paraelectric material of high dielectric constant is
735:
440:
4148:, or (equivalently) change physical shape if an external voltage is applied across the material. This property is called
3597:
111:
5250:
4005:
3641:(displacement of the electron cloud from the nucleus) and polarisation of molecules or combinations of ions or defects.
3585:
2349:
When both the type of electric field and the type of material have been defined, one then chooses the simplest function
1989:
600:
590:
575:
340:
207:
2164:
640:
330:
83:
893:
768:
665:
64:
3605:
3569:
2761:{\displaystyle {\hat {\varepsilon }}(\omega )=\varepsilon _{\infty }+{\frac {\Delta \varepsilon }{1+i\omega \tau }},}
2658:
type. The character of the distortion process depends on the structure, composition, and surroundings of the sample.
560:
3068:
1788:{\displaystyle \mathbf {P} (t)=\varepsilon _{0}\int _{-\infty }^{t}\chi _{e}\left(t-t'\right)\mathbf {E} (t')\,dt'.}
1431:
4296:
4257:
4192:
393:
2513:
In neurons, the types of ion channels in the membrane usually vary across different parts of the cell, giving the
90:
57:
3724:
2362:
2299:
gives rise to the behaviour of the dielectric, which, for a given material, can be characterised by the function
2247:
When the electric field is removed, the atom returns to its original state. The time required to do so is called
947:
908:
435:
425:
365:
360:
300:
4242:
4017:
2237:
878:
758:
445:
2563:
The ionic polarisation and molecular distortion polarisation can no longer track the electric field past the
5197:
5159:
4268:
4212:
4168:
4127:
4119:
2233:
1155:
1145:
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285:
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97:
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4222:
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that correctly predicts the phenomena of interest. Examples of phenomena that can be so modelled include:
705:
475:
250:
4341:
1804:
4237:
4197:
3820:
2270:
2170:
2085:
Moreover, the fact that the polarisation can only depend on the electric field at previous times (i.e.,
1467:
1072:
803:
490:
480:
430:
420:
167:
143:
79:
5309:
5002:
Nair, K. M.; Bhalla, Amar S.; Hirano, S.-I.; Suvorov, D.; Schwartz, Robert W.; Zhu, Wei (2012-04-11).
3179:
3138:
1345:
1311:
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5123:
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4798:
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4734:
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4227:
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1915:
1185:
1133:
1011:
1003:
928:
828:
793:
545:
410:
310:
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230:
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2841:
335:
4491:"Malignant cell characterisation via mathematical analysis of bio impedance and optical properties"
4232:
4207:
4067:
4044:
3220:
2816:
2601:
2542:
2377:
2133:
2079:
1993:
1888:
1336:
1038:
888:
868:
863:
670:
655:
540:
510:
405:
31:
3677:, and above this temperature it transforms into a disordered paraelectric phase. Similarly, other
2428:
Ionic polarisation is polarisation caused by relative displacements between positive and negative
1494:
1472:
1232:
1210:
5092:
4908:
4830:
4748:
Kuhn, U.; LĂŒty, F. (1965). "Paraelectric heating and cooling with OHâdipoles in alkali halides".
4581:
4526:
4378:
4078:
4071:
4001:
3708:
3656:
2499:
1192:
of the material and thus influences many other phenomena in that medium, from the capacitance of
763:
503:
305:
265:
3648:
phases where electric dipoles are unaligned and thus have the potential to align in an external
3610:
This is used when the dielectric loss is approximately constant for a wide range of frequencies.
4546:"Biodielectric phenomenon for actively differentiating malignant and normal cells: An overview"
3764:
produced a dielectric capable of operating at up to 125 GHz. The material was created via
1160:
5163:
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4604:
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2632:
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surfaces). Dielectric relaxation in changing electric fields could be considered analogous to
2484:
2069:{\displaystyle \mathbf {P} (\omega )=\varepsilon _{0}\chi _{e}(\omega )\mathbf {E} (\omega ).}
1129:
823:
4658:
5294:
5084:
5047:
4890:
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4857:
4814:
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4765:
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4502:
4461:
4453:
4404:
4396:
4262:
4164:
4149:
4145:
4104:
3620:
2552:
The dipolar polarisation can no longer follow the oscillations of the electric field in the
2357:
2284:
975:
923:
838:
798:
788:
675:
630:
613:
530:
465:
235:
159:
4110:
Because dielectrics resist the flow of electricity, the surface of a dielectric may retain
3704:
are insulators whose ability to store electrical charge changes when a voltage is applied.
5289:
5193:
5073:
Lyon, David (2013). "Gap size dependence of the dielectric strength in nano vacuum gaps".
4114:
excess electrical charges. This may occur accidentally when the dielectric is rubbed (the
3761:
3663:
3630:
2810:
2503:
2495:
2488:
2480:
2437:
1115:
1101:
1042:
1026:
999:
858:
783:
778:
645:
520:
485:
380:
345:
245:
4623:
James, Frank A.J.L., editor. The
Correspondence of Michael Faraday, Volume 3, 1841â1848,
3974:
Dielectric materials used for capacitors are also chosen such that they are resistant to
898:
5043:
4961:
4802:
4761:
4449:
4392:
104:
5149:
4466:
4433:
4409:
4366:
3649:
3626:
2613:
2522:
2389:
1197:
1084:
1068:
995:
991:
818:
813:
635:
525:
450:
400:
350:
323:
280:
255:
225:
218:
3688:
conditions raises the temperature, while removing the field lowers the temperature. A
2570:
The electronic polarisation loses its response in the ultraviolet region around 10 Hz.
1840:. The upper limit of this integral can be extended to infinity as well if one defines
1136:; therefore it stores and returns electrical energy as if it were an ideal capacitor.
1018:
molecules, those molecules not only become polarised, but also reorient so that their
5324:
4769:
4585:
4530:
4187:
4138:
4123:
3670:
3552:(1913). It is characteristic for dynamic polarisation with only one relaxation time.
2628:
2624:
2476:
2433:
2396:
2372:
2367:
2280:
1019:
1015:
933:
918:
903:
843:
555:
470:
455:
370:
355:
260:
4912:
3760:
In 2013, multi-sheet layers of strontium titanate interleaved with single layers of
2487:, energetically unfavourable transport of ions, and cell-to-cell communication (the
1801:
of the electric field at previous times with time-dependent susceptibility given by
1025:
The study of dielectric properties concerns storage and dissipation of electric and
4975:
Nair, K. M.; Guo, Ruyan; Bhalla, Amar S.; Hirano, S.-I.; Suvorov, D. (2012-04-11).
4834:
4313:
4247:
4182:
4100:
3841:
2507:
1189:
1149:
913:
808:
773:
715:
650:
535:
415:
290:
27:
Electrically insulating substance able to be polarised by an applied electric field
5096:
4861:
4561:
4506:
4144:
Some dielectrics can generate a potential difference when subjected to mechanical
570:
5183:
5153:
5117:
2471:
Ionic polarisation enables the production of energy-rich compounds in cells (the
5273:
4545:
4490:
4092:
4088:
3907:
3574:
This equation is used when the dielectric loss peak shows asymmetric broadening.
3549:
2621:
2574:
In the frequency region above ultraviolet, permittivity approaches the constant
2472:
1798:
1096:
1030:
833:
685:
515:
177:
46:
17:
4629:
4457:
4400:
3958:{\displaystyle c={\frac {\sigma _{\varepsilon }}{V}}={\frac {\varepsilon }{d}}}
3566:
This equation is used when the dielectric loss peak shows symmetric broadening.
