The Experts below are selected from a list of 297 Experts worldwide ranked by ideXlab platform
Wen Geyi - One of the best experts on this subject based on the ideXlab platform.
-
Stored electromagnetic field energies in general materials
Journal of the Optical Society of America B, 2019Co-Authors: Wen GeyiAbstract:The most general expressions for the stored field energies in the frequency domain, which are independent of any constitutive relations and microscopic models, are derived from the time-domain Poynting Theorem by using the complex frequency-domain approach. When the complex frequency-domain approach is applied to Maxwell’s equations, two energy balance relations are obtained simultaneously. The first relation is the well-known Poynting Theorem, while the second is new in its general form and contains the newly derived expressions for the stored field energies. In contrast to the well-established Poynting Theorem in frequency domain, the real part of the second energy balance relation gives an equation for the sum of stored electric and magnetic field energies and provides a natural definition for the stored energy around a radiator; the imaginary part involves an equation related to the difference between the dissipated electric and magnetic field energies. When media are lossless, the new expressions for the stored field energies are shown to agree with all previous studies; when media are lossy, they include new terms that were not shown in previous reports. These additional terms represent the dispersive part of the stored energies and reflect the influence of the losses on the stored energies.
-
Stored Electromagnetic Field Energies in General Materials
arXiv: Classical Physics, 2017Co-Authors: Wen GeyiAbstract:The most general expressions of the stored energies for time-harmonic electromagnetic fields are derived from the time-domain Poynting Theorem, and are valuable in characterizing the energy storage and transport properties of complex media. A new energy conservation law for the time-harmonic electromagnetic fields, which involves the derived general expressions of the stored energies, is introduced. In contrast to the well-established Poynting Theorem for time-harmonic fields, the real part of the new energy conservation law gives an equation for the sum of stored electric and magnetic field energies; the imaginary part involves an equation related to the difference between the dissipated electric and magnetic field energies. In a lossless isotropic and homogeneous medium, the new energy conservation law has a clear physical implication: the stored electromagnetic field energy of a radiating system enclosed by a surface is equal to the total field energy inside the surface subtracted by the field energy flowing out of the surface.
-
A method for the evaluation of small antenna Q
IEEE Transactions on Antennas and Propagation, 2003Co-Authors: Wen GeyiAbstract:A method is presented to calculate the quality factor (Q) of small antennas, which is based on the understanding that for a small antenna the total energy in Poynting Theorem can be easily separated into the stored energy and radiated energy by using the low frequency expansions. The Poynting Theorem in frequency domain provides an equation on the stored electric and magnetic energy while the Poynting Theorem in time domain can be used as another independent equation for the stored electric and magnetic energy. By solving these equations the stored electric and magnetic energy can be obtained, thus, making the Q calculation possible.
-
The Foster reactance Theorem for antennas and radiation Q
IEEE Transactions on Antennas and Propagation, 2000Co-Authors: Wen Geyi, P. JarmuszewskiAbstract:The calculation of antenna Q has been an interesting and a controversial topic for years. We first give a rigorous study of antenna Q by introducing a complete description of the complex power balance relation for an antenna system. Using the complex Poynting Theorem, we have shown that the antenna is essentially equivalent to a one port lossy network. The Foster reactance Theorem is usually stated for a lossless network. The main purpose of this paper is to determine whether the Foster reactance Theorem holds for antennas. By making use of a complex frequency domain version of the Poynting Theorem, we have shown that the Foster reactance Theorem is valid for an antenna. Finally, the Foster reactance Theorem for the antenna has been applied to demonstrate the widely held assumption Q/spl ap/1/B, provided Q/spl Gt/1, where B stands for the fractional bandwidth of an arbitrary antenna.
Tolga Yarman - One of the best experts on this subject based on the ideXlab platform.
