Punctiform charge, Maxwell’s equations and the meaning of the displacement current

Authors

DOI:

https://doi.org/10.15536/reducarmais.5.2021.2427

Keywords:

Punctiform charge, displacement current, Maxwell’s equations

Abstract

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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Author Biography

Paulo Cesar Facin, Universidade Estadual de Ponta Grossa/Departamento de Física

Possui graduação em Física pela Universidade Federal de Santa Maria (1987), mestrado em Física pela Universidade Federal da Paraíba (1991) e doutorado em Engenharia Mecânica pela Universidade Federal de Santa Catarina (2003). Atualmente é professor da Universidade Estadual de Ponta Grossa. Tem experiência na área de Física, com ênfase em Propriedades de Transportes de Matéria Condensada (Não Eletrônica), atuando principalmente nos seguintes temas: modelo de Boltzmann para escoamento de fluidos, permeabilidade intrínseca, energias alternativas, sustentabilidade e numeric simulation.

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.

Published

2021-06-14 — Updated on 2023-03-21

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How to Cite

Facin, P. C. (2023). Punctiform charge, Maxwell’s equations and the meaning of the displacement current. Educar Mais, 5(3), 698–708. https://doi.org/10.15536/reducarmais.5.2021.2427 (Original work published June 14, 2021)

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Articles