2216:
5203:
5088:
4931:
4894:
4096:
3975:
3678:
2655:
2609:
550:
5059:
4569:
4514:
4350:... are not a narrow class of so-called insulators, but the broad expanse of
4887:
2008 17th IEEE International
Symposium on the Applications of Ferroelectrics
4051:
3997:
3815:
3689:
3685:
3386:{\displaystyle {\hat {\varepsilon }}(\omega )=\varepsilon '-i\varepsilon ''}
3323:{\displaystyle {\hat {\varepsilon }}(\omega )=\varepsilon '+i\varepsilon ''}
2651:
2647:
2553:
2404:
2220:
Electric field interaction with an atom under the classical dielectric model
2160:
1193:
1088:
1029:
in materials. Dielectrics are important for explaining various phenomena in
873:
848:
660:
585:
182:
35:
4826:
4577:
4522:
4475:
4418:
5141:
4043:
can also be a useful, nearly lossless dielectric even though its relative
1106:
5158:. Monographs on the Physics & Chemistry of Materials (2nd ed.).
4434:"Recovery of Alumina Nanocapacitors after High and Low Voltage Breakdown"
4305:
4252:
4134:
4082:
4063:
2617:
2564:
2514:
2416:
2409:
2263:
1188:
in response to an electric field. This, in turn, determines the electric
625:
620:
240:
4810:
2502:. This electrical polarisation results from a complex interplay between
2259:
Is the electric field constant, or does it vary with time? At what rate?
4870:
4641:
The
Institution of Electrical Engineers, London, United Kingdom, 1996.
4301:
4160:
4156:
4152:. Piezoelectric materials are another class of very useful dielectrics.
4085:
provide a dielectric barrier between the substrate and its environment.
4059:
3645:
2639:
2459:. The transition caused by ionic polarisations in crystals is called a
1342:
The susceptibility of a medium is related to its relative permittivity
595:
5242:
5051:
4818:
3548:
This relaxation model was introduced by and named after the physicist
4040:
3674:
2400:
2229:
1423:
1204:
1034:
680:
187:
4383:
2545:: a frequency-dependent response of a medium for wave propagation.
1992:
and write this relationship as a function of frequency. Due to the
1299:{\displaystyle \mathbf {P} =\varepsilon _{0}\chi _{e}\mathbf {E} ,}
4709:. London: Elsevier Publishing Companys. pp. 231â232, 348â349.
4055:
3829:
3819:
2557:
2388:
Dipolar polarisation is a polarisation that is either inherent to
2240:, a vector quantity shown in the figure as the blue arrow labeled
2215:
142:
3897:{\displaystyle \sigma _{\varepsilon }=\varepsilon {\frac {V}{d}}}
3582:
This equation considers both symmetric and asymmetric broadening.
1203:
It is defined as the constant of proportionality (which may be a
3638:
2627:). Relaxation in general is a delay or lag in the response of a
2518:
2262:
Does the response depend on the direction of the applied field (
5246:
4039:
Dielectric materials can be solids, liquids, or gases. (A high
2429:
2276:
Do any boundaries or interfaces have to be taken into account?
1978:{\displaystyle \chi _{e}(\Delta t)=\chi _{e}\delta (\Delta t)}
1126:
40:
4927:
Semiconductor capacitor with praseodymium oxide as dielectric
4265:â variation of dielectric strength of gas related to pressure
3971:
leads to greater charge stored and thus greater capacitance.
3396:
The dielectric loss is also represented by the loss tangent:
998:. When a dielectric material is placed in an electric field,
4432:
Belkin, A.; Bezryadin, A.; Hendren, L.; Hubler, A. (2017).
3723:) is used for devices operating at low temperatures, while
1079:
is generally used to indicate electrical obstruction while
5076:
IEEE Transactions on
Dielectrics and Electrical Insulation
3852:
between two conducting plates with uniform charge density
1132:
infinite electrical conductivity), thus exhibiting only a
4126:, or it can be potentially destructive as in the case of
2340:{\displaystyle \mathbf {M} =\mathbf {F} (\mathbf {E} ).}
1184:
of a dielectric material is a measure of how easily it
2541:
This is one instance of a general phenomenon known as
2167:
on the real and imaginary parts of the susceptibility
3918:
3867:
3828:
Commercially manufactured capacitors typically use a
3404:
3336:
3273:
3248:
3223:
3182:
3141:
3109:
3071:
2871:
2844:
2819:
2688:
2309:
2173:
2136:
2091:
2002:
1988:
It is more convenient in a linear system to take the
1924:
1891:
1846:
1807:
1671:
1521:
1497:
1475:
1434:
1377:
1348:
1314:
1259:
1235:
1213:
1163:
5005:
Ceramic
Materials and Multilayer Electronic Devices
4684:. London: Elsevier Academic Press. pp. 92â93.
3681:also exhibit paraelectricity at high temperatures.
3267:representing real and imaginary parts are given by
71:. Unsourced material may be challenged and removed.
3957:
3896:
3538:
3385:
3322:
3259:
3234:
3209:
3168:
3127:
3095:
3055:
2855:
2830:
2760:
2339:
2195:
2151:
2122:
2068:
1977:
1906:
1877:
1832:
1787:
1648:
1505:
1483:
1456:
1412:
1361:
1327:
1298:
1243:
1221:
1176:
1002:do not flow through the material as they do in an
4626:"Letter 1798, William Whewell to Faraday, p. 442"
4183:Classification of materials based on permittivity
3393:. The above equation uses the latter convention.
2777:is the permittivity at the high frequency limit,
1125:is a material with zero electrical conductivity (
1071:. The latter is expressed by a number called the
4367:"Dielectric study on mixtures of ionic liquids"
3996:(DRO) is an electronic component that exhibits
3967:From this, it can easily be seen that a larger
2863:of the complex dielectric permittivity yields:
2805:is the static, low frequency permittivity, and
1413:{\displaystyle \chi _{e}\ =\varepsilon _{r}-1.}
1229:to the induced dielectric polarisation density
3859:. In this case the charge density is given by
3096:{\displaystyle {\hat {\varepsilon }}(\omega )}
2415:When an external electric field is applied at
5258:
2813:of the medium. Separating into the real part
955:
8:
4286:
4284:
2291:The relationship between the electric field
4167:. These materials are analogous to the way
1914:. An instantaneous response corresponds to
5265:
5251:
5243:
3217:. In the former convention, the functions
962:
948:
166:
150:
4869:
4660:Microwave Engineering â R. S. Rao (Prof.)
4465:
4408:
4382:
3945:
3931:
3925:
3917:
3884:
3872:
3866:
3527:
3517:
3507:
3494:
3471:
3458:
3446:
3423:
3403:
3338:
3337:
3335:
3275:
3274:
3272:
3247:
3222:
3181:
3140:
3108:
3073:
3072:
3070:
3040:
3030:
3003:
2990:
2980:
2952:
2942:
2924:
2911:
2904:
2895:
2872:
2870:
2843:
2818:
2726:
2717:
2690:
2689:
2687:
2673:of a medium as a function of the field's
2326:
2318:
2310:
2308:
2178:
2172:
2135:
2096:
2090:
2049:
2034:
2024:
2003:
2001:
1996:, the integral becomes a simple product,
1954:
1929:
1923:
1890:
1851:
1845:
1812:
1806:
1770:
1751:
1721:
1711:
1703:
1693:
1672:
1670:
1638:
1632:
1622:
1604:
1593:
1572:
1554:
1546:
1540:
1522:
1520:
1498:
1496:
1476:
1474:
1439:
1433:
1398:
1382:
1376:
1353:
1347:
1319:
1313:
1288:
1282:
1272:
1260:
1258:
1236:
1234:
1214:
1212:
1168:
1162:
131:Learn how and when to remove this message
4365:Thoms, E.; Sippel, P.; et., al. (2017).
