Electrodynamics Of The Dielectrics - Global Journals
Global Journal of Science Frontier Research: APhysics and Space ScienceVolume 18 Issue 6 Version 1.0 Year 2018Type: Double Blind Peer Reviewed International Research JournalPublisher: Global JournalsOnline ISSN: 2249-4626 & Print ISSN: 0975-5896Electrodynamics of the DielectricsBy F. F. MendeAbstract- In the scientific literature is in sufficient detail opened the role of the kinetic inductanceof charges in the conductors and the plasmo-like media, but it is not opened the role of thisparameter in the electrodynamics of dielectrics. This parameter in the electrodynamics ofdielectrics plays not less important role, than in the electrodynamics of conductors. In the articlethe electrodynamics of dielectrics taking into account the kinetic inductance of the charges,which form part of their atoms or molecules is examined. This most important question fell outfrom the field of the sight of scientists, and this article completes this deficiency.Keywords: dielectric, conductor, kinetic inductance of charges, dispersion of dielectric constant,plasmo-like medium.GJSFR-A Classification: FOR Code: 020302ElectrodynamicsoftheDielectricsStrictly as per the compliance and regulations of: 2018. F. F. Mende. This is a research/review paper, distributed under the terms of the Creative Commons AttributionNoncommercial 3.0 Unported License http://creativecommons.org/licenses/by-nc/3.0/), permitting all non commercial use,distribution, and reproduction in any medium, provided the original work is properly cited.
Electrodynamics of the DielectricsKeywords: dielectric, conductor, kinetic inductance ofcharges, dispersion of dielectric constant, plasmo-likemedium.IIntroductionI.n the scientific literature is in sufficient detail openedthe role of the kinetic inductance of charges in theconductors and the plasmo-like media [1-4], but it isnot opened the role of this parameter in theelectrodynamics of dielectrics. However, this parameterin this case plays not less important role, than in theelectrodynamics of the conductors [5-8]. This mostimportant question fell out from the field of the sight ofscientists and this article completes this deficiency.II. Electrodynamics Of The DielectricsLet us examine the simplest case, whenoscillating processes in atoms or molecules of dielectricobey the law of mechanical oscillator [5, 6]:e β2 E m ω rm m (1)Where rm - deviation of charges from theposition of equilibrium, β - coefficient of elasticity,which characterizes the elastic electrical binding forcesof charges in the atoms and the molecules. Introducingthe resonance frequency of the bound chargesω0 β m ,rot H j ε 0 E nev . t251That, finding the speed of charge carriers in thedielectric as the derivative of their displacement throughthe coordinatev rme E .22 tm(ω ωo ) tFrom relationship (2) we findrot H j ε0 E1 E . t L (ω 2 ω0 2 ) tkd(3)Let us note that the valueLkd m ( ne 2 )presents the kinetic inductance of the charges, enteringthe constitution of atom or molecules of dielectrics,when to consider charges free. Therefore (3) let usrewrite in the form: E1rot H1ε j 0 ε L (ω 2 ω 2 ) t .0 kd0 (4)Since the value1 ( ε 0 Lkd ) ω pd 2we obtain from (1)eErm .m(ω 2 ωo2 )Is evident that in relationship (2) as theparameter is present the natural vibration frequency, intowhich enters the mass of charge. This speaks, that theinertia properties of the being varied charges willinfluence oscillating processes in the atoms and themolecules.Since the general current density on mediumconsists of the bias current and conduction current(2)Author: Institute for Low Temperature Physics and Engineering of theNational Academy of Sciences of Ukraine.e-mail: fedormende@gmail.compresents the plasma frequency of charges in atoms andmolecules of dielectric, if we consider these chargesfree, then relationship (9.4) takes the form: ω 2 pd E.ε 0 1 2rot H j 2 tωω() 0 Yearthe role of the kinetic inductance of charges in the conductorsand the plasmo-like media, but it is not opened the role of thisparameter in the electrodynamics of dielectrics. Thisparameter in the electrodynamics of dielectrics plays not lessimportant role, than in the electrodynamics of conductors. Inthe article the electrodynamics of dielectrics taking intoaccount the kinetic inductance of the charges, which form partof their atoms or molecules is examined. This most importantquestion fell out from the field of the sight of scientists, andthis article completes this deficiency.(5) 2018 Global JournalsGlobal Journal of Science Frontier Research ( A ) Volume XVIII Issue VI Version IAbstract- In the scientific literature is in sufficient detail opened2018F. F. Mende
