Punctiform charge, Maxwell’s equations and the meaning of the displacement current
DOI:
https://doi.org/10.15536/reducarmais.5.2021.2427Keywords:
Punctiform charge, displacement current, Maxwell’s equationsAbstract
This paper considers the case of a punctiform charge displacement in relation to the laboratory reference in constant speed, the electric and magnetic fields given by the electromagnetic four-potential Lorentz transformation. By assuming a limit tending to zero for the charge volume, we demonstrated that, as expected, this choice for the fields respects perfectly the four Maxwell’s equations. In addition, to our surprise, the displacement current term generalizes the current density term and makes the Ampere-Mawell’s law more symmetric when compared to the Faraday’s law. Therefore, we could notice that the discrete nature of this problem allowed us to capture the electric field variation with time, which is fundamental for the understanding of the displacement current and the Ampere-Maxwell’s law.
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References
ROCHE, John. The present status of Maxwell’s displacement current. Eur. J. Phys. 19 (1998) 155–166. Printed in the UK
CULLWICK, E. G. The Fundamentals of Electromagnetism for Engineering Students. Cambridge University Press, Cambridge, 1916.
ARTHUR, J. W. An Elementary View of Maxwell's Displacement Current. IEEE Antennas and Propagation Magazine, vol. 51, No. 6, p. 58 – 68, 2009.
LANDAU, L. D., LIFSCHITZ, E. M. The Classical Theory of Fields, Moscou, vol. 2, 1947, 99 p.
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- 2023-03-21 (2)
- 2021-06-14 (1)
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Copyright (c) 2021 Paulo Cesar Facin
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