4133:Specially processed dielectrics, called
2408:the change of the electric field causes
2283:with respect to the field, or are there
4943:
4941:
4601:Biographical Encyclopedia of Scientists
4280:
3637:behaviour are distortion of individual
2600:is the momentary delay (or lag) in the
1491:is related to the polarisation density
711:Electromagnetism and special relativity
158:
5331:Electric and magnetic fields in matter
5189:Dielectric Sphere in an Electric Field
4091:is used extensively inside electrical
1067:typically means materials with a high
4343:Dielectric Materials and Applications
4016:From 2002 to 2004, the United States
2269:Is the response the same everywhere (
2123:{\displaystyle \chi _{e}(\Delta t)=0}
1878:{\displaystyle \chi _{e}(\Delta t)=0}
731:Maxwell equations in curved spacetime
7:
4783:
4781:
4779:
4550:Electromagnetic Biology and Medicine
4495:Electromagnetic Biology and Medicine
2567:or far-infrared region around 10 Hz,
69:adding citations to reliable sources
4137:(which should not be confused with
2548:When the frequency becomes higher:
2236:. A dipole is characterised by its
1833:{\displaystyle \chi _{e}(\Delta t)}
1337:electric permittivity of free space
3586:KohlrauschâWilliamsâWatts function
3508:
3472:
3004:
2925:
2896:
2729:
2718:
2196:{\displaystyle \chi _{e}(\omega )}
2137:
2105:
1966:
1938:
1892:
1860:
1821:
1707:
25:
4070:are the three most commonly used
3330:whereas in the latter convention
3065:Note that the above equation for
5202:
5184:Feynman's lecture on dielectrics
3210:{\displaystyle \exp(+i\omega t)}
3169:{\displaystyle \exp(-i\omega t)}
2327:
2319:
2311:
2228:This can be reduced to a simple
2050:
2004:
1752:
1673:
1639:
1605:
1555:
1547:
1523:
1499:
1477:
1362:{\displaystyle \varepsilon _{r}}
1328:{\displaystyle \varepsilon _{0}}
1289:
1261:
1237:
1215:
1114:) in response to a request from
45:
4707:Theory of Electric Polarisation
4544:Hossain, Shadeeb (2020-04-02).
4489:Hossain, Shadeeb (2020-12-27).
4118:). This can be useful, as in a
3994:dielectric resonator oscillator
3606:DjordjevicâSarkar approximation
3128:{\displaystyle 1-i\omega \tau }
2457:order-disorder phase transition
1797:That is, the polarisation is a
147:A polarised dielectric material
56:needs additional citations for
4682:Dielectric Phenomena in Solids
4031:in microwave tunable devices.
3592:stretched exponential function
3556:Variants of the Debye equation
3417:
3411:
3355:
3349:
3343:
3292:
3286:
3280:
3260:{\displaystyle \varepsilon ''}
3204:
3189:
3163:
3148:
3090:
3084:
3078:
3009:
2983:
2856:{\displaystyle \varepsilon ''}
2707:
2701:
2695:
2451:Ionic polarisation causes the
2331:
2323:
2190:
2184:
2111:
2102:
2060:
2054:
2046:
2040:
2014:
2008:
1972:
1963:
1944:
1935:
1866:
1857:
1827:
1818:
1767:
1756:
1683:
1677:
1457:{\displaystyle \chi _{e}\ =0.}
1:
4862:10.1016/j.pmatsci.2010.04.004
4850:Progress in Materials Science
4562:10.1080/15368378.2020.1737804
4507:10.1080/15368378.2020.1850471
4310:EncyclopĂŠdia Britannica, Inc.
3644:Paraelectricity can occur in
3235:{\displaystyle \varepsilon '}
2831:{\displaystyle \varepsilon '}
2152:{\displaystyle \Delta t<0}
1907:{\displaystyle \Delta t<0}
1207:) relating an electric field
736:Relativistic electromagnetism
4770:10.1016/0038-1098(65)90060-8
4024:for electronics components.
4006:dielectric resonator antenna
2251:time; an exponential decay.
2082:properties of the material.
1506:{\displaystyle \mathbf {P} }
1484:{\displaystyle \mathbf {D} }
1244:{\displaystyle \mathbf {P} }
1222:{\displaystyle \mathbf {E} }
4103:capacitors to help prevent
3578:HavriliakâNegami relaxation
2483:, the establishment of the
2461:displacive phase transition
5352:
5032:Journal of Applied Physics
4950:Revista Mexicana de Fisica
4750:Solid State Communications
4603:. CRC Press. p. 943.
4458:10.1038/s41598-017-01007-9
4401:10.1038/s41598-017-07982-3
4258:Rotational Brownian motion
4193:Clausius-Mossotti relation
4035:Some practical dielectrics
3985:
3813:
3618:
3103:is sometimes written with
2581:in every substance, where
2165:KramersâKronig constraints
1143:
461:LiĂ©nardâWiechert potential
29:
5280:
5155:Principles of Dielectrics
5119:Classical Electrodynamics
5089:10.1109/TDEI.2013.6571470
5008:. John Wiley & Sons.
4981:. John Wiley & Sons.
4895:10.1109/ISAF.2008.4693753
4705:Böttcher, C.J.F. (1952).
4107:and increase capacitance.
3725:barium strontium titanate
2363:Group velocity dispersion
2303:defined by the equation:
1177:{\displaystyle \chi _{e}}
726:Mathematical descriptions
436:Electromagnetic radiation
426:Electromagnetic induction
366:Magnetic vector potential
361:Magnetic scalar potential
4243:Linear response function
4018:Army Research Laboratory
3598:Curieâvon Schweidler law
1659:Dispersion and causality
1083:is used to indicate the
30:Not to be confused with
5233:EncyclopĂŠdia Britannica
5198:University of Cambridge
5160:Oxford University Press
4340:, in his seminal work,
4297:EncyclopĂŠdia Britannica
4269:Separator (electricity)
4213:Dielectric spectroscopy
4169:ferromagnetic materials
4128:electrostatic discharge
4120:Van de Graaff generator
2838:and the imaginary part
2234:superposition principle
2207:Dielectric polarisation
1156:electric susceptibility
1146:Electric susceptibility
1140:Electric susceptibility
1012:dielectric polarisation
1008:dielectric polarisation
276:Electrostatic induction
271:Electrostatic discharge
5236:(11th ed.). 1911.
5218:Encyclopedia Americana
4925:MĂŒssig, Hans-Joachim.
4680:Kao, Kwan Chi (2004).
4223:EIA Class 2 dielectric
4218:EIA Class 1 dielectric
3959:
3898:
3825:
3766:molecular beam epitaxy
3570:ColeâDavidson equation
3540:
3387:
3324:
3261:
3236:
3211:
3170:
3129:
3097:
3057:
2857:
2832:
2809:is the characteristic
2762:
2403:and surrounding local
2341:
2295:and the dipole moment
2221:
2197:
2153:
2124:
2070:
1979:
1908:
1879:
1834:
1789:
1650:
1507:
1485:
1458:
1414:
1363:
1329:
1300:
1245:
1223:
1178:
706:Electromagnetic tensor
148:
5207:Texts on Wikisource:
5150:Scaife, Brendan K. P.
5124:John Wiley & Sons
4932:U.S. patent 7,113,388
4735:John Wiley & Sons
4599:Daintith, J. (1994).
4198:Dielectric absorption
3960:
3899:
3823:
3590:Fourier transform of
3541:
3388:
3325:
3262:
3237:
3212:
3171:
3130:
3098:
3058:
2858:
2833:
2763:
2644:dielectric relaxation
2598:Dielectric relaxation
2593:Dielectric relaxation
2535:dielectric dispersion
2529:Dielectric dispersion
2342:
2219:
2198:
2154:
2125:
2071:
1980:
1909:
1880:
1835:
1790:
1651:
1508:
1486:
1468:electric displacement
1459:
1415:
1364:
1330:
1301:
1246:
1224:
1179:
1073:relative permittivity
1061:electrical conduction
699:Covariant formulation
491:Synchrotron radiation
431:Electromagnetic pulse
421:Electromagnetic field
146:
5300:antiferroelectricity
5152:(3 September 1998).