-
Poynting Theorem, Relativistic Transformation of Total Energy–Momentum and Electromagnetic Energy–Momentum Tensor
Foundations of Physics, 2016Co-Authors: Alexander Kholmetskii, Oleg Missevitch, Tolga YarmanAbstract:We address to the Poynting Theorem for the bound (velocity-dependent) electromagnetic field, and demonstrate that the standard expressions for the electromagnetic energy flux and related field momentum, in general, come into the contradiction with the relativistic transformation of four-vector of total energy–momentum. We show that this inconsistency stems from the incorrect application of Poynting Theorem to a system of discrete point-like charges, when the terms of self-interaction in the product $${\varvec{j}} \cdot {\varvec{E}}$$ j · E (where the current density $${\varvec{j}}$$ j and bound electric field $${\varvec{E}}$$ E are generated by the same source charge) are exogenously omitted. Implementing a transformation of the Poynting Theorem to the form, where the terms of self-interaction are eliminated via Maxwell equations and vector calculus in a mathematically rigorous way (Kholmetskii et al., Phys Scr 83:055406, 2011 ), we obtained a novel expression for field momentum, which is fully compatible with the Lorentz transformation for total energy–momentum. The results obtained are discussed along with the novel expression for the electromagnetic energy–momentum tensor.
-
Poynting Theorem relativistic transformation of total energy momentum and electromagnetic energy momentum tensor
Foundations of Physics, 2016Co-Authors: Alexander Kholmetskii, Oleg Missevitch, Tolga YarmanAbstract:We address to the Poynting Theorem for the bound (velocity-dependent) electromagnetic field, and demonstrate that the standard expressions for the electromagnetic energy flux and related field momentum, in general, come into the contradiction with the relativistic transformation of four-vector of total energy–momentum. We show that this inconsistency stems from the incorrect application of Poynting Theorem to a system of discrete point-like charges, when the terms of self-interaction in the product \({\varvec{j}} \cdot {\varvec{E}}\) (where the current density \({\varvec{j}}\) and bound electric field \({\varvec{E}}\) are generated by the same source charge) are exogenously omitted. Implementing a transformation of the Poynting Theorem to the form, where the terms of self-interaction are eliminated via Maxwell equations and vector calculus in a mathematically rigorous way (Kholmetskii et al., Phys Scr 83:055406, 2011), we obtained a novel expression for field momentum, which is fully compatible with the Lorentz transformation for total energy–momentum. The results obtained are discussed along with the novel expression for the electromagnetic energy–momentum tensor.
-
Poynting Theorem, Relativistic Transformation of Total Energy–Momentum and Electromagnetic Energy–Momentum Tensor
Foundations of Physics, 2015Co-Authors: Alexander Kholmetskii, Oleg Missevitch, Tolga YarmanAbstract:We address to the Poynting Theorem for the bound (velocity-dependent) electromagnetic field, and demonstrate that the standard expressions for the electromagnetic energy flux and related field momentum, in general, come into the contradiction with the relativistic transformation of four-vector of total energy–momentum. We show that this inconsistency stems from the incorrect application of Poynting Theorem to a system of discrete point-like charges, when the terms of self-interaction in the product \({\varvec{j}} \cdot {\varvec{E}}\) (where the current density \({\varvec{j}}\) and bound electric field \({\varvec{E}}\) are generated by the same source charge) are exogenously omitted. Implementing a transformation of the Poynting Theorem to the form, where the terms of self-interaction are eliminated via Maxwell equations and vector calculus in a mathematically rigorous way (Kholmetskii et al., Phys Scr 83:055406, 2011), we obtained a novel expression for field momentum, which is fully compatible with the Lorentz transformation for total energy–momentum. The results obtained are discussed along with the novel expression for the electromagnetic energy–momentum tensor.
-
4 3 problem Poynting Theorem and electromagnetic energy momentum tensor
Canadian Journal of Physics, 2015Co-Authors: A L Kholmetskii, O Missevitch, Tolga YarmanAbstract:We show that the familiar 4/3 problem originates from the incorrect determination of the momentum of the electromagnetic field generated by an isolated charged particle, which results from an incor...
-
Continuity equations for bound electromagnetic field and the electromagnetic energy–momentum tensor
Physica Scripta, 2011Co-Authors: Alexander Kholmetskii, Oleg Missevitch, Tolga YarmanAbstract:We analyze the application of the Poynting Theorem to the bound (velocity-dependent) electromagnetic (EM) field and show that an often-used arbitrary elimination of the term of self-interaction in the product j·E (where j is the current density and E the electric field) represents, in general, an illegitimate operation, which leads to incorrect physical consequences. We propose correct ways of eliminating the terms of self-interaction from the Poynting Theorem to transform it into the form that is convenient for problems with bound EM field, which yield the continuity equations for the proper EM energy density, the interaction part of EM energy density and the total EM energy density of bound fields, respectively. These equations indicate the incompleteness of the common EM energy–momentum tensor, and in our analysis, we find a missed term in its structure, which makes its trace non-vanished. Some implications of these results are discussed, in particular, in view of the notion of EM mass of charged particles.
