Volume 20, Issue 3, October 2013, Pages 440 - 450
Magnetic fields in 2D and 3D sphere
Authors
Jose L. Cabrerizo
Department of Geometry and Topology, University of Seville, c/ Tarfia s/n Seville, 41012, Spain,jaraiz@us.es
Received 25 June 2013, Accepted 8 September 2013, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2013.855052How to use a DOI?
- Keywords
- Magnetic field; Killing field; Riemannian manifold
- 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.
- Copyright
- © 2013 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Jose L. Cabrerizo PY - 2021 DA - 2021/01/06 TI - Magnetic fields in 2D and 3D sphere JO - Journal of Nonlinear Mathematical Physics SP - 440 EP - 450 VL - 20 IS - 3 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2013.855052 DO - 10.1080/14029251.2013.855052 ID - Cabrerizo2021 ER -