4338:Arthur R. von Hippel
4165:ferroelectric effect
4116:triboelectric effect
4099:, are often used in
3988:Dielectric resonator
3982:Dielectric resonator
3916:
3865:
3834:capacitor dielectric
3402:
3334:
3271:
3246:
3221:
3180:
3139:
3107:
3069:
2869:
2842:
2817:
2686:
2453:ferroelectric effect
2384:Dipolar polarisation
2307:
2171:
2159:), a consequence of
2134:
2089:
2000:
1922:
1916:Dirac delta function
1889:
1844:
1805:
1669:
1519:
1495:
1473:
1432:
1422:So in the case of a
1375:
1346:
1312:
1257:
1233:
1211:
1161:
1134:displacement current
1022:align to the field.
1004:electrical conductor
988:electrical insulator
741:Stressâenergy tensor
666:Reluctance (complex)
411:Displacement current
65:improve this article
5274:Polarization states
5116:(10 August 1998) .
5114:Jackson, John David
5044:2002JAP....92..475C
4962:2004RMxF...50..232C
4811:10.1038/nature12582
4803:2013Natur.502..532L
4762:1965SSCom...3...31K
4729:Chiang, Y. (1997).
4450:2017NatSR...7..932B
4393:2017NatSR...7.7463T
4208:Dielectric strength
4079:Industrial coatings
4072:gaseous dielectrics
4068:sulfur hexafluoride
4045:dielectric constant
3702:Tunable dielectrics
3176:whereas others use
2602:dielectric constant
2543:material dispersion
2467:In biological cells
2378:Harmonic generation
1994:convolution theorem
1716:
1039:solid-state physics
656:Magnetomotive force
541:Electromotive force
511:Alternating current
446:Jefimenko equations
406:Cyclotron radiation
32:dielectric constant
4002:dissipation factor
3955:
3894:
3826:
3709:strontium titanate
3657:strontium titanate
3562:ColeâCole equation
3536:
3383:
3320:
3257:
3232:
3207:
3166:
3125:
3093:
3053:
3051:
2853:
2828:
2758:
2500:membrane potential
2446:ionic polarisation
2424:Ionic polarisation
2337:
2222:
2212:Basic atomic model
2193:
2149:
2120:
2066:
1975:
1904:
1875:
1830:
1785:
1699:
1646:
1503:
1481:
1454:
1410:
1359:
1325:
1296:
1241:
1219:
1174:
1123:perfect dielectric
1053:Although the term
504:Electrical network
341:Gauss magnetic law
306:Static electricity
266:Electric potential
149:
5318:
5317:
5169:978-0-198-56557-4
5133:978-0-471-30932-1
5052:10.1063/1.1484231
4904:978-1-4244-2744-4
4797:(7472): 532â536.
4731:Physical Ceramics
4691:978-0-12-396561-5
4610:978-0-7503-0287-6
4228:High-Îș dielectric
4203:Dielectric losses
3953:
3940:
3910:per unit area by
3892:
3686:adiabatic process
3534:
3441:
3346:
3283:
3081:
3047:
2959:
2753:
2698:
2675:angular frequency
2633:Gibbs free energy
2556:region around 10
2485:resting potential
2273:of the material)?
2266:of the material)?
1990:Fourier transform
1617:
1611:
1567:
1561:
1535:
1529:
1447:
1390:
1130:perfect conductor
984:dielectric medium
972:
971:
671:Reluctance (real)
641:Gyratorâcapacitor
586:Resonant cavities
476:Maxwell equations
141:
140:
133:
115:
16:(Redirected from
5343:
5310:ferrielectricity
5295:ferroelectricity
5267:
5260:
5253:
5244:
5237:
5222:
5206:
5173:
5145:
5122:(3rd ed.).
5101:
5100:
5083:(4): 1467â1471.
5070:
5064:
5063:
5026:
5020:
5019:
4999:
4993:
4992:
4972:
4966:
4965:
4945:
4936:
4934:
4923:
4917:
4916:
4882:
4876:
4875:
4873:
4845:
4839:
4838:
4785:
4774:
4773:
4745:
4739:
4738:
4726:
4720:
4717:
4711:
4710:
4702:
4696:
4695:
4677:
4671:
4670:
4668:
4667:
4655:
4649:
4640:
4638:
4637:
4628:. Archived from
4621:
4615:
4614:
4596:
4590:
4589:
4541:
4535:
4534:
4486:
4480:
4479:
4469:
4429:
4423:
4422:
4412:
4386:
4362:
4356:
4335:
4329:
4328:
4323:
4321:
4316:on 27 April 2021
4288:
4233:Low-Îș dielectric
4150:piezoelectricity
4105:corona discharge
4047:is only unity.)
3964:
3962:
3961:
3956:
3954:
3946:
3941:
3936:
3935:
3926:
3903:
3901:
3900:
3895:
3893:
3885:
3877:
3876:
3800:
3799:
3798:
3790:
3789:
3781:
3780:
3771:Systems such as
3756:
3755:
3754:
3746:
3745:
3737:
3736:
3722:
3721:
3720:
3621:Ferroelectricity
3545:
3543:
3542:
3537:
3535:
3533:
3532:
3531:
3522:
3521:
3512:
3511:
3499:
3498:
3488:
3481:
3477:
3476:
3475:
3463:
3462:
3447:
3442:
3440:
3432:
3424:
3392:
3390:
3389:
3384:
3382:
3368:
3348:
3347:
3339:
3329:
3327:
3326:
3321:
3319:
3305:
3285:
3284:
3276:
3266:
3264:
3263:
3258:
3256:
3241:
3239:
3238:
3233:
3231:
3216:
3214:
3213:
3208:
3175:
3173:
3172:
3167:
3134:
3132:
3131:
3126:
3102:
3100:
3099:
3094:
3083:
3082:
3074:
3062:
3060:
3059:
3054:
3052:
3048:
3046:
3045:
3044:
3035:
3034:
3018:
3008:
3007:
2995:
2994:
2981:
2972:
2960:
2958:
2957:
2956:
2947:
2946:
2930:
2929:
2928:
2916:
2915:
2905:
2900:
2899:
2883:
2862:
2860:
2859:
2854:
2852:
2837:
2835:
2834:
2829:
2827:
2797:
2767:
2765:
2764:
2759:
2754:
2752:
2735:
