Abstract
A geometric representation of magnetic fields in terms of plane bundles in R 3 is examined, and for two examples, the magnetic flux string and the monopole, it is shown how the field configurations can be related to the geometry of cones and spheres. Using the normal vector of the planes as a dynamical variable we treat the structure of the magnetic field in a way similar to that of an ordered medium. We especially compare it with the structure of the O(3) non-linear σ-model. Finally a geometric interpretation of electric charge is introduced by associating with charged particles a rotating, body-fixed frame which is constrained to rotate around the normal vector of the planes. The close connection with the Kaluza-Klein model is discussed.
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