Shuang-ren Zhao - One of the best experts on this subject based on the ideXlab platform.
-
Electromagnetic Field, Photon and Quantum with Advanced wave and Time-reversal wave Based on Mutual Energy Principle and Self-energy Principle (Volume I)
2020Co-Authors: Shuang-ren ZhaoAbstract:Abstract Absorber theory of Wheeler and Feynman tell us that if the is put in a empty space it cannot shine. That means only with the source, the radiation cannot be produced. The radiation is phenomena of an action-at-a-distance. The action at a distance needs at least two object: the source and the sink or the emitter and the absorber. Only with one charge even it has the acceleration, it still cannot make any radiation. However this result is not reflect at the Maxwell's theory. According to the theory of Maxwell a single charge can produce the radiation without any help of the absorber. Hence Maxwell theory is different with the absorber theory of Wheeler and Feynman, this author thought that Wheeler and Feynman is correct, hence Maxwell's theory needs to be corrected. According to the absorber theory, Wheeler and Feynman and also their many follower all knew the problem of Maxwell equations, however they think even Maxwell equations have the problem, it still cannot replace the Maxwell equations. The axiom of the electromagnetic fields still need to use Maxwell equations. The author has introduced the mutual energy Theorem in early 1987, recently the author found that the mutual energy Theorem is similar to the Welch's reciprocity Theorem (1960), Rumsey's reciprocity Theorem (1963) and de Hoop's reciprocity Theorem (end 1987). In the time the mutual energy Theorem was introduced, the author didn't know the reciprocity Theorem of Welch and Rumsey. The only important difference the mutual energy Theorem with other 3 reciprocity Theorem is this formula is a reciprocity Theorem or an energy Theorem. As a reciprocity Theorem the two fields in the Theorem can be one real/physic and one virtual/mathematical. If the formula is an energy Theorem both field must real/physic. The problem is that the two field for these Theorems one is retarded field which is sent out from a transmitting antenna, another is advanced wave which is sent from the receiving antenna. Advanced wave can be accept easily for the reciprocity Theorem because it is only a virtual or mathematical field. If the same Theorem is an energy Theorem, the advanced wave must be accept. The author believe that the mutual energy Theorem is true a reciprocity Theorem but it is clear also an energy Theorem. Since one of the fields in the mutual energy Theorem is advanced wave, the advanced wave must be real. The author noticed the absorber theory of Wheeler and Feynman (1945) and also the transactional interpretation of quantum mechanics of John Cramer(1980). The author agree with the most idea of absorber theory, i.e., the advanced wave is real/physic. Recently the author has proved that the mutual energy Theorem can be a sub-Theorem of Poynting Theorem hence it is also an energy Theorem. Further more the author extended the mutual energy Theorem as mutual energy flow Theorem. The shape of the mutual energy flow looks very like the photon. We know that photon is point to point transfer the energy, the energy is not decrease with distance. The mutual energy flow is thin in the two ends and thick in the middle between the two ends and hence similar to the photon. Mutual energy flow can explain the wave particle duality because when it is emitter and absorber it looks like a particle, but in the middle between emitting and absorbing it looks like wave. The author begin use the mutual energy flow to explain photon and further for other particle for example electron. Finally the author found the mutual energy Theorem is not just an energy Theorem, it is also the energy conservation law for two charges (an emitter and an absorber). The mutual energy Theorem can be extended to N charges. From the N-charge mutual energy formula it can be easily seen as an energy conservation law. The author try to derive the energy conservation law for Maxwell equations and superposition principle, but it is not possible. Started from Maxwell equations, we can only prove the formula of the mutual energy Theorem is an energy Theorem but not an energy conservation law. From the author's understanding, this is a bug of Maxwell equations, Maxwell equations must be corrected. After the correction, it should be derive the concept of absorber theory that means the sun cannot shine if it is put in a empty space. The author introduced the new axioms which is called the mutual energy principle and self-energy principle. Started from the mutual energy principle and self-energy principle the Maxwell equations still can be established. However the Maxwell equations must established as at least a pair. In the pair one is for the retarded wave and the another is for the advanced wave. Further more the two wave the retarded wave sent from the emitter and the advance wave sent from the absorber must