New approach to the classical radiation fields of moving dipoles

Progress In Electromagnetics Research, 2012

Maxwell's equations specify that electromagnetic radiation fields are generated by accelerating charges. However, the electromagnetic radiation fields of an accelerating charge are seldom used to derive the electromagnetic fields of radiating systems. In this paper, the equations pertinent to the electromagnetic fields generated by accelerating charges are utilized to evaluate the electromagnetic fields of a current path of length l for the case when a pulse of current propagates with constant velocity. According to these equations, radiation is generated only at the end points of the channel where charges are being accelerated or decelerated. The electromagnetic fields of a short dipole are extracted from these equations when r l, where r is the distance to the point of observation. The speed of propagation of the pulse enters into the electromagnetic fields only in the terms that are second order in l and they can be neglected in the dipole approximation. The results illustrate how the radiation fields emanating from the two ends of the dipole give rise to field terms varying as 1/r and 1/r 2 , while the time-variant stationary charges at the ends of the dipole contribute to field terms varying as 1/r 2 and 1/r 3 .

Metamaterials: Fundamentals and Applications 2014, 2014

The classical theory of electrodynamics is built upon Maxwell's equations and the concepts of electromagnetic field, force, energy and momentum, which are intimately tied together by Poynting's theorem and the Lorentz force law. Whereas Maxwell's macroscopic equations relate the electric and magnetic fields to their material sources (i.e., charge, current, polarization and magnetization), Poynting's theorem governs the flow of electromagnetic energy and its exchange between fields and material media, while the Lorentz law regulates the back-and-forth transfer of momentum between the media and the fields. The close association of momentum with energy thus demands that the Poynting theorem and the Lorentz law remain consistent with each other, while, at the same time, ensuring compliance with the conservation laws of energy, linear momentum, and angular momentum. This paper shows how a consistent application of the aforementioned laws of electrodynamics to moving permanent dipoles (both electric and magnetic) brings into play the rest-mass of the dipoles. The rest mass must vary in response to external electromagnetic fields if the overall energy of the system is to be conserved. The physical basis for the inferred variations of the rest-mass appears to be an interference between the internal fields of the dipoles and the externally applied fields. We use two different formulations of the classical theory in which energy and momentum relate differently to the fields, yet we find identical behavior for the restmass in both formulations.

Radio Science, 1999

The radiation Q of several dipole fields in free space are determined using the time-dependent Poynting theorem. Earlier works on this subject, recently summarized by McLean [1996], are based upon the complex Poynting theorem. It was previously shown [Grimes and Grimes, 1997] that the full complex Poynting theorem is correct only for single-mode radiation fields. The time-dependent theorem shows that three numbers are necessary to completely specify time-varying power, and complex numbers supply but two; the third piece of information, a phase, is discarded when complex notation is formed. Omissions inherent in the complex Poynting theorem affect the calculated value of standing energy about an antenna and hence the calculated value of Q. To avoid such omissions, we develop a method of determining Q based upon the time-dependent Poynting theorem that builds upon and extends our earlier work [Grimes and Grimes, 1997]. The purposes of this paper are to (1) provide a time domain basis for calculating Q in mixed modal radiation fields, (2) determine the Q of electric and magnetic dipoles, alone and in combination, and (3) demonstrate how source structure and relative phasing affect the physics of several combinations of electric and magnetic dipole radiation fields. The primary conclusion of this work is that the minimum possible Q of a radiation source established by Chu [1948] does not extend to properly mixed and phased multimodal radiation fields. A radiation source is presented for which, by our analysis, the radiation Q is zero. 282 GRIMES AND GRIMES: RADIATION Q OF DIPOLE GENERATED FIELDS equation (27)] shows the power on the surface of a virtual circumscribing sphere using the complex Poynting theorem: ,r 4F• 2 24F32 Pc(or) = •5-•-(1 + iT1) + (1 + iT3) (1) 7

2005

An exact calculation of the retarded electric field in the source region of a system of individual charges, expanded to third order in velocity, shows that all nonrelativistic accelerated charges in a system emit dipole electromagnetic energy at the Larmor rate. In general, some of the emitted dipole power is reabsorbed by doing work on other charges in the system, and some is radiated. If the system has zero net dipole moment, all the emitted dipole power is reabsorbed, and none is radiated.

European Journal of Physics, 2012

We show that the expression for the force on a moving point-like dipole we derived in Kholmetskii et al (2011 Eur. J. Phys. 32 873) is correct and indicate an error in the criticism by Vekstein. We also show that with the inclusion of a 'hidden' momentum contribution, our expression has the general character and can be reduced to the expressions by Hnizdo or by Vekstein in the approximations they adopted. Concurrently, we recognize that the mathematical side of the paper by Vekstein (1997 Eur. J. Phys. 18 113) is correct. Recently we published the paper [1], where we obtained the force on a moving point-like dipole in the form of

American Journal of Physics, 2011

We derive from Jefimenko's equations 1 a multipole expansion in order to obtain the exact expressions for the electric and magnetic fields of an electric dipole with an arbitrary time dependence. A few comments are also made about the usual expositions found in most common undergraduate and graduate textbooks as well as in the literature on this topic.

European Journal of Physics, 2009

The dipole radiation from an oscillating charge is treated using the Hamiltonian approach to electrodynamics where the concept of cavity modes plays a central role. We show that the calculation of the radiation field can be obtained in a closed form within this approach by emphasizing the role of coherence between the cavity modes, which is discarded in the calculation of the radiation power. We believe that this simple case can elucidate some basic questions students pose when introduced to quantum electrodynamics or perturbation theory in quantum mechanics.

American Journal of Physics, 2018

An expression for the intensity of the electromagnetic field radiation is derived up to the order next to the dipole approximation. Our approach is based on the fundamental equations from the introductory course of classical electrodynamics and the derivation is carried out using straightforward mathematical transformations.

Astrophysics and Space Science, 1995

Using the methods of Haxton and Ruffini the multipole expansion of the radiation field of an arbitrarily fast rotating magnetic dipole, with its axis inclined relative to the rotation axis, is obtained. This result is compared with the Fourier decomposition of the radiation emitted by the rotating dipole, obtained by Belinsky et al.

International Journal of Geomagnetism and Aeronomy, 2006

Radiation of an oscillating electric dipole which is travelling with a constant velocity in homogeneous isotropic medium with given dispersion characteristic is studied. The cases of cold plasma and the medium with the dispersion of a resonant type are considered. It is shown that in the case of the resonantly dispersive medium, the radiation spectrum consists (depending on the problem parameters) either of two separated frequency ranges or of one frequency range. Regularities characterizing the dependence of the radiated power on the source motion velocity at various values of the resonant and plasma frequencies are derived. The case when the dipole travels in a moving medium the velocity of which is parallel or antiparallel to the source motion velocity is also considered. It is noted in particular that at some parameters of the problem, the energy loss of the source are negative.