A Simplified Trajectory for a Radiating Charge Moving in a Uniform Magnetic Field

Paolo Tritella

doi:doi:10.11648/j.ajz.20250802.13

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A Simplified Trajectory for a Radiating Charge Moving in a Uniform Magnetic Field

Paolo Tritella^*

Published in American Journal of Zoology (Volume 8, Issue 2)

Received: 8 February 2025 Accepted: 11 March 2025 Published: 21 June 2025

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Abstract

Is shown that a radiating charge moving in a constant uniform magnetic field has an approximated trajectory that copies the Euler spiral. Is made a classical study for the motion with some plausible approximations. By comparing the graph of Cornu’s spiral, which is considered not from the initial point, but from an advanced point to satisfy the initial conditions, and the image obtained with the bubble chamber, a strong correspondence can be seen. This simple result is the springboard for an exact result in which starting from a formula adapted to overcome the inconsistencies of the current formulas for the radiation reaction force, one obtains again the same result presented in this article as a limiting case. This suggests that the new formula can describe the phenomenon of the radiation reaction force with more accuracy, combined with the fact that the new formula, which I hope to be able to present in a future article, provides in other cases of motion without the magnetic field, quite plausible results.

Published in	American Journal of Zoology (Volume 8, Issue 2)
DOI	10.11648/j.ajz.20250802.13
Page(s)	38-42
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2025. Published by Science Publishing Group

Keywords

Pair Production, Trajectory, Magnetic Field, Cornu Spiral, Bubble Chamber, Radiation Reaction Force

References

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[2]	L. D. Landau - E. M. Lifsits, Teoria dei campi, edited by Editori Riuniti, 1981.
[3]	K. Lechner, Campi elettromagnetici, it.scribd.com
[4]	Misne Thorn Wheeler, Gravitation, edited by W. H. Freeman and Company, New York, 1973.
[5]	Benn-Tucker, An Introduction to Spinors and Geometry with Application in Physics, edited by Adam Hilger (IOP Publishing Ltd, 1989).
[6]	M. Bramanti, Esercitazioni di Analisi 2, edited by Esculapio, Bologna, 2012.
[7]	Richard T. Hammond, Relativistic Particle Motion and Radiation Reaction in Electrodynamics, EJTP 7, No. 23, 221 (2010).
[8]	Paul McKenna, High Field QED Experiments with ELI-NP 2x10PW Laser, http://www.nipne.ro/indico/getFile.py/access?contribId=45&resId=0&materialId=slides&confId=141
[9]	Oyvind Gron, Electrodynamics of Radiating Charges, Advances in Mathematical Physics Volume 2012 (2012), Article ID 528631, 29 pages.
[10]	F. Rohrlich, The Principle of equivalence, Annals of Physics 22, 169-191 (1963).
[11]	F. Crimin, B. M. Garraway, J. Verd?, The quantum theory ofthePenningtrap, https://www.tandfonline.com/doi/full/ 10.1080/09500340.2017.1393570
[12]	Eisberg Resnik, Quantum physics of atoms, nuclei, molecules, solids, nuclei,and particles, (second edition) edited by John Wiley & Sons (New York, 1985).
[13]	H. Goldstein, Meccanica classica, edited by Zanichelli, Bologna, 1986.
[14]	H. P. A. M. Dirac, Proc. Roy. Soc. A, (London) A167, 148 (1938).
[15]	E Eriksen and O Gron ,Relativistic dynamics in uniformly accelerated reference frames with application to the clock paradox, 1990 Eur. J. Phys. 11 39 (1990).
[16]	A. D. Yagjian, Relativistic Dynamics of a Charged Sphere, 2nd ed. Springer 2006.
[17]	P. A. M. Dirac, Proc. Roy. Soc. (London) A 167, 148 (1938).
[18]	G. Ares de Parga, R. Mares and S. Dominguez, “Landau-Lifshitz equation of motion for a charged particle revisited”, Am. J. Annales de la Fondation Louis de Broglie, Volume 30 no 3-4, 2005.
[19]	F. Rohrlich, Classical Charged Particles, 3rd ed. (World Scientific 2007.
[20]	H. Spohn, The critical manifold of the Lorentz-Dirac equation, Europhys. Lett. 50, 287 (2000).
[21]	I presocratici. Testimonianze e frammenti, a cura di Gabriele Giannantoni, Bari, Laterza, 1969.
[22]	F. Gaiffi, Istituzioni di storia della filosofia 1. issrtoscana, anno accademico 2020-2021.

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Tritella, P. (2025). A Simplified Trajectory for a Radiating Charge Moving in a Uniform Magnetic Field. American Journal of Zoology, 8(2), 38-42. https://doi.org/10.11648/j.ajz.20250802.13

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ACS Style

Tritella, P. A Simplified Trajectory for a Radiating Charge Moving in a Uniform Magnetic Field. Am. J. Zool. 2025, 8(2), 38-42. doi: 10.11648/j.ajz.20250802.13

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AMA Style

Tritella P. A Simplified Trajectory for a Radiating Charge Moving in a Uniform Magnetic Field. Am J Zool. 2025;8(2):38-42. doi: 10.11648/j.ajz.20250802.13

