Maxwell’s equations revisited – mental imagery and mathematical symbols

Matthias Geyer; Jan Hausmann; Konrad Kitzing; Madlyn Senkyr; Stefan Siegmund

Archivum Mathematicum (2023)

  • Volume: 059, Issue: 1, page 47-68
  • ISSN: 0044-8753

Abstract

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Using Maxwell’s mental imagery of a tube of fluid motion of an imaginary fluid, we derive his equations curl 𝐄 = - ∂ 𝐁 ∂ t , curl 𝐇 = ∂ 𝐃 ∂ t + 𝐣 , div 𝐃 = ϱ , div 𝐁 = 0 , which together with the constituting relations 𝐃 = ε 0 𝐄 , 𝐁 = μ 0 𝐇 , form what we call today Maxwell’s equations. Main tools are the divergence, curl and gradient integration theorems and a version of Poincare’s lemma formulated in vector calculus notation. Remarks on the history of the development of electrodynamic theory, quotations and references to original and secondary literature complement the paper.

How to cite

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Geyer, Matthias, et al. "Maxwell’s equations revisited – mental imagery and mathematical symbols." Archivum Mathematicum 059.1 (2023): 47-68. <http://eudml.org/doc/298979>.

@article{Geyer2023,
abstract = {Using Maxwell’s mental imagery of a tube of fluid motion of an imaginary fluid, we derive his equations $\operatorname\{curl\} \mathbf \{E\} = -\frac\{\partial \mathbf \{B\}\}\{\partial t\}$, $\operatorname\{curl\} \mathbf \{H\} = \frac\{\partial \mathbf \{D\}\}\{\partial t\} + \mathbf \{j\}$, $\operatorname\{div\} \mathbf \{D\} = \varrho $, $\operatorname\{div\} \mathbf \{B\} = 0$, which together with the constituting relations $\mathbf \{D\} = \varepsilon _0 \mathbf \{E\}$, $\mathbf \{B\} = \mu _0 \mathbf \{H\}$, form what we call today Maxwell’s equations. Main tools are the divergence, curl and gradient integration theorems and a version of Poincare’s lemma formulated in vector calculus notation. Remarks on the history of the development of electrodynamic theory, quotations and references to original and secondary literature complement the paper.},
author = {Geyer, Matthias, Hausmann, Jan, Kitzing, Konrad, Senkyr, Madlyn, Siegmund, Stefan},
journal = {Archivum Mathematicum},
keywords = {Maxwell’s equations},
language = {eng},
number = {1},
pages = {47-68},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Maxwell’s equations revisited – mental imagery and mathematical symbols},
url = {http://eudml.org/doc/298979},
volume = {059},
year = {2023},
}

TY - JOUR
AU - Geyer, Matthias
AU - Hausmann, Jan
AU - Kitzing, Konrad
AU - Senkyr, Madlyn
AU - Siegmund, Stefan
TI - Maxwell’s equations revisited – mental imagery and mathematical symbols
JO - Archivum Mathematicum
PY - 2023
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 059
IS - 1
SP - 47
EP - 68
AB - Using Maxwell’s mental imagery of a tube of fluid motion of an imaginary fluid, we derive his equations $\operatorname{curl} \mathbf {E} = -\frac{\partial \mathbf {B}}{\partial t}$, $\operatorname{curl} \mathbf {H} = \frac{\partial \mathbf {D}}{\partial t} + \mathbf {j}$, $\operatorname{div} \mathbf {D} = \varrho $, $\operatorname{div} \mathbf {B} = 0$, which together with the constituting relations $\mathbf {D} = \varepsilon _0 \mathbf {E}$, $\mathbf {B} = \mu _0 \mathbf {H}$, form what we call today Maxwell’s equations. Main tools are the divergence, curl and gradient integration theorems and a version of Poincare’s lemma formulated in vector calculus notation. Remarks on the history of the development of electrodynamic theory, quotations and references to original and secondary literature complement the paper.
LA - eng
KW - Maxwell’s equations
UR - http://eudml.org/doc/298979
ER -

References

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