Electrodynamics of the DielectricsIt is possible to name the value ω 2 pd ε (ω ) ε 0 1 2 (ω ω 2 ) 0 (6)by the effective dielectric constant of dielectric and itdepends on frequency. But this mathematical parameteris not the physical dielectric constant of dielectric, buthas composite nature. It includes three those notdepending on the frequency of the value: electricalconstant, natural frequency of atoms or molecules andplasma frequency for the charge carriers, entering theircomposition, if we consider charges free[7].Let us examine two limiting cases:261 a) Ifω ω0 , then from (5) we obtainGlobal Journal of Science Frontier Research ( A ) Volume XVIII Issue VI Version IYear2018 b) The case is exponential ω pd 2 Eε 0 1 2 .rot H j ω0 t (7)In this case the coefficient, confronting thederivative, does not depend on frequency, and itpresents the static dielectric constant of dielectric. Aswe see, it depends on the natural frequency ofoscillation of atoms or molecules and on plasmafrequency. This result is intelligible. Frequency in thiscase proves to be such low that the charges manage tofollow the field and their inertia properties do notinfluence electrodynamic processes. In this case thebracketed expression in the right side of relationship (7)presents the static dielectric constant of dielectric. Aswe see, it depends on the natural frequency ofoscillation of atoms or molecules and on plasmafrequency. Hence immediately we have a prescriptionfor creating the dielectrics with the high dielectricconstant. In order to reach this, should be in theassigned volume of space packed a maximum quantityof molecules with maximally soft connections betweenthe charges inside molecule itself.ω ω0 . In this case ω pd 2 Erot Hε 0 1 2 j ω t dielectric became conductor (plasma) since. Theobtained relationship exactly coincides with theequation, which describes plasma.One cannot fail to note the circumstance that inthis case again nowhere was used this concept aspolarization vector, but examination is carried out by theway of finding the real currents in the dielectrics on thebasis of the equation of motion of charges in thesemedia. In this case in this mathematical model as theinitial electrical characteristics of medium are used thevalues, which do not depend on frequency.From relationship (5) is evident that in the caseof fulfilling the equality ω ω0 ,the amplitude offluctuations is equal to infinity. This indicates thepresence of resonance at this point. The infiniteamplitude of fluctuations occurs because of the fact thatthey were not considered losses in the resonancesystem; in this case its quality was equal to infinity. In acertain approximation it is possible to consider thatlower than the point indicated we deal concerning thedielectric, whose dielectric constant is equal to its staticvalue. Higher than this point we deal already actuallyconcerning the metal, whose density of current carriersis equal to the density of atoms or molecules in thedielectric.Now it is possible to examine the question ofwhy dielectric prism decomposes polychromatic lightinto monochromatic components or why rainbow isformed. For this the phase speed of electromagneticwaves on Wednesday must depend on frequency(frequency wave dispersion). Let us add to (5) the firstMaxwell equation [8]: ω 2 pd E H,ε 0 1 2rot E µ0; rot H 2 tωω() t 0 from where we immediately find the wave equation: ω pd 2 2E. E µ0ε 0 1 2 ω ω 2 t 20 2If one considers thatµ0ε 0 1 c 2 ,Where c - the speed of light then is easy to seethe presence in dielectrics of frequency dispersion. But 20181 Global Journalsthe dependence of phase speed on the frequency isconnected not with the dependence on it of physicaldielectric constant. In the formation of this dispersion itwill participate immediately three, which do not dependon the frequency, physical quantities: the self-resonantfrequency of atoms themselves or molecules, theplasma frequency of charges, if we consider it their free,and the dielectric constant of vacuum.Now let us show the weak places of thetraditional approach, based on the use of a concept ofpolarization vector.