2727:
2722:
2721:
2700:
2699:
2691:
2667:Debye relaxation
2662:Debye relaxation
2504:ion transporters
2397:chemical bonding
2358:Refractive index
2346:
2344:
2343:
2338:
2330:
2322:
2314:
2279:Is the response
2202:
2200:
2199:
2194:
2183:
2182:
2158:
2156:
2155:
2150:
2129:
2127:
2126:
2121:
2101:
2100:
2075:
2073:
2072:
2067:
2053:
2039:
2038:
2029:
2028:
2007:
1984:
1982:
1981:
1976:
1959:
1958:
1934:
1933:
1913:
1911:
1910:
1905:
1884:
1882:
1881:
1876:
1856:
1855:
1839:
1837:
1836:
1831:
1817:
1816:
1794:
1792:
1791:
1786:
1781:
1766:
1755:
1750:
1746:
1745:
1726:
1725:
1715:
1710:
1698:
1697:
1676:
1655:
1653:
1652:
1647:
1642:
1637:
1636:
1627:
1626:
1615:
1609:
1608:
1603:
1599:
1598:
1597:
1577:
1576:
1565:
1559:
1558:
1550:
1545:
1544:
1533:
1527:
1526:
1512:
1510:
1509:
1504:
1502:
1490:
1488:
1487:
1482:
1480:
1463:
1461:
1460:
1455:
1445:
1444:
1443:
1424:classical vacuum
1419:
1417:
1416:
1411:
1403:
1402:
1388:
1387:
1386:
1368:
1366:
1365:
1360:
1358:
1357:
1334:
1332:
1331:
1326:
1324:
1323:
1305:
1303:
1302:
1297:
1292:
1287:
1286:
1277:
1276:
1264:
1250:
1248:
1247:
1242:
1240:
1228:
1226:
1225:
1220:
1218:
1183:
1181:
1180:
1175:
1173:
1172:
1000:electric charges
976:electromagnetism
964:
957:
950:
631:Electric machine
614:Magnetic circuit
576:Parallel circuit
566:Network analysis
531:Electric current
466:London equations
311:Triboelectricity
301:Potential energy
170:
160:Electromagnetism
151:
136:
129:
125:
122:
116:
114:
73:
49:
41:
21:
18:Debye relaxation
5351:
5350:
5346:
5345:
5344:
5342:
5341:
5340:
5321:
5320:
5319:
5314:
5305:helielectricity
5290:paraelectricity
5276:
5271:
5225:
5210:
5180:
5170:
5148:
5134:
5112:
5109:
5107:Further reading
5104:
5072:
5071:
5067:
5028:
5027:
5023:
5016:
5001:
5000:
4996:
4989:
4974:
4973:
4969:
4947:
4946:
4939:
4930:
4924:
4920:
4905:
4884:
4883:
4879:
4847:
4846:
4842:
4787:
4786:
4777:
4747:
4746:
4742:
4728:
4727:
4723:
4718:
4714:
4704:
4703:
4699:
4692:
4679:
4678:
4674:
4665:
4663:
4657:
4656:
4652:
4635:
4633:
4624:
4622:
4618:
4611:
4598:
4597:
4593:
4543:
4542:
4538:
4488:
4487:
4483:
4431:
4430:
4426:
4364:
4363:
4359:
4336:
4332:
4319:
4317:
4290:
4289:
4282:
4278:
4273:
4178:
4037:
4014:
3990:
3984:
3927:
3914:
3913:
3868:
3863:
3862:
3857:
3818:
3812:
3807:
3797:
3794:
3793:
3792:
3788:
3785:
3784:
3783:
3779:
3776:
3775:
3774:
3772:
3762:strontium oxide
3753:
3750:
3749:
3748:
3744:
3741:
3740:
3739:
3735:
3732:
3731:
3730:
3728:
3719:
3716:
3715:
3714:
3712:
3699:
3667:
3652:and weaken it.
3631:electric dipole
3623:
3617:
3615:Paraelectricity
3558:
3523:
3513:
3503:
3490:
3489:
3467:
3454:
3453:
3449:
3448:
3433:
3425:
3400:
3399:
3375:
3361:
3332:
3331:
3312:
3298:
3269:
3268:
3249:
3244:
3243:
3224:
3219:
3218:
3178:
3177:
3137:
3136:
3105:
3104:
3067:
3066:
3050:
3049:
3036:
3026:
3019:
2999:
2986:
2982:
2973:
2965:
2962:
2961:
2948:
2938:
2931:
2920:
2907:
2906:
2891:
2884:
2876:
2867:
2866:
2845:
2840:
2839:
2820:
2815:
2814:
2811:relaxation time
2803:
2795:
2788:
2778:
2775:
2736:
2728:
2713:
2684:
2683:
2664:
2614:magnetic fields
2595:
2587:
2580:
2531:
2498:, known as the
2496:plasma membrane
2481:plasma membrane
2469:
2426:
2390:polar molecules
2386:
2305:
2304:
2214:
2209:
2174:
2169:
2168:
2132:
2131:
2092:
2087:
2086:
2030:
2020:
1998:
1997:
1950:
1925:
1920:
1919:
1918:susceptibility
1887:
1886:
1847:
1842:
1841:
1808:
1803:
1802:
1774:
1759:
1738:
1731:
1727:
1717:
1689:
1667:
1666:
1661:
1628:
1618:
1589:
1582:
1578:
1568:
1536:
1517:
1516:
1493:
1492:
1471:
1470:
1435:
1430:
1429:
1394:
1378:
1373:
1372:
1349:
1344:
1343:
1315:
1310:
1309:
1278:
1268:
1255:
1254:
1231:
1230:
1209:
1208:
1164:
1159:
1158:
1152:
1144:Main articles:
1142:
1116:Michael Faraday
1102:William Whewell
1051:
1043:cell biophysics
1027:magnetic energy
968:
939:
938:
754:
746:
745:
701:
691:
690:
646:Induction motor
616:
606:
605:
521:Current density
506:
496:
495:
486:Poynting vector
396:
394:Electrodynamics
386:
385:
381:Right-hand rule
346:Magnetic dipole
336:BiotâSavart law
326:
316:
315:
251:Electric dipole
246:Electric charge
221:
137:
126:
120:
117:
74:
72:
62:
50:
39:
28:
23:
22:
15:
12:
11:
5:
5349:
5347:
5339:
5338:
5333:
5323:
5322:
5316:
5315:
5313:
5312:
5307:
5302:
5297:
5292:
5287:
5281:
5278:
5277:
5272:
5270:
5269:
5262:
5255:
5247:
5241:
5240:
5239:
5238:
5223:
5200:
5191:
5186:
5179:
5178:External links
5176:
5175:
5174:
5168:
5146:
5132:
5108:
5105:
5103:
5102:
5065:
5038:(1): 475â483.
5021:
5014:
4994:
4987:
4967:
4937:
4918:
4903:
4877:
4856:(8): 840â893.
