Faraday's Law of Induction and the Electromagnetic Vector Potential

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Faraday's Law of Induction and the Electromagnetic Vector Potential. UNPUBLISHED. WORK IN PROGRESS

Jeffrey F. Gold Department of Physics, Department of Mathematics University of Utah

Abstra ct Faraday's Law of Induction is characterized by two expressions- the line integral form f E 路dl, and the rate of change of flux , -~fit J B 路da. These equations describe two different manifestations of the same phenomenon but are equivalent under very specific circumstances. It is possible to hypothesize a Gedanken experiment in which the equality of the two forms of Faraday's Law does not hold. Although the physical conditions for this hypothesis do not exist, an exploration of this issue raises important points about the role of the electromagnetic vector potential and the topology of the space in which it resides. The physical situation described possibly alludes to a generalization of the Aharonov-Bohm effect [1].

Introduction In 1831, Michael Faraday presented his findings on electromagnetic induction which were published in 1839 as Experimental Researches in Electricity. According to this established phenomenon, a current is generated in a sensing wire r if the magnetic flux <I>", through a surface a bounded by the wire, changes

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