Electrodynamics of the Dielectricsthat introduced thus, it depends on frequency.After introducing this induction into the secondMaxwell equation, we will obtain:rot Hε0 j capacity is equal to the static dielectric constant ofdielectric minus the capacity of the equal dielectricconstant of vacuum. In this case outline itself proves tobe that shunted by the capacity, equal to the specificdielectric constant of vacuum. For the proof of this let usexamine the sequential oscillatory circuit, when theinductance L and the capacity C are connected inseries.The connection between the current I C , whichflows through the capacity C , and the voltageU C ,applied to it, is determined by the relationships: E P . t tUC Orrot H j ε0 wherej E ne1 E ,m (ω 2 ω0 2 ) t tIC C2(9)- the summed current, which flows throughthe model. In expression (9) the first member of rightside presents bias current in the vacuum, and thesecond - current, connected with the presence of boundcharges in atoms or molecules of dielectric. In thisexpression again appeared the specific kineticinductance of the charges, which participate in theoscillating processLkd m ne 2 ,the determining inductance of bound charges, and (9)takes the form:ε0rot H j E11 E. 22 t L (ω ω0 ) tkdObtained expression exactly coincides withrelationship (3). Consequently, the eventual result ofexamination by both methods coincides, and there areno claims to the method from a mathematical point ofview. But from a physical point of view, and especially inthe part of the awarding to the parameter, introduced inaccordance with relationship (8) of the designation ofelectrical induction, are large claims, which wediscussed. These are the physical quantity of electricalinduction, but the certain composite mathematical1 I C dt ,CdU Cdt.(10)This connection will be written down for the inductance:IL dI L1. U L dt ; U L LdtLIf the current, which flows through the seriescircuit, changes according to the law I I 0 sin ωtthen a voltage drop across inductance and capacitythey are determined by the relationshipsU L ω LI 0 cos ωt ; U C 1I cos ωt .ωC 0And total stress applied to the outline is equal U ( ω L 1 ( ωC ) ) I0cos ωt .In this relationship the value, which stands in thebrackets, presents the reactance of sequential resonantcircuit, which depends on frequency. The stresses,generated on the capacity and the inductance, arelocated in the reversed phase, and, depending onfrequency, outline can have the inductive, the weathercapacitive reactance. At the point of resonance thesummary reactance of outline is equal to zero.It is obvious that the connection between thetotal voltage applied to the outline and the current,which flows through the outline, will be determined bythe relationship. 2018 Global Journals2018ne 21D ε 0E PE ε 0E 2E , (8)m (ω ω02 )whose inductance is the kinetic inductance Lkd , andYearIts dependence on the frequency is connectedwith the presence of mass in the charges, entering theconstitution of atom and molecules of dielectrics. Theinertness of charges is not allowed for this vector,following the electric field, to reach that value, which itwould have in the permanent fields. Since the electricalinduction is determined by the relationshipparameter. In the essence, physically substantiated isthe introduction to electrical induction in the dielectricsonly in the static electric fields.Let us show that the equivalent the schematic ofdielectric presents the sequential resonant circuit,271Global Journal of Science Frontier Research ( A ) Volume XVIII Issue VI Version Ine 21P 2E.m (ω ω02 )
Electrodynamics of the Dielectrics U 1I ω (ω L 1 (ωC ) ) tThe resonance frequencydetermined by the relationshipω0 1(11).ofoutlineisThe equivalent the schematic of the dielectric,located between the planes of long line is shown inFigure 1.d) Whenω ω0I LC ,therefore let us write down U I (1 ω 2 ω02 ) tYear2018C1 U ω 2 L t.(15)Taking into account that for the harmonic signal(12).Comparing this expression (12) with relationship281 (10) it is not difficult to see that the sequential resonantcircuit, which consists of the inductance L andcapacity C , it is possible to present to the capacity of inthe form dependent on the frequency:Global Journal of Science Frontier Research ( A ) Volume XVIII Issue VI Version I, we have(ω ) C (1 ω 2 ω0 2 )C U ω 2 U dt , twe obtain from (15):IL 1 U dt .L(13)The inductance is not lost with this idea, since itenters into the resonance frequency of the outline ω0 .Relationships (12)Consequently, valueand(11) are equivalent.C (ω ) is not the physicalcapacitance value of outline, being the certaincomposite mathematical parameter.Relationship (11) can be rewritten and differently:I U 1L (ω 2 ω0 2 ) t,and to consider thatC (ω ) 1.L (ω 2 ω0 2 )(14)Is certain, the parameter of, introduced inaccordance with relationships (13) and (14) no tocapacity refers.Let us examine relationship (12) for two limitingcases:c) Whenω ω0 , we haveI C U . tThis result is intelligible, since at the lowfrequencies the reactance of the inductance, connectedin series with the capacity, is considerably lower thanthe capacitive and it is possible not to consider it. 20181 Global JournalsFigure 1: а - equivalent the schematic of the section ofthe line, filled with dielectric, for the by dielectric, for thecase ω ω ;0