synchronized. The synchronized retarded wave and advanced wave become the mutual energy flow. Since, the axiom of the electromagnetic field has changed from the Maxwell equations to the mutual energy principle and self-energy principle the derived theory are different with the result of Maxwell equations but agree with the absorber theory. The sun really cannot shine without the help of the absorber surrounding it. In the new theory a new kind of electromagnetic field is introduced which is the time-reversal fields corresponding the retarded wave and the advanced wave. Hence in this new theory the electromagnetic field has 4 kinds, the retarded wave, the advanced wave and two time-reversal waves. Each wave has a corresponding self-energy flows. The retarded wave and the advanced wave can also create a mutual energy flow. It is possible also has a time-reversal mutual energy flow which can be the anti-photon. The anti-photon can be half photon or partial photon. The author believe the anti-photon eliminate the half photon and partial photon. But normally the anti-photon doesn't not eliminate the complete photon. Started from the mutual energy principle and self-energy principle is assume the absorber are uniformly distributed on the big sphere, Maxwell equations can be proved with big amount of photons. That means that the mutual energy principle and the self-energy principle is the in microscopic law, and the Maxwell equations still can be applied as macroscopic law which can be derived from the microscopic law. This book with 3 volume will show the whole story about the concept of the mutual energy, the mutual energy Theorem, the mutual energy flow Theorem, the mutual energy principle, the self-energy principle. The volume I is the electromagnetic field theory with advanced field, shows the work has been done by the author surrounding the target of mutual energy principle. The volume II is derivation of the mutual energy principle and the self-energy principle and the application to the electromagnetic field theory. The volume III is that the concept of mutual energy applied to the quantum mechanics. The interpretation based on the mutual energy flow is introduced, the theory with 4-waves and 2 mutual energy flows is extended to an arbitrary particles. Path integral will be replaced as mutual energy flow stream integral.
-
Photon models are derived using the mutual energy principle which solves the bugs in Poynting and Maxwell theory
2019Co-Authors: Shuang-ren ZhaoAbstract:It is found that the Poynting Theorem is conflict with the energy conservation principle. It is a bug of the Poynting Theorem. The Poynting Theorem is derived from Maxwell equations by using the superimposition principle of the fields. Hence, this bug also existed at either in superimposition principle or in the Maxwell equations. The Poynting Theorem is corrected in this article. After the correction the energy is not quadratic and hence the field is also not linear. The concept of the superposition of fields need also to be corrected. Hence the new definitions for the inner product and cross product are proposed. The corrected Poynting Theorem become the mutual energy formula, it is strongly related to the mutual energy Theorems. It is shown that starting from the mutual energy formula, the whole electromagnetic theory can be reconstructed. The Poynting Theorem can be proved from the mutual energy formula by adding pseudo items. The Maxwell equations can be derived from Poynting Theorem as sufficient conditions. Hence if the mutual energy formula is corrected, the Maxwell equations still can be applied with knowing its problem. Most the problems originally caused by Maxwell equations are solved. Examples of this problems are: (1) electric field infinity which need to be re-normalized in quantum physics; (2) collapse of the electromagnetic field, the waves has to be collapsed to its absorber, otherwise the energy is not conserved; (3) the emitter can send energy without absorber, this is conflict to the direct interaction principle and absorber theory; (4) if our universe is not completely opaque, the charges will continually send energy to the outside of our universe, our universe will have a continual loss of energy. However there is no testimony supporting that our universe is opaque. The new theory supports the existence of advanced wave, hence also strongly support the absorber theory and transactional interpretation of quantum physics. It can offer an equation for photon and a good explanation for the duality of the photon. If photon and electromagnetic field obeys the mutual energy formula, it is very possible that all other quanta also obey their similar mutual energy formula. Hence the mutual energy formula can be applied as a principle or axiom for the electromagnetic theory and quantum physics. According to this theory the asychronous retarded wave and the asychronous advanced wave of electromagnetic fields both are an ability or probability waves, which is also partly agree with Copenhagen interpretation.
