Physics
Electromagnetic Momentum
Electromagnetic momentum refers to the momentum carried by electromagnetic fields. In classical electromagnetism, it is defined as the momentum density of the electromagnetic field. This concept is important in understanding the transfer of momentum between electromagnetic fields and matter, as well as in the study of electromagnetic waves and their interactions with matter.
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6 Key excerpts on "Electromagnetic Momentum"
eBook - PDFGravitation
Foundations and Frontiers
- T. Padmanabhan(Author)
- 2010(Publication Date)
- Cambridge University Press(Publisher)
How will one then formulate special relativity and interpret the universal speed c ? 2.9 Energy and momentum of the electromagnetic field By including the electromagnetic fields in the action we are treating them as dynamical entities with degrees of freedom of their own. When a charge moves under the influence of an electromagnetic field, its momentum and energy will change. Since the total momentum (or energy) of a closed system is a constant, it follows that the change of energy and momentum of the charged particle must be compensated for by a change of the energy and momentum of the field. To show this explicitly, we need to obtain the expressions for the energy and momentum of the electromagnetic field. Let us consider the energy-momentum tensor corresponding to the last term in Eq. (2.111) describing the action for the electromagnetic field. We have already seen that the canonical momentum corresponding to the vector field A l is given 2.9 Energy and momentum of the electromagnetic field 91 by P ( l ) k = − (1 / 4 π ) F kl . One should interpret this expression as giving the four-momentum (indexed by k ) for each component of the field (indexed by l ). The energy-momentum tensor in Eq. (2.17) is now defined through T k i = − [ ∂ i A l P ( l ) k − δ k i L ] . (2.138) Note that in the first term we are summing over l , which indicates the differ-ent components of the vector field. This is an illustration of the comment we made earlier (at the end of Section 2.3.1 ) that, in the case of a multi-component field, we merely sum up the expression for the energy-momentum tensor for each component. Substituting P ( l ) k = − (1 / 4 π ) F kl into this expression we get T ik = 1 4 π F k l ∂ i A l − 1 16 π η ik F lm F lm . (2.139) This is an example of an energy-momentum tensor which is not symmetric. However, we can make it symmetric by adding the quantity − F k l 4 π ∂ l A i = − 1 4 π ∂ l ( A i F kl ) , (2.140) which is of the form given in Eq.
eBook - PDF- Fritz Rohrlich(Author)
- 2007(Publication Date)
- WSPC(Publisher)
CHAPTER 5 Electromagnetic Radiation While in principle it is possible to consider all electromagnetic fields siniply as intermediaries, transmitting interactions between charges, they are no doubt useful concepts to be studied in their own right, irrespective of the charges in- volved in their production or absorption. The radziztion fields, however, have importance which goes beyond that. Radiation has so many of the physical attributes associated with matter that it receives a status almost at par with it in classical physics. In quantum physics this status is elevated to full emancipa- tion when the photon emerges as a full-fledged particle, just as “fundamental” as any charged particle of matter. The present chapter takes account of this situation and is devoted to electromagnetic radiation in its own right. 5-1 MOMENTUM AND ENERGY OF RADIATION Given the world line of a point charge #(r) , the electromagnetic field strengths P ( z ) due to that charge, at an arbitrary point z in spacetime, are determined by the Maxwell-Lorentz equations and the retardation condition.* They are given by Eq. (4-98) in terms of the four-velocity tl” and the four-acceleration upl Here we use units such that c = 1 and the notation a‘”b”l = $(a%“ - aW), (5-2) which often helps to prevent certain expressions from becoming unwieldy. Our aini is to express the energy and niomentuni carried by the radiation in ternis of the dynamical variables of the moving source charge. We start, there- fore, with the electroniagnetic energy-momentum four-vector PZ,,, defined in (4-123) (4-123’) where the integration extends over a spacelike plane. The notation d3cP in- dicates the three-dimensional nature of this plane explicitly. As was discussed * In the present chapter all fields are retarded, so that the subscript “ret” used in Chapter 4 can be dropped without causing ambiguity. 106
eBook - PDF- A L Fabrikant, Yury A Stepanyants(Authors)
- 1998(Publication Date)
- World Scientific(Publisher)
Chapter 1 Wave Energy and Momentum in a Moving Medium The laws of conservation of energy and momentum are broadly used in investigations of wave motions in hydrodynamic flows. The definition of these notions, however, is concerned with certain difficulties that are often ignored. For example, calculations of momentum and energy, which are the quantities of the second order of smallness with respect to wave amplitude, must take into account the variations of average parameters of the medium, in particular, wave induced flows. There arises a problem of unambiguous differentiation between mean and wave fields of physical variables. A similar problem was encoun-tered in electrodynamics, that is, the celebrated Abraham - Minkowski controversy over the momentum of electromagnetic waves in the dielec-tric media (Ginzburg and Ugarov, 1976). The momentum of quasi-monochromatic waves has for a long time been a controversial issue in hydrodynamic problems (Mclntyre, 1981). Wave momentum is often an auxiliary concept in the formal solu-tion of linear problems and its definition reduces to the choice of suitable terminology. However, an understanding of the physics of many linear 7 8 Wave energy and momentum wave processes in inhomogeneous media, as well as investigations of some nonlinear processes, demands a detailed analysis of the entire com-plex of hydrodynamic effects accompanying the propagation of waves in the medium. This refers, in the first place, to nonstationary induced flows that emerge in the emission, absorption, and scattering of waves. Besides, there is a need for a universal language (as in the general the-ory of oscillations and waves) that would define uniquely the energy and momentum of waves of different types independent of their origin. Numerous approaches to the definition of wave momentum employed today impede the exchange of ideas and results in different branches of physics.