4840:
4775:
4740:
4721:
4712:
4697:
4690:
4672:
4650:
4616:
4609:
4591:
4536:
4481:
4424:
4357:
4330:
4312:Archived from
4279:
4277:
4274:
4272:
4271:
4266:
4260:
4255:
4250:
4245:
4240:
4235:
4230:
4225:
4220:
4215:
4210:
4205:
4200:
4195:
4190:
4185:
4179:
4177:
4174:
4173:
4172:
4153:
4142:
4139:ferroelectrics
4131:
4108:
4086:
4036:
4033:
4013:
4012:BST thin films
4010:
3986:Main article:
3983:
3980:
3952:
3949:
3944:
3939:
3934:
3930:
3924:
3921:
3891:
3888:
3883:
3880:
3875:
3871:
3855:
3848:and thickness
3814:Main article:
3811:
3808:
3806:
3803:
3795:
3786:
3777:
3751:
3742:
3733:
3717:
3698:
3695:
3665:
3650:electric field
3627:electric field
3616:
3613:
3612:
3611:
3608:
3603:
3600:
3595:
3588:
3583:
3580:
3575:
3572:
3567:
3564:
3557:
3554:
3530:
3526:
3520:
3516:
3510:
3506:
3502:
3497:
3493:
3487:
3484:
3480:
3474:
3470:
3466:
3461:
3457:
3452:
3445:
3439:
3436:
3431:
3428:
3422:
3419:
3416:
3413:
3410:
3407:
3381:
3378:
3374:
3371:
3367:
3364:
3360:
3357:
3354:
3351:
3345:
3342:
3318:
3315:
3311:
3308:
3304:
3301:
3297:
3294:
3291:
3288:
3282:
3279:
3255:
3252:
3230:
3227:
3206:
3203:
3200:
3197:
3194:
3191:
3188:
3185:
3165:
3162:
3159:
3156:
3153:
3150:
3147:
3144:
3124:
3121:
3118:
3115:
3112:
3092:
3089:
3086:
3080:
3077:
3043:
3039:
3033:
3029:
3025:
3022:
3017:
3014:
3011:
3006:
3002:
2998:
2993:
2989:
2985:
2979:
2976:
2974:
2971:
2968:
2964:
2963:
2955:
2951:
2945:
2941:
2937:
2934:
2927:
2923:
2919:
2914:
2910:
2903:
2898:
2894:
2890:
2887:
2885:
2882:
2879:
2875:
2874:
2851:
2848:
2826:
2823:
2801:
2793:
2786:
2773:
2757:
2751:
2748:
2745:
2742:
2739:
2734:
2731:
2725:
2720:
2716:
2712:
2709:
2706:
2703:
2697:
2694:
2663:
2660:
2594:
2591:
2585:
2578:
2572:
2571:
2568:
2561:
2530:
2527:
2479:) and, at the
2468:
2465:
2436:(for example,
2434:ionic crystals
2425:
2422:
2385:
2382:
2381:
2380:
2375:
2370:
2365:
2360:
2336:
2333:
2329:
2325:
2321:
2317:
2313:
2289:
2288:
2285:nonlinearities
2277:
2274:
2267:
2260:
2213:
2210:
2208:
2205:
2192:
2189:
2186:
2181:
2177:
2148:
2145:
2142:
2139:
2119:
2116:
2113:
2110:
2107:
2104:
2099:
2095:
2065:
2062:
2059:
2056:
2052:
2048:
2045:
2042:
2037:
2033:
2027:
2023:
2019:
2016:
2013:
2010:
2006:
1974:
1971:
1968:
1965:
1962:
1957:
1953:
1949:
1946:
1943:
1940:
1937:
1932:
1928:
1903:
1900:
1897:
1894:
1874:
1871:
1868:
1865:
1862:
1859:
1854:
1850:
1829:
1826:
1823:
1820:
1815:
1811:
1784:
1780:
1777:
1773:
1769:
1765:
1762:
1758:
1754:
1749:
1744:
1741:
1737:
1734:
1730:
1724:
1720:
1714:
1709:
1706:
1702:
1696:
1692:
1688:
1685:
1682:
1679:
1675:
1660:
1657:
1645:
1641:
1635:
1631:
1625:
1621:
1614:
1607:
1602:
1596:
1592:
1588:
1585:
1581:
1575:
1571:
1564:
1557:
1553:
1549:
1543:
1539:
1532:
1525:
1501:
1479:
1453:
1450:
1442:
1438:
1409:
1406:
1401:
1397:
1393:
1385:
1381:
1356:
1352:
1322:
1318:
1295:
1291:
1285:
1281:
1275:
1271:
1267:
1263:
1239:
1217:
1198:speed of light
1171:
1167:
1141:
1138:
1100:was coined by
1069:polarisability
1050:
1047:
996:electric field
994:by an applied
970:
969:
967:
966:
959:
952:
944:
941:
940:
937:
936:
931:
926:
921:
916:
911:
906:
901:
896:
891:
886:
881:
876:
871:
866:
861:
856:
851:
846:
841:
836:
831:
826:
821:
816:
811:
806:
801:
796:
791:
786:
781:
776:
771:
766:
761:
755:
752:
751:
748:
747:
744:
743:
738:
733:
728:
723:
721:Four-potential
718:
713:
708:
702:
697:
696:
693:
692:
689:
688:
683:
678:
673:
668:
663:
658:
653:
648:
643:
638:
636:Electric motor
633:
628:
623:
617:
612:
611:
608:
607:
604:
603:
598:
593:
591:Series circuit
588:
583:
578:
573:
568:
563:
561:Kirchhoff laws
558:
553:
548:
543:
538:
533:
528:
526:Direct current
523:
518:
513:
507:
502:
501:
498:
497:
494:
493:
488:
483:
481:Maxwell tensor
478:
473:
468:
463:
458:
453:
451:Larmor formula
448:
443:
438:
433:
428:
423:
418:
413:
408:
403:
401:Bremsstrahlung
397:
392:
391:
388:
387:
384:
383:
378:
373:
368:
363:
358:
353:
351:Magnetic field
348:
343:
338:
333:
327:
324:Magnetostatics
322:
321:
318:
317:
314:
313:
308:
303:
298:
293:
288:
283:
278:
273:
268:
263:
258:
256:Electric field
253:
248:
243:
238:
233:
228:
226:Charge density
222:
219:Electrostatics
217:
216:
213:
212:
211:
210:
205:
200:
195:
190:
185:
180:
172:
171:
163:
162:
156:
155:
154:Articles about
139:
138:
53:
51:
44:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
5348:
5337:
5334:
5332:
5329:
5328:
5326:
5311:
5308:
5306:
5303:
5301:
5298:
5296:
5293:
5291:
5288:
5286:
5283:
5282:
5279:
5275:
5268:
5263:
5261:
5256:
5254:
5249:
5248:
5245:
5235:
5234:
5229:
5224:
5220:
5219:
5214:
5209:
5208:
5205:
5201:
5199:
5195:
5192:
5190:
5187:
5185:
5182:
5181:
5177:
5171:
5165:
5161:
5157:
5156:
5151:
5147:
5143:
5139:
5135:
5129:
5125:
5121:
5120:
5115:
5111:
5110:
5106:
5098:
5094:
5090:
5086:
5082:
5078:
5077:
5069:
5066:
5061:
5057:
5053:
5049:
5045:
5041:
5037:
5033:
5025:
5022:
5017:
5015:9781118406762
5011:
5007:
5006:
4998:
4995:
4990:
4988:9781118408193
4984:
4980:
4979:
4971:
4968:
4963:
4959:
4955:
4951:
4944:
4942:
4938:
4933:
4928:
4922:
4919:
4914:
4910:
4906:
4900:
4896:
4892:
4889:. p. 1.
