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Electrodynamics of Radiating Charges in a Gravitational Field

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Springer Handbook of Spacetime

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Abstract

The electrodynamics of a radiating charge and its electromagnetic field based upon the Lorentz–Abraham–Dirac (GlossaryTerm

LAD

) equation are discussed both with reference to an inertial reference frame and a uniformly accelerated reference frame. It is demonstrated that energy and momentum are conserved during runaway motion of a radiating charge and during free fall of a charge in a field of gravity. This does not mean that runaway motion is really happening. It may be an unphysical solution of the GlossaryTerm

LAD

equation of motion of a radiating charge due to the unrealistic point particle model of the charge upon which it is based. However it demonstrates the consistency of classical electrodynamics, including the GlossaryTerm

LAD

equation which is deduced from Maxwell’s equations and the principle of energy-momentum conservation applied to a radiating charge and its electromagnetic field. The decisive role of the Schott energy in this connection is made clear and an answer is given to the question: What sort of energy is the Schott energy and where is it found? It is the part of the electromagnetic field energy which is proportional to (minus) the scalar product of the velocity and acceleration of a moving accelerated charged particle. In the case of the electromagnetic field of a point charge it is localized at the particle. This energy is negative if the acceleration is in the same direction as the velocity and positive if it is in the opposite direction. During runaway motion the Schott energy becomes more and more negative and in the case of a charged particle with finite extension, it is localized in a region with increasing extension surrounding the particle. The Schott energy provides the radiated energy of a freely falling charge. Also it is pointed out that a proton and a neutron fall with the same acceleration in a uniform gravitational field, although the proton radiates and the neutron does not. It is made clear that the question as to whether or not a charge radiates has a reference-dependent answer. An accelerated charge is not observed to radiate by an observer comoving with the charge, although an inertial observer finds that it radiates.

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Abbreviations

LAD:

Lorentz–Abraham–Dirac

LL:

Landau–Lifschitz

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Author information

Authors and Affiliations

  1. Oslo and Akershus University College of Applied Sciences, 0130, Oslo, Norway

    Øyvind Grøn

  2. Institute of Physics, University of Oslo, 0316, Oslo, Norway

    Øyvind Grøn

Authors
  1. Øyvind Grøn
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Correspondence to Øyvind Grøn .

Editor information

Editors and Affiliations

  1. Department of Physics, Pennsylvania State University, 16802, University Park, PA, USA

    Abhay Ashtekar

  2. Institute for Foundational Studies Hermann Minkowski, Montreal, Quebec, Canada

    Vesselin Petkov

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Grøn, Ø. (2014). Electrodynamics of Radiating Charges in a Gravitational Field. In: Ashtekar, A., Petkov, V. (eds) Springer Handbook of Spacetime. Springer Handbooks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41992-8_9

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  • DOI: https://doi.org/10.1007/978-3-642-41992-8_9

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