eBook - PDFElectromagnetic Vortices
Wave Phenomena and Engineering Applications
- Zhi Hao Jiang, Douglas H. Werner, Zhi Hao Jiang, Douglas H. Werner(Authors)
- 2021(Publication Date)
- Wiley-IEEE Press(Publisher)
This signal ‘ pulse ’ will then be located in a finite volume V 0 between two concentric spherical shells, one with radius r 0 = ct 0 relative to the reference point x 0 in V (see Figure 2.A.1), and another with radius r 0 + Δ r 0 where Δ r 0 = c Δ t 0 [5]. According to the conservation laws (2.A.128) and (2.A.158), the cycle averaged field momentum p EM and angular momentum J EM contained in this spatially limited volume do not fall off asymptotically at large distances from the source, but tend to constant values. Consequently, both linear and angular electromagnetic field momenta can propagate and hence be used for information transfer over in principle arbitrarily long distances. Of course, the magni-tude and angular distribution of the respective momentum densities depend on the specific spati-otemporal properties of the actual radiating and receiving transducers ( ‘ antennas ’ ) used. Some transducers, such as one-dimensional linear dipole antennas used in radio today, are effective radiators and sensors of linear momentum, whereas well-defined coherent superpositions of angu-lar momentum eigenmodes are more optimally radiated and sensed by transducers that make full use of two-or three-dimensional current distributions. 2.3.1 Wireless Information Transfer with Linear Momentum If we identify the individual terms in the global law of conservation of linear momentum in a closed volume, Eq. (2.A.128), we can rewrite this equation as a balance equation between the time rate change of mechanical linear momentum, i.e. the force on the matter (the charged mechanical par-ticles) in V , the time rate change of field linear momentum in V , and the flow of field linear momen-tum into V , across the surface S bounding V , as follows: V d 3 x f Force F on the matter + d d t V d 3 x ε 0 E × B Field momentum + S d 2 x n T Linear momentum flow = 0 2 39 which, of course, is nothing but a generalized version of Newton ’ s second law, or rather Euler ’ s first law of motion.
- Ali Akdagli(Author)
- 2011(Publication Date)
- IntechOpen(Publisher)
1.2 Coordination of the electromagnetic impulse with the substance Firstly, consider the one-dimensional task the electric part of electromagnetic field momentum with the dielectric substance, which posses a certain numerical concentration n of centrosymmetrical atoms – oscillators. For the certainty of the analysis we suggest the atom to be one-electronic. It is also agreed, that no micro current or free charge are present in the medium. The peculiarities of interaction between magnetic aspect of momentum and the atoms will be considered later. We accept that there takes place the interaction of quantum of electromagnetic radiation with nuclear electrons, thus quantum are absorbed by the electrons. By gaining the energy of quantum the electrons shift to the advanced power levels. Further, by means of resonate shift of electrons back, appears the quantum radiation forward. The considered medium lacks non-radiating shift of electrons, i.d. the power of quantum is not transfered to the atom. Behaviour of Electromagnetic Waves in Different Media and Structures 142 Thus, the absorption of electromagnetic radiation in the case of its power dissipation in the substance, owing to SIT, is disregarded. There appears the atomic sypraradiation of quantum. Thus, the forefront of momentum passes the power on to the atomic electrons of the medium, forming its back front. The probabilities of quantum's absorption and radiation by the electrons in the unity of time, with a large quantity of quantum in the impulse, according to Einstein, can be referred to as the approximately identical [6]. For the separate interaction of the with the electron this very probability is the same and is proportional to the cube of the fine-structure constant ~ (1/137) 3 [7]. Consider a random quantity – the number of interactions of quantum with atomic electrons in the momentum.
eBook - PDF- William Moebs, Samuel J. Ling, Jeff Sanny(Authors)
- 2016(Publication Date)
- Openstax(Publisher)
The signal is then converted into an audio and/or video format. Use this simulation (https://openstaxcollege.org/l/21radwavsim) to broadcast radio waves. Wiggle the transmitter electron manually or have it oscillate automatically. Display the field as a curve or vectors. The strip chart shows the electron positions at the transmitter and at the receiver. 16.3 | Energy Carried by Electromagnetic Waves Learning Objectives By the end of this section, you will be able to: • Express the time-averaged energy density of electromagnetic waves in terms of their electric and magnetic field amplitudes • Calculate the Poynting vector and the energy intensity of electromagnetic waves • Explain how the energy of an electromagnetic wave depends on its amplitude, whereas the energy of a photon is proportional to its frequency 712 Chapter 16 | Electromagnetic Waves This OpenStax book is available for free at http://cnx.org/content/col12074/1.3 Anyone who has used a microwave oven knows there is energy in electromagnetic waves. Sometimes this energy is obvious, such as in the warmth of the summer Sun. Other times, it is subtle, such as the unfelt energy of gamma rays, which can destroy living cells. Electromagnetic waves bring energy into a system by virtue of their electric and magnetic fields. These fields can exert forces and move charges in the system and, thus, do work on them. However, there is energy in an electromagnetic wave itself, whether it is absorbed or not. Once created, the fields carry energy away from a source. If some energy is later absorbed, the field strengths are diminished and anything left travels on. Clearly, the larger the strength of the electric and magnetic fields, the more work they can do and the greater the energy the electromagnetic wave carries. In electromagnetic waves, the amplitude is the maximum field strength of the electric and magnetic fields (Figure 16.10). The wave energy is determined by the wave amplitude.
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