Self inductance of a wire loop as a curve integral
It is shown that the self inductance of a wire loop can be written as a curve integral akin to the Neumann formula for the mutual inductance of two wire loops. The only difference is that contributions where the two integration variables get too close to each other must be excluded from the curve i...
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Advanced Electromagnetics
2016-01-01
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| Series: | Advanced Electromagnetics |
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| Online Access: | https://aemjournal.org/index.php/AEM/article/view/331 |
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doaj-c11a09f9d6f145e5ad006f06901a5c282020-11-25T01:53:46ZengAdvanced ElectromagneticsAdvanced Electromagnetics2119-02752016-01-015110.7716/aem.v5i1.331331Self inductance of a wire loop as a curve integralR. Dengler0Rohde and Schwarz GmbH and Co KG It is shown that the self inductance of a wire loop can be written as a curve integral akin to the Neumann formula for the mutual inductance of two wire loops. The only difference is that contributions where the two integration variables get too close to each other must be excluded from the curve integral and evaluated in detail. The contributions of these excluded segments depend on the distribution of the current in the cross section of the wire. They add to a simple constant proportional to the wire length. The error of the new expression is of first order in the wire radius if there are sharp corners and of second order in the wire radius for smooth wire loops. https://aemjournal.org/index.php/AEM/article/view/331self inductancecalculation |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
R. Dengler |
| spellingShingle |
R. Dengler Self inductance of a wire loop as a curve integral Advanced Electromagnetics self inductance calculation |
| author_facet |
R. Dengler |
| author_sort |
R. Dengler |
| title |
Self inductance of a wire loop as a curve integral |
| title_short |
Self inductance of a wire loop as a curve integral |
| title_full |
Self inductance of a wire loop as a curve integral |
| title_fullStr |
Self inductance of a wire loop as a curve integral |
| title_full_unstemmed |
Self inductance of a wire loop as a curve integral |
| title_sort |
self inductance of a wire loop as a curve integral |
| publisher |
Advanced Electromagnetics |
| series |
Advanced Electromagnetics |
| issn |
2119-0275 |
| publishDate |
2016-01-01 |
| description |
It is shown that the self inductance of a wire loop can be written as a curve integral akin to the Neumann formula for the mutual inductance of two wire loops. The only difference is that contributions where the two integration variables get too close to each other must be excluded from the curve integral and evaluated in detail. The contributions of these excluded segments depend on the distribution of the current in the cross section of the wire. They add to a simple constant proportional to the wire length. The error of the new expression is of first order in the wire radius if there are sharp corners and of second order in the wire radius for smooth wire loops.
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| topic |
self inductance calculation |
| url |
https://aemjournal.org/index.php/AEM/article/view/331 |
| work_keys_str_mv |
AT rdengler selfinductanceofawireloopasacurveintegral |
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