Magnetic fields in 2D and 3D sphere |
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| Authors: | Jose L. Cabrerizo |
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| Affiliation: | 1. Department of Geometry and Topology, University of Seville, c/ Tarfia s/n Seville, 41012, Spain jaraiz@us.es |
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| Abstract: | In this note we study the Landau–Hall problem in the 2D and 3D unit sphere, that is, the motion of a charged particle in the presence of a static magnetic field. The magnetic flow is completely determined for any Riemannian surface of constant Gauss curvature, in particular, the unit 2D sphere. For the 3D case we consider Killing magnetic fields on the unit sphere, and we show that the magnetic flowlines are helices with the given Killing vector field as its axis. |
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| Keywords: | Magnetic field Killing field Riemannian manifold |
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