ω ω0 , when the properties of dielectric correspondto conductor; ω ω0 , when - to dielectric with thestatic dielectric constant ε ε 0 (1 ω pd 2 ω0 2 ) .Thus, the use of a term “dielectric constant ofdielectrics” in the context of its dependence on thefrequency is not completely correct. If the discussiondeals with the dielectric constant of dielectrics, withwhich the accumulation of potential energy isconnected, then correctly examine only staticpermeability, which is been the constant, which does notdepend on the frequency. Specifically, it enters into allrelationships, which characterize the electrodynamiccharacteristics of dielectrics.Application of such new approaches mostinterestingly precisely for the dielectrics. Then eachconnected pair of charges is a separate unitary unit withits individual characteristics, and its interaction with theelectromagnetic field (without taking into account theconnections between the pairs) is strictly individual.Certainly, in the dielectrics not all dipoles have differentcharacteristics, but there are different groups with similarcharacteristics, and each group of bound charges withthe identical characteristics will resound at its frequency.Moreover the intensity of absorption and in the excitedstate and emission, at this frequency will depend on arelative quantity of pairs of this type. Therefore it ispossible to introduce the appropriate partial coefficients.Furthermore, these processes will influence theanisotropy of the dielectric properties of moleculesthemselves, which have the specific electrical orientationin crystal lattice. By these circumstances is determinedthe variety of resonances and their intensities, which isobserved in the dielectric media. With the electricIII. ConclusionIn the scientific literature is in sufficient detailopened the role of the kinetic inductance of charges inthe conductors and the plasmo-like media, but it is notopened the role of this parameter in the electrodynamicsof dielectrics. This parameter in the electrodynamics ofdielectrics plays not less important role, than in theelectrodynamics of conductors. In the article theelectrodynamics of dielectrics taking into account thekinetic inductance of the charges, which form part oftheir atoms or molecules is examined. This mostimportant question fell out from the field of the sight ofscientists and this article completes this deficiency. Letus emphasize the important circumstance, which did notreceive thus far proper estimation. In all relationships forany material media (conductors and dielectrics) togetherwith the dielectric and magnetic constant figures thekinetic inductance of the charges, which indicates notless important role of this parameter.References Références Referencias1. Ф. Ф. Менде. Роль и место родинамике, Инженерная физика, 11, 2012.c. 10-19.2. F. F. Mende. Kinetic Induktance Charges and itsRole in Classical Electrodynamics. Global Journal,Volume 14, Issue 5, Version 1.0, Year 2014, pp.51-54.3. F. F. Mende, Transverse Plasma Resonans Mode inan Nonmagnetized Plasma and Its PracticalApplications, American Journal of Electrical andElectronic Engineering, Vol. 2, No. 5, (2014),152-1584. F. F. Mende . Transversal plasma resonance in anonmagnetized plasma and possibilities of practicalemployment of it. arXiv.org/abs/physics//0506081.5. F. F. Mende. Updated Electrodynamics. AASCITJournal of Physics, 2015, Vol.1, No. 3, p. 149-170.6. Ф. Ф. Менде. Существуют ли ошибки всовременной физике. Харьков: Константа, 2003. 2018 Global JournalsYear0в - the equivalent the schematic of the section of line forentire frequency band.In this case the reactance of capacity isconsiderably less than in inductance and chain hasinductive reactance.The carried out analysis speaks, that is inpractice very difficult to distinguish the behavior ofresonant circuits of the inductance or of the capacity.For understanding of true design of circuits it isnecessary to remove its amplitude and phase responsein the range of frequencies. In the case of resonantcircuit this dependence will have the typical resonancenature, when on both sides resonance the nature ofreactance is different. However, this does not mean thatreal circuit elements: capacity or inductance dependson frequency.In Figure 5аand 5бare shown two limiting cases.coupling between the separate groups of emitters thelines of absorption or emission can be converted intothe strips. Such individual approach to the types of theconnected pairs of charges is absent from the availabletheories.Let us emphasize the important circumstance,which did not receive thus far proper estimation. In allrelationships for any material media (conductors anddielectrics) together with the dielectric and magneticconstant figures the kinetic inductance of the charges,which indicates not less important role of this parameter.This is for the first time noted in a number of thementioned sources, including in the works [9, 10].129Global Journal of Science Frontier Research ( A ) Volume XVIII Issue VI Version Iб - the equivalent the schematic of the section of line forthe case of ω ω ;2018Electrodynamics of the Dielectrics
Electrodynamics of the DielectricsGlobal Journal of Science Frontier Research ( A ) Volume XVIII Issue VI Version IYear20187. F. F. Mende. On refinement of certain laws ofclassical electrodynamics, arXiv, physics/0402084.8. F. F. Mende. Conception of the scalar-vectorpotential in contemporary electrodynamics, arXiv.org/abs/physics/0506083.9. F. F. Mende. Concept of the dispersion of electricand magnetic inductivities and its physicalinterpretation. Global Journal of Researches inEngineering: A Mechanical and MechanicsEngineering, 2014, Vol. 14, No. 8, p.11-18.10. F. F. Mende. Concept of the Dispersion of Electricand Magnetic Inductivities and its PhysicalInterpretation. Global Journal of Researches inEngineering: A Mechanical and MechanicsEngineering, Volume 1, 4 Issue 8, Version 1.0, Year2014,pp. 11-18.130 20181 Global Journals
Electrodynamics of the Dielectrics . By F. F. Mende . Abstract- In the scientific literature is in sufficient detail opened the role of the kinetic inductance of charges in the conductors and the plasmo-like media, but it is not opened the role of this parameter in the electrodynamics of dielectrics. This parameter in the electrodynamics of
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