Electromagnetism in a Multiconnected Universe. Issue 3 (1st March 2016)

• Record Type: Journal Article
• Authors: Mertens, Tom; Weeks, Jeff
• Is Part Of: American Mathematical Monthly. Volume 123:Issue 3(2016)
• Page Start: 280
• Page End: 286
• Publication Date: 2016-03-01
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.4169/amer.math.monthly.123.3.280
• Languages: English
• ISSNs: 0002-9890

Abstract

Abstract: 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 Ampere-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.