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Electromagnetism in a Multiconnected Universe

Our raw intuition tells us that the topology of the universe shouldn′t affect the behavior of a current-carrying wire, but when the wire wraps all the way around a multiconnected space, our intuition is wrong. While an infinitely long perfectly conducting wire in Euclidean space may carry a constant...

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Detalles Bibliográficos
Autores principales: Mertens, Tom, Weeks, Jeff
Lenguaje:eng
Publicado: 2016
Materias:
Acceso en línea:https://dx.doi.org/10.4169/amer.math.monthly.123.3.280
http://cds.cern.ch/record/2267158
Descripción
Sumario:Our raw intuition tells us that the topology of the universe shouldn′t affect the behavior of a current-carrying wire, but when the wire wraps all the way around a multiconnected space, our intuition is wrong. While an infinitely long perfectly conducting wire in Euclidean space may carry a constant current, a simple application of the Ampère–Maxwell circuital law shows that the analogous wire in a 3-torus may not. Instead, we find that the current spontaneously oscillates, and the wire acts like an antenna, gradually radiating away its energy.