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Abstract
Although Poynting's theorem receives general acceptance in the treatment of electromagnetic energy, an alternative theorem, Macdonald's, has equal claim to validity at the present state of our knowledge. In a comparison of many results derived from the two, Macdonald's theorem exhibits sufficient superiority to warrant its consideration more generally in electromagnetics.
... , and discussed in scores of papers: See e.g. Hines [16], who sided with Macdonald, or Lai [19], who unknowingly repeated Slepian's proposal [21], thus rekindling the debate 30 years later-a debate not yet closed, as testified by relatively recent work [8,9]. ...
... At material interfaces where the permeability µ is discontinuous, |H| 2 is discontinuous too, so we may have to deal with the product of two distributions, a notoriously difficult problem [7], and though it can satisfactorily be solved in the present case [5], the following approach may look preferable. Suppose one knows a 2-tensor T such that div T = f, the vector field displayed in (16), and let S be a surface embedded in a material interface. Build a pillbox from S as previously described, and integrate the vector T · n over the pillbox boundary: Going to the limit with respect to the pillbox's thickness will give the part of the magnetic force concentrated on S. ...
Many alternatives to the classical Poynting vector P have been proposed, but they lack a property of locality that makes P special and makes it the right choice to represent the energy flux. We give a geometrical proof of this uniqueness. Similar considerations apply to the Maxwell stress tensor.
... In der Literatur wurden viele Alternativen vorgeschlagen (siehe z.B. [47]). Im folgenden sollen neben der Poyntingschen jedoch nur die von Lai [26] und Hines [19] vorgeschlagenen diskutiert und einem dritten Vorschlag gegenübergestellt werden, der bisher noch nicht diskutiert worden ist. ...
... Ausgangspunkt des Vorschlages von Hines [19] ist eine von Macdonald [31] vorgeschlagene Darstellung, die einer Festlegung (3.19) entspricht. Nachdem Hines einige Einwände gegen diese Darstellung entkräftet hat, erweitert er sie folgendermaßen: ...
... The author then derived multiple alternative energy conservation principles. Also in [10] the author argues that alternative formulations of energy conservation principle are equally valid, as long as E · J is the only observationally relevant term. Alternative formulations of energy conservation principle for longitudinal electric waves, where no Poynting vector is present, were formulated in [28]. ...
In this work by using the assumptions that wavelength is much smaller than charge separation distance of an electric dipole, which in turn is much smaller than a distance up to the point of observation, the new results for radiation of an electric dipole were obtained. These results generalize and extend the standard classical solution, and they indicate that under the above assumptions the electric dipole emits both long-range longitudinal electric and transverse electromagnetic waves. For a specific values of the dipole system parameters the longitudinal and transverse electric fields are displayed. Total power emitted by electric and electromagnetic waves are calculated and compared. It was shown that under the standard assumption of charge separation distance being much smaller than wavelength: a) classical solution correctly describes the transverse electromagnetic waves only; b) longitudinal electric waves are non-negligible; c) total radiated power is proportional to the fourth degree of frequency and to the second degree of the charge separation distance; d) transverse component of our solution reduces to classical solution. In case wavelength is much smaller than charge separation distance: a) the classical solution is not valid and it overestimates the total radiated power; b) longitudinal electric waves are dominant and transverse electromagnetic waves are negligible; c) total radiated power is proportional to the third degree of frequency and to the charge separation distance; d) most of the power is emitted in a narrow beam along the dipole axis, thus emission of waves is focused as with lasers.
... Later, a similar version to MacDonald's vector was proposed by Hines. 26 This adoption was analyzed by Wallace and O'Connell, 27 who showed that Hines's version does not always lead to correct radiation. ...
This paper will analyze how the energy flux of Poynting’s vector is compared to the power flow in electrical engineering, where the power, instead, is defined by voltages and currents. There are alternatives to Poynting’s energy flux vector that agree more with circuit theory methods such that the energy flow is in the current conductor and not in the insulation surrounding it. One such basic formulation would only consist of the total current density and the voltage potential, but it would need an alternative theorem for energy transfer. Another formulation proposed by Slepian would instead still agree with Poynting’s energy transfer theorem, but it needs to add the power of alternating magnetic vector potential. The alternatives to Poynting’s vector may better illustrate the energy flow in electrical engineering, but two things could be considered in their generality. First, since they are expressed by potentials, they are gauge invariant and depend on the definition of the potentials. Second, Poynting’s vector is used to formulate the electromagnetic momentum, and any alternative energy flow vectors would not. These two notes are of minor importance in electrical engineering, and the alternatives could be used as good alternatives for describing power flow. The main purpose of this paper is to bridge the differences between the physical theory of energy flux and the methods in electrical power engineering. This could simplify the use of energy flux and Poynting’s vector in engineering problems.