4888:
4881:
4878:
4872:
4867:
4863:
4859:
4855:
4851:
4844:
4841:
4836:
4832:
4828:
4824:
4820:
4816:
4812:
4808:
4804:
4800:
4796:
4792:
4784:
4782:
4780:
4776:
4771:
4767:
4763:
4759:
4755:
4751:
4744:
4741:
4736:
4732:
4725:
4722:
4716:
4713:
4708:
4701:
4698:
4693:
4687:
4683:
4676:
4673:
4662:
4661:
4654:
4651:
4648:
4647:0-86341-250-5
4644:
4632:on 2016-12-23
4631:
4627:
4620:
4617:
4612:
4606:
4602:
4595:
4592:
4587:
4583:
4579:
4575:
4571:
4567:
4563:
4559:
4555:
4551:
4547:
4540:
4537:
4532:
4528:
4524:
4520:
4516:
4512:
4508:
4504:
4500:
4496:
4492:
4485:
4482:
4477:
4473:
4468:
4463:
4459:
4455:
4451:
4447:
4443:
4439:
4435:
4428:
4425:
4420:
4416:
4411:
4406:
4402:
4398:
4394:
4390:
4385:
4380:
4376:
4372:
4368:
4361:
4358:
4353:
4349:
4345:
4344:
4339:
4334:
4331:
4327:
4315:
4311:
4307:
4303:
4299:
4298:
4293:
4287:
4285:
4281:
4275:
4270:
4267:
4264:
4263:Paschen's law
4261:
4259:
4256:
4254:
4251:
4249:
4246:
4244:
4241:
4239:
4236:
4234:
4231:
4229:
4226:
4224:
4221:
4219:
4216:
4214:
4211:
4209:
4206:
4204:
4201:
4199:
4196:
4194:
4191:
4189:
4188:Paramagnetism
4186:
4184:
4181:
4180:
4175:
4170:
4166:
4162:
4158:
4154:
4151:
4147:
4143:
4140:
4136:
4132:
4129:
4125:
4124:electrophorus
4121:
4117:
4113:
4109:
4106:
4102:
4098:
4094:
4090:
4087:
4084:
4080:
4077:
4076:
4075:
4073:
4069:
4065:
4061:
4057:
4053:
4048:
4046:
4042:
4034:
4032:
4028:
4025:
4021:
4019:
4011:
4009:
4007:
4003:
3999:
3995:
3989:
3981:
3979:
3977:
3972:
3970:
3965:
3950:
3947:
3942:
3937:
3932:
3928:
3922:
3919:
3911:
3909:
3904:
3889:
3886:
3881:
3878:
3873:
3869:
3860:
3858:
3851:
3847:
3843:
3837:
3835:
3831:
3822:
3817:
3809:
3804:
3802:
3769:
3767:
3763:
3758:
3726:
3710:
3705:
3703:
3696:
3694:
3691:
3687:
3682:
3680:
3676:
3672:
3671:ferroelectric
3668:
3660:
3658:
3653:
3651:
3647:
3642:
3640:
3636:
3632:
3628:
3622:
3614:
3609:
3607:
3604:
3601:
3599:
3596:
3593:
3589:
3587:
3584:
3581:
3579:
3576:
3573:
3571:
3568:
3565:
3563:
3560:
3559:
3555:
3553:
3551:
3546:
3528:
3524:
3518:
3514:
3504:
3500:
3495:
3491:
3485:
3482:
3478:
3468:
3464:
3459:
3455:
3450:
3443:
3437:
3434:
3429:
3426:
3420:
3414:
3408:
3405:
3397:
3394:
3379:
3376:
3372:
3369:
3365:
3362:
3358:
3352:
3340:
3316:
3313:
3309:
3306:
3302:
3299:
3295:
3289:
3277:
3253:
3250:
3228:
3225:
3201:
3198:
3195:
3192:
3186:
3183:
3160:
3157:
3154:
3151:
3145:
3142:
3122:
3119:
3116:
3113:
3110:
3087:
3075:
3063:
3041:
3037:
3031:
3027:
3023:
3020:
3015:
3012:
3000:
2996:
2991:
2987:
2977:
2975:
2969:
2966:
2953:
2949:
2943:
2939:
2935:
2932:
2921:
2917:
2912:
2908:
2901:
2892:
2888:
2886:
2880:
2877:
2864:
2849:
2846:
2824:
2821:
2812:
2808:
2804:
2796:
2789:
2782:
2776:
2768:
2755:
2749:
2746:
2743:
2740:
2737:
2732:
2723:
2714:
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2672:
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2630:
2629:linear system
2626:
2623:
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2607:
2603:
2599:
2592:
2590:
2584:
2577:
2569:
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2526:
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2509:
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2497:
2492:
2490:
2489:Na+/K+-ATPase
2486:
2482:
2478:
2474:
2466:
2464:
2462:
2458:
2454:
2449:
2447:
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2439:
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2368:Birefringence
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2356:
2355:
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2347:
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2238:dipole moment
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1010:. Because of
1009:
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700:
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582:
579:
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574:
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569:
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562:
559:
557:
556:Joule heating
554:
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539:
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471:Lorentz force
469:
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464:
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402:
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390:
389:
382:
379:
377:
374:
372:
371:Magnetization
369:
367:
364:
362:
359:
357:
356:Magnetic flux
354:
352:
349:
347:
344:
342:
339:
337:
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312:
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294:
292:
289:
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284:
282:
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269:
267:
264:
262:
261:Electric flux
259:
257:
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252:
249:
247:
244:
242:
239:
237:
234:
232:
229:
227:
224:
223:
220:
215:
214:
209:
206:
204:
201:
199:
198:Computational
196:
194:
191:
189:
186:
184:
181:
179:
176:
175:
174:
173:
169:
165:
164:
161:
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153:
152:
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135:
132:
124:
121:December 2022
113:
110:
106:
103:
99:
96:
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89:
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82: â
81:
77:
76:Find sources:
70:
66:
60:
59:
54:This article
52:
48:
43:
42:
37:
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5284:
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5216:
5154:
5118:
5080:
5074:
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4977:
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4886:
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4849:
4843:
4794:
4790:
4753:
4749:
4743:
4733:. New York:
4730:
4724:
4715:
4706:
4700:
4681:
4675:
4664:. Retrieved
4659:
4653:
4634:. Retrieved
4630:the original
4619:
4600:
4594:
4556:(2): 89â96.
4553:
4549:
4539:
4501:(1): 65â83.
4498:
4494:
4484:
4441:
4437:
4427:
4374:
4370:
4360:
4351:
4347:
4342:
4333:
4325:
4318:. Retrieved
4314:the original
4295:
4292:"Dielectric"
4248:Metamaterial
4111:
4101:high voltage
4093:transformers
4049:
4038:
4029:
4026:
4022:
4015:
3993:
3991:
3973:
3968:
3966:
3912:
3905:
3861:
3853:
3849:
3845:
3842:permittivity
3838:
3833:
3827:
3805:Applications
3770:
3759:
3706:
3701:
3700:
3683:
3661:
3654:
3643:
3635:paraelectric
3634:
3624:
3547:
3398:
3395:
3064:
2865:
2806:
2799:
2791:
2784:
2780:
2771:
2769:
2682:
2677:
2670:
2666:
2665:
2643:
2637:
2612:in changing
2597:
2596:
2582:
2575:
2573:
2547:
2540:
2534:
2533:In physics,
2532:
2512:
2508:ion channels
2493:
2477:mitochondria
2470:
2460:
2456:
2450:
2445:
2442:
2427:
2414:
2394:
2387:
2350:
2348:
2300:
2296:
2292:
2290:
2253:
2246:
2241:
2227:
2225:the figure.
2223:
2084:
2077:
1987:
1796:
1665:
1662:
1515:
1465:
1428:
1421:
1371:
1341:
1307:
1253:
1202:
1190:permittivity
1153:
1150:Permittivity
1122:
1120:
1111:
1105:
1095:
1093:
1080:
1076:
1064:
1059:implies low
1054:
1052:
1024:
1007:
990:that can be
983:
979:
973:
716:Four-current
651:Linear motor
536:Electrolysis
416:Eddy current
376:Permeability
296:Polarization
291:Permittivity
127:
118:
108:
101:
94:
87:
80:"Dielectric"
75:
63:Please help
58:verification
55:
5336:Dielectrics
4871:10356/93905
4377:(1): 7463.
4348:Dielectrics
4346:, stated: "
4320:20 November
4155:Some ionic
4089:Mineral oil
4058:, and most
3908:capacitance
3707:Generally,
3679:perovskites
3673:below 1430
3669:crystal is
3550:Peter Debye
2622:transformer
2473:proton pump
2271:homogeneity
1799:convolution
1049:Terminology
1031:electronics
686:Transformer
516:Capacitance
441:Faraday law
236:Coulomb law
178:Electricity
5325:Categories
5285:dielectric
5228:Dielectric
5213:Dielectric
4956:(3): 232.
4819:2117/21213
4666:2013-11-08
4636:2012-05-18
4444:(1): 932.
4384:1703.05625
4355:NY, 1954).
4276:References
4097:castor oil
3976:ionisation
3810:Capacitors
3697:Tunability
3619:See also:
2656:oscillator
2616:(e.g., in
2610:hysteresis
2606:conducting
2412:and heat.
2249:relaxation
2232:using the
2163:, imposes
2080:dispersion
1251:such that
1194:capacitors
1097:dielectric
1081:dielectric
1065:dielectric
980:dielectric
753:Scientists
601:Waveguides
581:Resistance
551:Inductance
331:AmpĂšre law
91:newspapers
5196:from the
5060:0021-8979
4756:(2): 31.
