Maxwell’s equations revisited – mental imagery and mathematical symbols

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

Archivum mathematicum, Tome 59 (2023) no. 1, pp. 47-68

Abstract (VO)

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.

Détail

DOI : 10.5817/AM2023-1-47

Classification : 78A25
Keywords: Maxwell’s equations

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