... The discussion of whether the Poynting vector gives the local energy flow or not has a century-long history, see, e.g., a review [22]. In particular, an alternative definition of the Poynting vector has been proposed which is more in harmony with the notion of group velocity [23]. However, we are not going to dig into the problem here and simply refer to [20] (section 6.7), where it is stated that if one takes into account that the Poynting vector defines also the momentum density of the field and the definition must not violate the theory of relativity, the common expression for the Poynting vector is unique. ...
... The discussion of whether the Poynting vector gives the local energy flow or not has a century-long history, see, e.g., a review [21]. In particular, an alternative definition of the Poynting vector has been proposed which is more in harmony with the notion of group velocity [22]. However, we are not going to dig into the problem here and simply refer to [20] (sec. ...
Electromagnetic energy backflow is a phenomenon occurring in regions where the direction of the Poynting vector is opposite to that of the propagation of the wave field. It is particularly remarkable in the nonparaxial regime and has been exhibited in the focal region of sharply focused beams, for vector Bessel beams, and vector-valued spatiotemporally localized waves. A detailed study is undertaken of this phenomenon and the conditions for its appearance are examined in detail in the case of a superposition of four plane waves in free space, the simplest electromagnetic arrangement for the observation of negative energy flow, as well as its comprehensive and transparent physical interpretation. It is shown that the state of polarization of the constituent components of the electromagnetic plane wave quartet determines whether energy backflow takes place or not and what values the energy flow velocity assumes. Depending on the polarization angles, the latter can assume any value from c (the speed of light in vacuum) to -c in certain spatiotemporal regions of the field.
... The author then derived multiple alternative energy conservation principles. Also in Hines (1952) the author argues that alternative formulations of energy conservation principle are equally valid, as long as E·J is the only observationally relevant term. Alternative formulations of energy conservation principle for longitudinal electric waves, where no Poynting vector is present, were formulated in Zaimidoroga (2016). ...
In this work, by using the assumptions that wavelength is much smaller than charge separation distance of an electric dipole, which in turn is much smaller than a distance up to the point of observation, the new results for radiation of an electric dipole were obtained. These results generalize and extend the standard classical solution, and they indicate that under the above assumptions, the electric dipole emits both long‐range longitudinal electric and transverse electromagnetic waves. For a specific values of the dipole system parameters, the longitudinal and transverse electric fields are displayed. Total power emitted by electric and electromagnetic waves are calculated and compared. It was shown that under the standard assumption of charge separation distance being much smaller than wavelength, (a) classical solution correctly describes the transverse electromagnetic waves only; (b) longitudinal electric waves are nonnegligible; (c) total radiated power is proportional to the fourth degree of frequency and to the second degree of the charge separation distance; and (d) transverse component of our solution reduces to classical solution. In case wavelength is much smaller than charge separation distance, (a) the classical solution is not valid, and it overestimates the total radiated power; (b) longitudinal electric waves are dominant and transverse electromagnetic waves are negligible; (c) total radiated power is proportional to the third degree of frequency and to the charge separation distance; and (d) most of the power is emitted in a narrow beam along the dipole axis; thus, emission of waves is focused as with lasers.
The propagation of disturbances ill dispersite nledia. Cambridge 'Tracts in BIathenlatical Physics
- H Avelocic
H.AVELOCIC, ' T. H. The propagation of disturbances i l l dispersite nledia. Cambridge 'Tracts in BIathenlatical Physics. 1914.
The theory of electricity
- G H Livens
LIVENS, G. H. The theory of electricity. 211d ed. Calnbridgc Unitersity Press. 1926.
Electron~agnetic radiation
- G A Schott
SCHOTT, G. A. Electron~agnetic radiation. Cambridge University Press. 1912.
Electromagnetic theory. London
- J A Srattok
S~RATTOK, J. A. Electromagnetic theory. WIcGraw-Hill Book Co., Inc., Kcw York and London. 1941.
Treatise 011 electricity and magnetisll
- J C Miswell