-
Photon models are derived using the mutual energy principle and self-energy principle
2018Co-Authors: Shuang-ren ZhaoAbstract:It is found that the Poynting Theorem is conflict with the energy conservation principle. It is a bug of the Poynting Theorem. The Poynting Theorem is derived from Maxwell equations by using the superimposition principle of the fields. Hence, this bug also existed at either in superimposition principle or in the Maxwell equations. The Poynting Theorem is corrected in this article. After the correction the energy is not quadratic and hence the field is also not linear. The concept of the superposition of fields need also to be corrected. Hence the new definitions for the inner product and cross product are proposed. The corrected Poynting Theorem become the mutual energy formula, it is strongly related to the mutual energy Theorems. It is shown that starting from the mutual energy formula, the whole electromagnetic theory can be reconstructed. The Poynting Theorem can be proved from the mutual energy formula by adding pseudo items. The Maxwell equations can be derived from Poynting Theorem as sufficient conditions. Hence if the mutual energy formula is corrected, the Maxwell equations still can be applied with knowing its problem. Most the problems originally caused by Maxwell equations are solved. Examples of this problems are: (1) electric field infinity which need to be re-normalized in quantum physics; (2) collapse of the electromagnetic field, the waves has to be collapsed to its absorber, otherwise the energy is not conserved; (3) the emitter can send energy without absorber, this is conflict to the direct interaction principle and absorber theory; (4) if our universe is not completely opaque, the charges will continually send energy to the outside of our universe, our universe will have a continual loss of energy. However there is no testimony supporting that our universe is opaque. The new theory supports the existence of advanced wave, hence also strongly support the absorber theory and transactional interpretation of quantum physics. It can offer an equation for photon and a good explanation for the duality of the photon. If photon and electromagnetic field obeys the mutual energy formula, it is very possible that all other quanta also obey their similar mutual energy formula. Hence the mutual energy formula can be applied as a principle or axiom for the electromagnetic theory and quantum physics. According to this theory the asychronous retarded wave and the asychronous advanced wave of electromagnetic fields both are an ability or probability waves, which is also partly agree with Copenhagen interpretation.
-
The theoretic proof that the macroscopic electromagnetic wave can be built from photons
2018Co-Authors: Shuang-ren ZhaoAbstract:Einstein has guessed that the macroscopic electromagnetic wave is built by photons. But since he only knew the energy of the photons E=h\nu. From that, it is difficult to prove that the macroscopic electromagnetic wave is built from photons. Recently the author has proposed that the mutual energy principle and self-energy principle can serve as axioms for microscopic wave of electromagnetic fields. The author has proved that photon can be described as the mutual energy flow and the mutual energy flow can be derived from mutual energy principle and the self-energy principle. The self-energy principle has told us that there are time reversal waves which is a new kind of electromagnetic fields. Hence, there are 4 waves for electromagnetic fields: the retarded wave, the advanced wave and the 2 time reversal waves corresponding to the retarded wave and the advanced wave. The mutual energy principle can derive the mutual energy flow Theorem which describe the photon. These all open a door to prove that the macroscopic electromagnetic wave can be composed by infinite more photons. If the author claim that photon satisfy the mutual energy principle and self-energy principle, it is his duty to prove from the mutual energy principle and self-energy principle that the macroscopic electromagnetic wave can be built. This article the author will prove that the macroscopic waves which is built by infinite photons will satisfy the Poynting Theorem and Maxwell equations, please notice that in this theory the Maxwell equation is not applied as axioms. The axioms are mutual energy principle and self-energy principle. We have the experience that the Poynting Theorem and Maxwell equation are good at least for macroscopic wireless waves. Hence the author needs to prove that even starting from the mutual energy principle and self-energy principle, the Poynting Theorem is still satisfied for the macroscopic wireless waves. Please notice that in the mutual energy principle the retarded wave and the advanced wave are assumed. Hence photon is composed from the retarded wave and advanced wave and time reversal waves. These wave can be seen as microscopic waves. But when many photons together they can build a macroscopic wave which is purely retarded.