4586:212565141
4570:1536-8378
4531:229694503
4515:1536-8378
4352:nonmetals
4135:electrets
4052:porcelain
3998:resonance
3948:ε
3933:ε
3929:σ
3882:ε
3874:ε
3870:σ
3816:Capacitor
3690:heat pump
3525:τ
3515:ω
3509:∞
3505:ε
3492:ε
3486:τ
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3473:∞
3469:ε
3465:−
3456:ε
3435:ε
3427:ε
3415:δ
3409:
3377:ε
3370:−
3363:ε
3353:ω
3344:^
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3300:ε
3290:ω
3281:^
3278:ε
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3158:ω
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3088:ω
3079:^
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3028:ω
3016:τ
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3005:∞
3001:ε
2997:−
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2967:ε
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2926:∞
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2878:ε
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2733:ε
2730:Δ
2719:∞
2715:ε
2705:ω
2696:^
2693:ε
2652:resonance
2648:frequency
2554:microwave
2523:cell body
2515:dendrites
2405:viscosity
2188:ω
2176:χ
2161:causality
2138:Δ
2106:Δ
2094:χ
2058:ω
2044:ω
2032:χ
2022:ε
2012:ω
1967:Δ
1961:δ
1952:χ
1939:Δ
1927:χ
1893:Δ
1861:Δ
1849:χ
1822:Δ
1810:χ
1736:−
1719:χ
1708:∞
1705:−
1701:∫
1691:ε
1630:ε
1620:ε
1591:χ
1570:ε
1538:ε
1437:χ
1405:−
1396:ε
1380:χ
1351:ε
1317:ε
1280:χ
1270:ε
1186:polarises
1166:χ
1094:The term
1089:capacitor
1077:Insulator
1056:insulator
992:polarised
909:Steinmetz
839:Kirchhoff
824:Jefimenko
819:Hopkinson
804:Helmholtz
799:Heaviside
661:Permeance
546:Impedance
286:Insulator
281:Gauss law
231:Conductor
208:Phenomena
203:Textbooks
183:Magnetism
36:dialectic
4913:15835472
4827:24132232
4578:32138569
4523:33356700
4476:28428625
4438:Sci. Rep
4419:28785071
4371:Sci. Rep
4306:Illinois
4253:RC delay
4176:See also
4157:crystals
4112:stranded
4083:Parylene
4081:such as
4064:nitrogen
4060:plastics
3906:and the
3438:′
3430:″
3380:″
3366:′
3317:″
3303:′
3254:″
3229:′
2970:″
2881:′
2850:″
2825:′
2618:inductor
2565:infrared
2417:infrared
2410:friction
2264:isotropy
1779:′
1764:′
1743:′
1112:electric
986:) is an
934:Wiechert
889:Poynting
779:Einstein
626:DC motor
621:AC motor
456:Lenz law
241:Electret
5221:. 1920.
5040:Bibcode
4958:Bibcode
4835:4457286
4799:Bibcode
4758:Bibcode
4467:5430567
4446:Bibcode
4410:5547043
4389:Bibcode
4302:Chicago
4238:Leakage
4161:polymer
4062:. Air,
4008:(DRA).
3646:crystal
2640:physics
1335:is the
1196:to the
919:Thomson
894:Ritchie
884:Poisson
869:Neumann
864:Maxwell
859:Lorentz
854:Liénard
784:Faraday
769:Coulomb
596:Voltage
571:Ohm law
193:History
105:scholar
5166:
5142:535998
5140:
5130:
5097:709782
5095:
5058:
5012:
4985:
4911:
4901:
4833:
4825:
4791:Nature
4688:
4645:
4607:
4584:
4576:
4568:
4529:
4521:
4513:
4474:
4464:
4417:
4407:
4146:stress
4041:vacuum
2798:where
2770:where
2521:, and
2401:torque
2281:linear
2230:dipole
1616:
1610:
1566:
1560:
1534:
1528:
1446:
1389:
1308:where
1205:tensor
1104:(from
1085:energy
1035:optics
1016:bonded
904:Singer
899:Savart
879:Ărsted
844:Larmor
834:Kelvin
789:Fizeau
759:AmpĂšre
681:Stator
188:Optics
107:
100:
93:
86:
78:
5093:S2CID
4909:S2CID
4831:S2CID
4582:S2CID
4527:S2CID
4379:arXiv
4056:glass
3830:solid
3713:SrTiO
3664:LiNbO
2625:cores
929:Weber
924:Volta
914:Tesla
829:Joule
814:Hertz
809:Henry
794:Gauss
676:Rotor
112:JSTOR
98:books
5164:ISBN
5138:OCLC
5128:ISBN
5056:ISSN
5010:ISBN
4983:ISBN
4899:ISBN
4823:PMID
4686:ISBN
4643:ISBN
4605:ISBN
4574:PMID
4566:ISSN
4519:PMID
4511:ISSN
4472:PMID
4415:PMID
4322:2021
4159:and
4066:and
3662:The
3639:ions
3242:and
2519:axon
2506:and
2438:NaCl
2430:ions
2144:<
2130:for
1899:<
1885:for
1466:The
1154:The
1148:and
1041:and
982:(or
978:, a
849:Lenz
774:Davy
764:Biot
84:news
5230:".
5215:".
5085:doi
5048:doi
4891:doi
4866:hdl
4858:doi
4815:hdl
4807:doi
4795:502
4766:doi
4558:doi
4503:doi
4462:PMC
4454:doi
4405:PMC
4397:doi
4122:or
3791:TiO
3778:1âx
3747:TiO
3734:1âx
3406:tan
3184:exp
3143:exp
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2620:or
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1369:by
1127:cf.
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3293:)
3287:(
3205:)
3202:t
3196:i
3193:+
3190:(
3164:)
3161:t
3155:i
3149:(
3117:i
3111:1
3091:)
3085:(
3042:2
3032:2
3024:+
3021:1
3010:)
2992:s
2984:(
2978:=
2954:2
2944:2
2936:+
2933:1
2913:s
2902:+
2889:=
2807:Ï
2802:s
2800:Δ
2794:â
2792:Δ
2787:s
2785:Δ
2781:Δ
2779:Î
2774:â
2772:Δ
2756:,
2744:i
2741:+
2738:1
2724:+
2711:=
2708:)
2702:(
2678:Ï
2671:Δ
2586:0
2583:Δ
2579:0
2576:Δ
2560:,
2351:F
2335:.
2332:)
2328:E
2324:(
2320:F
2316:=
2312:M
2301:F
2297:M
2293:E
2287:?
2242:M
2191:)
2185:(
2180:e
2147:0
2141:t
2118:0
2115:=
2112:)
2109:t
2103:(
2098:e
2064:.
2061:)
2055:(
2051:E
2047:)
2041:(
2036:e
2026:0
2018:=
2015:)
2009:(
2005:P
1973:)
1970:t
1964:(
1956:e
1948:=
1945:)
1942:t
1936:(
1931:e
1902:0
1896:t
1873:0
1870:=
1867:)
1864:t
1858:(
1853:e
1828:)
1825:t
1819:(
1814:e
1783:.
1776:t
1772:d
1768:)
1761:t
1757:(
1753:E
1748:)
1740:t
1733:t
1729:(
1723:e
1713:t
1695:0
1687:=
1684:)
1681:t
1678:(
1674:P
1644:.
1640:E
1634:r
1624:0
1613:=
1606:E
1601:)
1595:e
1587:+
1584:1
1580:(
1574:0
1563:=
1556:P
1552:+
1548:E
1542:0
1531:=
1524:D
1500:P
1478:D
1449:=
1441:e
1400:r
1392:=
1384:e
1355:r
1321:0
1294:,
1290:E
1284:e
1274:0
1266:=
1262:P
1238:P
1216:E
1170:e
963:e
956:t
949:v
134:)
128:(
123:)
119:(
109:·
102:·
95:·
88:·
61:.
38:.
20:)
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