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Title: Maxwell’s equations revisited – mental imagery and mathematical symbols (English)
Author: Geyer, Matthias
Author: Hausmann, Jan
Author: Kitzing, Konrad
Author: Senkyr, Madlyn
Author: Siegmund, Stefan
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 59
Issue: 1
Year: 2023
Pages: 47-68
Summary lang: English
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Category: math
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Summary: 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. (English)
Keyword: Maxwell’s equations
MSC: 78A25
idZBL: Zbl 07675574
idMR: MR4563016
DOI: 10.5817/AM2023-1-47
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Date available: 2023-02-22T14:26:22Z
Last updated: 2023-05-04
Stable URL: http://hdl.handle.net/10338.dmlcz/151550
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