Abstract
We investigate in detail the electromagnetic fields of a uniformly accelerated charge, in order to ascertain whether such a charge does ‘emit’ radiation, especially in view of the Poynting flow computed at large distances and taken as an evidence of radiation emitted by the charge. In this context, certain important aspects of the fields need to be taken into account. First and foremost is the fact that in the case of a uniformly accelerated charge, one cannot ignore the velocity fields. This then leads to other equally vital points. The net field energy turns out to be exactly the same as that of a non-accelerated charge having a uniform velocity equal to the instantaneous velocity of the uniformly accelerated charge. Further, the Poynting vector, seen with respect to the ’present’ location of the uniformly accelerated charge, during the deceleration phase, possesses everywhere a radial component pointing inward toward the charge, becoming nil when the charge becomes momentarily stationary, and during the acceleration phase, points away from the charge position. Last, but not least, when the leading spherical front of the relativistically beamed Poynting flux, advances forward at a large time t to a far-off distance \(r=ct\), the charge too is not lagging far behind. In fact, these relativistically beamed fields, increasingly resemble fields of a charge moving in an inertial frame with a uniform velocity \(v_0\), with a convective flow of fields in that frame along with the movement of the charge. There is no other Poynting flow in the far-zones that could be termed as radiation emitted by the charge which, in turn, is fully consistent with the absence of radiation reaction and is also fully conversant with the strong principle of equivalence.
Similar content being viewed by others
References
Jackson, J.D.: Classical Electrodynamics, 2nd edn. Wiley, New York (1975)
Panofsky, W.K.H., Phillips, M.: Classical Electricity and Magnetism, 2nd edn. Addison-Wesley, Massachusetts (1962)
Griffith, D.J.: Introduction to Electrodynamics, 3rd edn. Prentice, New Jersey (1999)
Abraham, M.: Theorie der elektrizitat, Vol II: Elektromagnetische theorie der strahlung. Teubner, Leipzig (1905)
Lorentz, H.A.: The Theory of Electron. Teubner, Leipzig (1909); 2nd ed. Dover, New York (1952)
Page, L., Adams, N.I., Jr.: Electrodynamics. D. Van Nostrand, New York (1940)
Heitler, W.: The Quantum Theory of Radiation. Clarendon, Oxford (1954)
Yaghjian, A.D.: Relativistic Dynamics of a Charged Sphere, 2nd edn. Springer, New York (2006)
Singal, A.K.: Radiation reaction from electromagnetic fields in the neighborhood of a point charge. Am. J. Phys. 85, 202–206 (2017)
Page, L.: Is a moving mass retarded by the reaction of its own radiation. Phys. Rev. 11, 376–400 (1918)
Rohrlich, F.: The dynamics of a charged sphere and the electron. Am. J. Phys. 65, 1051–1056 (1997)
Teitelboim, C.: Splitting of the Maxwell tensor: radiation reaction without advanced fields. Phys. Rev. D 1, 1572–1582 (1970)
Hammond, R.T.: Relativistic particle motion and radiation reaction in electrodynamics. Electron. J. Theor. Phys. 23, 221–258 (2010)
Grøn, Ø.: Electrodynamics of radiating charges. Adv. Math. Phys. 2012, 528631 (2012)
Pauli, W.: Relativitätstheorie in Encyklopadie der Matematischen Wissenschaften, V 19. Teubner, Leipzig (1921) : Translated as Theory of relativity. Pergamon, London (1958)
Singal, A.K.: The equivalence principle and an electric charge in a gravitational field. Gen. Relat. Grav. 27, 953–967 (1995)
Singal, A.K.: The equivalence principle and an electric charge in a gravitational field II. A uniformly accelerated charge does not radiate. Gen. Relat. Grav. 29, 1371–1390 (1997)
Fulton, T., Rohrlich, F.: Classical radiation from a uniformly accelerated charge. Ann. Phys. 9, 499–517 (1960)
Boulware, D.G.: Radiation from a uniformly accelerated charge. Ann. Phys. 124, 169–188 (1980)
Parrott, S.: Radiation from a uniformly accelerated charge and the equivalence principle. Found. Phys. 32, 407–440 (2002)
de Almeida, C., Saa, A.: The radiation of a uniformly accelerated charge is beyond the horizon: a simple derivation. Am. J. Phys. 74, 154–158 (2006)
Schott, G.A.: Electromagnetic Radiation. Univ. Press, Cambridge (1912)
Eriksen, E., Grøn, Ø.: Electrodynamics of hyperbolically accelerated charges. III. Energy-momentum of the field of a hyperbolically moving charge. Ann. Phys. 286, 373–399 (2000)
Heras, J.A., O’Connell, R.F.: Generalization of the Schott energy in electrodynamic radiation theory. Am. J. Phys. 74, 150–153 (2006)
Grøn, Ø.: The significance of the Schott energy for energy-momentum conservation of a radiating charge obeying the Lorentz-Abraham-Dirac equation. Am. J. Phys. 79, 115–122 (2011)
Singal, A.K.: Discrepancy between power radiated and the power loss due to radiation reaction for an accelerated charge. Symmetry 12, 1833 (2020)
Singal, A.K.: The fallacy of Schott energy-momentum. Phys. Ed. (IAPT). 36, No. 1, 4 (2020)
Singal, A.K.: A discontinuity in the electromagnetic field of a uniformly accelerated charge. J. Phys. Commun. 4, 095023 (2020)
Born, M.: Die Theorie des starren Elektrons in der Kinematik des Relativitätsprinzips. Ann. Phys. 30, 1–56 (1909)
Rohrlich, F.: Classical Charged Particles. World Scientific, Singapore (2007)
Singal, A.K.: A first principles derivation of the electromagnetic fields of a point charge in arbitrary motion. Am. J. Phys. 79, 1036–1041 (2011)
Feynman, R.P., Morinigo, F.B., Wagner, W.G.: Feynman Lectures on Gravitation. Addison-Wesley, Massachusetts (1995)
Purcell, E.M.: Electricity and Magnetism - Berkeley Phys. Course vol. 2, 2nd ed. McGraw, New York (1985)
Singal, A.K.: Poynting flux in the neighbourhood of a point charge in arbitrary motion and radiative power losses. Eur. J. Phys. 37, 045210 (2016)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Singal, A.K. Implications of a Non-zero Poynting Flux at Infinity Sans Radiation Reaction for a Uniformly Accelerated Charge. Found Phys 51, 81 (2021). https://doi.org/10.1007/s10701-021-00486-1
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10701-021-00486-1