https://doi.org/10.1140/epjp/s13360-025-06228-w
Regular Article
Generalized Runcorn’s theorem and crustal magnetism
Department of Physics, Faculty of Science, University of Zagreb, Bijenička cesta 32, 10000, Zagreb, Croatia
Received:
17
October
2024
Accepted:
17
March
2025
Published online:
8
April
2025
During the era of NASA’s Apollo missions, Keith S. Runcorn proposed an explanation of discrepancy between the Moon’s negligible global magnetic field and magnetized samples of lunar regolith, based on identical vanishing of external magnetic field of a spherical shell, magnetized by an internal source which is no longer present. We revisit and generalize the Runcorn’s result, showing that it is a consequence of a (weighted) orthogonality of gradients of harmonic functions on a spherical shell in arbitrary number of dimensions. Furthermore, we explore bounds on external magnetic field in the case when the idealized spherical shell is replaced with a more realistic geometric shape and when the thermoremanent magnetization susceptibility deviates from the spherical symmetry. Finally, we analyse a model of thermoremanent magnetization acquired by crustal inward cooling of a spherical astrophysical body and put some general bounds on the associated magnetic field.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
