The Maxwell Conjecture is False
- View PDF HTML (experimental) Abstract:We exhibit a configuration of five point charges in Euclidean space whose electrostatic potential admits at least 24 critical points all of which are non-degenerate.
- Maxwell's conjecture that the field of \(n\) point charges has at most \((n-1)^2\) critical points which are all non-degenerate is therefore false.
- Subjects: Classical Physics (physics.class-ph); Mathematical Physics (math-ph) Cite as: arXiv:2607.27197 [physics.class-ph] (or arXiv:2607.27197v1 [physics.class-ph] for this version) https://doi.org/10.48550/arXiv.2607.27197 arXiv-issued DOI via D
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- View PDF HTML (experimental) Abstract:We exhibit a configuration of five point charges in Euclidean space whose electrostatic potential admits at least 24 critical points all of which are non-degenerate.
- Maxwell's conjecture that the field of \(n\) point charges has at most \((n-1)^2\) critical points which are all non-degenerate is therefore false.
- Subjects: Classical Physics (physics.class-ph); Mathematical Physics (math-ph) Cite as: arXiv:2607.27197 [physics.class-ph] (or arXiv:2607.27197v1 [physics.class-ph] for this version) https://doi.org/10.48550/arXiv.2607.27197 arXiv-issued DOI via D
Sources: Arxiv