Address:
Institute for Materials Science and Max Bergmann Center of Biomaterials & Dresden Center for Computational Materials Science (DCMS), TU Dresden, Germany
Faculty of Mathematics, TU Dresden, Germany
Faculty of Mathematics, Institute of Analysis, TU Dresden, Germany
Faculty of Mathematics, TU Dresden, Germany
Faculty of Mathematics, Center for Dynamics and Institute of Analysis, TU Dresden, Germany
E-mail: konrad.kitzing@tu-dresden.de
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.
AMSclassification: primary 78A25.
Keywords: Maxwell’s equations.
DOI: 10.5817/AM2023-1-47