-
Photon Models Are Derived by Solving a Bug in Poynting and Maxwell Theory
viXra, 2017Co-Authors: Shuang-ren ZhaoAbstract:It is found that the Poynting Theorem is conflict with the energy conservation principle. It is a bug of the Poynting Theorem. The Poynting Theorem is derived from Maxwell equations by using the superimposition principle of the fields. Hence, this bug also existed at either in superimposition principle or in the Maxwell equations. The Poynting Theorem is corrected in this article. After the correction the energy is not quadratic and hence the field is also not linear. The concept of the superposition of fields need also to be corrected. Hence the new definitions for the inner product and cross product are proposed. The corrected Poynting Theorem become the mutual energy formula, it is strongly related to the mutual energy Theorems. It is shown that starting from the mutual energy formula, the whole electromagnetic theory can be reconstructed. The Poynting Theorem can be proved from the mutual energy formula by adding pseudo items. The Maxwell equations can be derived from Poynting Theorem as sufficient conditions. Hence if the mutual energy formula is corrected, the Maxwell equations still can be applied with knowing its problem. Most the problems originally caused by Maxwell equations are solved. Examples of this problems are: (1) electric field infinity which need to be re-normalized in quantum physics; (2) collapse of the electromagnetic field, the waves has to be collapsed to its absorber, otherwise the energy is not conserved; (3) the emitter can send energy without absorber, this is conflict to the direct interaction principle and absorber theory; (4) if our universe is not completely opaque, the charges will continually send energy to the outside of our universe, our universe will have a continual loss of energy. However there is no testimony supporting that our universe is opaque. The new theory supports the existence of advanced wave, hence also strongly support the absorber theory and transactional interpretation of quantum physics. It can offer an equation for photon and a good explanation for the duality of the photon. If photon and electromagnetic field obeys the mutual energy formula, it is very possible that all other quanta also obey their similar mutual energy formula. Hence the mutual energy formula can be applied as a principle or axiom for the electromagnetic theory and quantum physics. According to this theory the asychronous retarded wave and the asychronous advanced wave of electromagnetic fields both are an ability or probability waves, which is also partly agree with Copenhagen interpretation.
Alexander Kholmetskii - One of the best experts on this subject based on the ideXlab platform.
-
Poynting Theorem, Relativistic Transformation of Total Energy–Momentum and Electromagnetic Energy–Momentum Tensor
Foundations of Physics, 2016Co-Authors: Alexander Kholmetskii, Oleg Missevitch, Tolga YarmanAbstract:We address to the Poynting Theorem for the bound (velocity-dependent) electromagnetic field, and demonstrate that the standard expressions for the electromagnetic energy flux and related field momentum, in general, come into the contradiction with the relativistic transformation of four-vector of total energy–momentum. We show that this inconsistency stems from the incorrect application of Poynting Theorem to a system of discrete point-like charges, when the terms of self-interaction in the product $${\varvec{j}} \cdot {\varvec{E}}$$ j · E (where the current density $${\varvec{j}}$$ j and bound electric field $${\varvec{E}}$$ E are generated by the same source charge) are exogenously omitted. Implementing a transformation of the Poynting Theorem to the form, where the terms of self-interaction are eliminated via Maxwell equations and vector calculus in a mathematically rigorous way (Kholmetskii et al., Phys Scr 83:055406, 2011 ), we obtained a novel expression for field momentum, which is fully compatible with the Lorentz transformation for total energy–momentum. The results obtained are discussed along with the novel expression for the electromagnetic energy–momentum tensor.
-
Poynting Theorem relativistic transformation of total energy momentum and electromagnetic energy momentum tensor
Foundations of Physics, 2016Co-Authors: Alexander Kholmetskii, Oleg Missevitch, Tolga YarmanAbstract:We address to the Poynting Theorem for the bound (velocity-dependent) electromagnetic field, and demonstrate that the standard expressions for the electromagnetic energy flux and related field momentum, in general, come into the contradiction with the relativistic transformation of four-vector of total energy–momentum. We show that this inconsistency stems from the incorrect application of Poynting Theorem to a system of discrete point-like charges, when the terms of self-interaction in the product \({\varvec{j}} \cdot {\varvec{E}}\) (where the current density \({\varvec{j}}\) and bound electric field \({\varvec{E}}\) are generated by the same source charge) are exogenously omitted. Implementing a transformation of the Poynting Theorem to the form, where the terms of self-interaction are eliminated via Maxwell equations and vector calculus in a mathematically rigorous way (Kholmetskii et al., Phys Scr 83:055406, 2011), we obtained a novel expression for field momentum, which is fully compatible with the Lorentz transformation for total energy–momentum. The results obtained are discussed along with the novel expression for the electromagnetic energy–momentum tensor.