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@article{10.11648/j.ajz.20250802.13,
  author = {Paolo Tritella},
  title = {A Simplified Trajectory for a Radiating Charge Moving in a Uniform Magnetic Field},
  journal = {American Journal of Zoology},
  volume = {8},
  number = {2},
  pages = {38-42},
  doi = {10.11648/j.ajz.20250802.13},
  url = {https://doi.org/10.11648/j.ajz.20250802.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajz.20250802.13},
  abstract = {Is shown that a radiating charge moving in a constant uniform magnetic field has an approximated trajectory that copies the Euler spiral. Is made a classical study for the motion with some plausible approximations. By comparing the graph of Cornu’s spiral, which is considered not from the initial point, but from an advanced point to satisfy the initial conditions, and the image obtained with the bubble chamber, a strong correspondence can be seen. This simple result is the springboard for an exact result in which starting from a formula adapted to overcome the inconsistencies of the current formulas for the radiation reaction force, one obtains again the same result presented in this article as a limiting case. This suggests that the new formula can describe the phenomenon of the radiation reaction force with more accuracy, combined with the fact that the new formula, which I hope to be able to present in a future article, provides in other cases of motion without the magnetic field, quite plausible results.},
 year = {2025}
}

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TY  - JOUR
T1  - A Simplified Trajectory for a Radiating Charge Moving in a Uniform Magnetic Field
AU  - Paolo Tritella
Y1  - 2025/06/21
PY  - 2025
N1  - https://doi.org/10.11648/j.ajz.20250802.13
DO  - 10.11648/j.ajz.20250802.13
T2  - American Journal of Zoology
JF  - American Journal of Zoology
JO  - American Journal of Zoology
SP  - 38
EP  - 42
PB  - Science Publishing Group
SN  - 2994-7413
UR  - https://doi.org/10.11648/j.ajz.20250802.13
AB  - Is shown that a radiating charge moving in a constant uniform magnetic field has an approximated trajectory that copies the Euler spiral. Is made a classical study for the motion with some plausible approximations. By comparing the graph of Cornu’s spiral, which is considered not from the initial point, but from an advanced point to satisfy the initial conditions, and the image obtained with the bubble chamber, a strong correspondence can be seen. This simple result is the springboard for an exact result in which starting from a formula adapted to overcome the inconsistencies of the current formulas for the radiation reaction force, one obtains again the same result presented in this article as a limiting case. This suggests that the new formula can describe the phenomenon of the radiation reaction force with more accuracy, combined with the fact that the new formula, which I hope to be able to present in a future article, provides in other cases of motion without the magnetic field, quite plausible results.
VL  - 8
IS  - 2
ER  -

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Author Information

Paolo Tritella

Associazione Estone della Lingua e Cultura Italiana, Tallin, Estonia

Contact Email

http://orcid.org/0000-0003-4765-3917

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APA Style

Tritella, P. (2025). A Simplified Trajectory for a Radiating Charge Moving in a Uniform Magnetic Field. American Journal of Zoology, 8(2), 38-42. https://doi.org/10.11648/j.ajz.20250802.13

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ACS Style

Tritella, P. A Simplified Trajectory for a Radiating Charge Moving in a Uniform Magnetic Field. Am. J. Zool. 2025, 8(2), 38-42. doi: 10.11648/j.ajz.20250802.13

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AMA Style

Tritella P. A Simplified Trajectory for a Radiating Charge Moving in a Uniform Magnetic Field. Am J Zool. 2025;8(2):38-42. doi: 10.11648/j.ajz.20250802.13

Copy | Download

@article{10.11648/j.ajz.20250802.13,
  author = {Paolo Tritella},
  title = {A Simplified Trajectory for a Radiating Charge Moving in a Uniform Magnetic Field},
  journal = {American Journal of Zoology},
  volume = {8},
  number = {2},
  pages = {38-42},
  doi = {10.11648/j.ajz.20250802.13},
  url = {https://doi.org/10.11648/j.ajz.20250802.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajz.20250802.13},
  abstract = {Is shown that a radiating charge moving in a constant uniform magnetic field has an approximated trajectory that copies the Euler spiral. Is made a classical study for the motion with some plausible approximations. By comparing the graph of Cornu’s spiral, which is considered not from the initial point, but from an advanced point to satisfy the initial conditions, and the image obtained with the bubble chamber, a strong correspondence can be seen. This simple result is the springboard for an exact result in which starting from a formula adapted to overcome the inconsistencies of the current formulas for the radiation reaction force, one obtains again the same result presented in this article as a limiting case. This suggests that the new formula can describe the phenomenon of the radiation reaction force with more accuracy, combined with the fact that the new formula, which I hope to be able to present in a future article, provides in other cases of motion without the magnetic field, quite plausible results.},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - A Simplified Trajectory for a Radiating Charge Moving in a Uniform Magnetic Field
AU  - Paolo Tritella
Y1  - 2025/06/21
PY  - 2025
N1  - https://doi.org/10.11648/j.ajz.20250802.13
DO  - 10.11648/j.ajz.20250802.13
T2  - American Journal of Zoology
JF  - American Journal of Zoology
JO  - American Journal of Zoology
SP  - 38
EP  - 42
PB  - Science Publishing Group
SN  - 2994-7413
UR  - https://doi.org/10.11648/j.ajz.20250802.13
AB  - Is shown that a radiating charge moving in a constant uniform magnetic field has an approximated trajectory that copies the Euler spiral. Is made a classical study for the motion with some plausible approximations. By comparing the graph of Cornu’s spiral, which is considered not from the initial point, but from an advanced point to satisfy the initial conditions, and the image obtained with the bubble chamber, a strong correspondence can be seen. This simple result is the springboard for an exact result in which starting from a formula adapted to overcome the inconsistencies of the current formulas for the radiation reaction force, one obtains again the same result presented in this article as a limiting case. This suggests that the new formula can describe the phenomenon of the radiation reaction force with more accuracy, combined with the fact that the new formula, which I hope to be able to present in a future article, provides in other cases of motion without the magnetic field, quite plausible results.
VL  - 8
IS  - 2
ER  -

Copy | Download