-
Poynting Theorem, Relativistic Transformation of Total Energy–Momentum and Electromagnetic Energy–Momentum Tensor
Foundations of Physics, 2015Co-Authors: Alexander Kholmetskii, Oleg Missevitch, Tolga YarmanAbstract:We address to the Poynting Theorem for the bound (velocity-dependent) electromagnetic field, and demonstrate that the standard expressions for the electromagnetic energy flux and related field momentum, in general, come into the contradiction with the relativistic transformation of four-vector of total energy–momentum. We show that this inconsistency stems from the incorrect application of Poynting Theorem to a system of discrete point-like charges, when the terms of self-interaction in the product \({\varvec{j}} \cdot {\varvec{E}}\) (where the current density \({\varvec{j}}\) and bound electric field \({\varvec{E}}\) are generated by the same source charge) are exogenously omitted. Implementing a transformation of the Poynting Theorem to the form, where the terms of self-interaction are eliminated via Maxwell equations and vector calculus in a mathematically rigorous way (Kholmetskii et al., Phys Scr 83:055406, 2011), we obtained a novel expression for field momentum, which is fully compatible with the Lorentz transformation for total energy–momentum. The results obtained are discussed along with the novel expression for the electromagnetic energy–momentum tensor.
-
Continuity equations for bound electromagnetic field and the electromagnetic energy–momentum tensor
Physica Scripta, 2011Co-Authors: Alexander Kholmetskii, Oleg Missevitch, Tolga YarmanAbstract:We analyze the application of the Poynting Theorem to the bound (velocity-dependent) electromagnetic (EM) field and show that an often-used arbitrary elimination of the term of self-interaction in the product j·E (where j is the current density and E the electric field) represents, in general, an illegitimate operation, which leads to incorrect physical consequences. We propose correct ways of eliminating the terms of self-interaction from the Poynting Theorem to transform it into the form that is convenient for problems with bound EM field, which yield the continuity equations for the proper EM energy density, the interaction part of EM energy density and the total EM energy density of bound fields, respectively. These equations indicate the incompleteness of the common EM energy–momentum tensor, and in our analysis, we find a missed term in its structure, which makes its trace non-vanished. Some implications of these results are discussed, in particular, in view of the notion of EM mass of charged particles.
Kaiser Gerald - One of the best experts on this subject based on the ideXlab platform.
-
Completing the complex Poynting Theorem: Conservation of reactive energy in reactive time
2016Co-Authors: Kaiser GeraldAbstract:The complex Poynting Theorem is extended canonically to a time-scale domain $(t, s)$ by replacing the phasors of time-harmonic fields by the analytic signals $X(r, t+is)$ of fields $X(r,t)$ with general time dependence. The imaginary time $s>0$ is shown to play the role of a time resolution scale, and the extended Poynting Theorem splits into two conservation laws: its real part gives the conservation in $t$ of the scale-averaged active energy at fixed $s$, and its imaginary part gives the conservation in $s$ of the scale-averaged reactive energy at fixed $t$. At coarse scales (large $s$, slow time), where the system reduces to the circuit level, this may have applications to the theory of electric power transmission and conditioning. At fine scales (small $s$, fast time) it describes reactive energy dynamics in radiating systems.Comment: 21 pages, no figure
-
Conservation of reactive electromagnetic energy in reactive time
2015Co-Authors: Kaiser GeraldAbstract:The complex Poynting Theorem (CPT) is extended to a canonical time-scale domain $(t,s)$. Time-harmonic phasors are replaced by the positive-frequency parts of general fields, which extend analytically to complex time $t+is$, with $s>0$ interpreted as a time resolution scale. The real part of the extended CPT gives conservation in $t$ of a time-averaged field energy, and its imaginary part gives conservation in $s$ of a time-averaged reactive energy. In both cases, the averaging windows are determined by a Cauchy kernel of width $\Delta t\sim \pm s$. This completes the time-harmonic CPT, whose imaginary part is generally supposed to be vaguely `related to' reactive energy without giving a conservation law, or even an expression, for the latter. The interpretation of $s$ as reactive time, tracking the leads and lags associated with stored capacitative and inductive energy, gives a simple explanation of the volt-ampere reactive (var) unit measuring reactive power: a var is simply one Joule per reactive second. The related 'complex radiation impedance density' is introduced to represent the field's local reluctance to radiate.Comment: 2 pages, no figures, paper submitted by invitation to special session on Fundamental Considerations of Electromagnetic Energy and Interactions: Theory and Applications at IEEE APS/URSI 2015 Symposium http://www.2015apsursi.or