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The Magnetic Interaction Energy between an Infinite Solenoid and a Passing Point Charge
KTH, School of Engineering Sciences (SCI), Mechanics. Royal Inst Technol KTH, Dept Mech, Stockholm, Sweden..ORCID iD: 0000-0003-0130-9643
Univ Helsinki, Dept Math & Stat, Helsinki, Finland..
2018 (English)In: Progress In Electromagnetics Research M, ISSN 1937-8726, Vol. 71, p. 145-156Article in journal (Refereed) Published
Abstract [en]

The standard expression for the magnetic interaction energy used in the study of the Aharonov-Bohm effect is investigated. We calculate the magnetic interaction energy between a point charge and an infinite solenoid from first principles. Two alternative expressions are used: the scalar products of the currents with the vector potentials and the scalar product of the magnetic fields. The alternatives are seen to agree. The latter approach also involves taking into account surface integrals at infinity, which are shown to be zero. Our model problem indicates no classical Aharonov-Bohm effect, but we also discuss the normally neglected fact of energy non-conservation. The problem is treated from the point of view of Lagrangian and Hamiltonian mechanics.

Place, publisher, year, edition, pages
ELECTROMAGNETICS ACAD , 2018. Vol. 71, p. 145-156
National Category
Energy Systems
Identifiers
URN: urn:nbn:se:kth:diva-237179DOI: 10.2528/PIERM18052908ISI: 000446219200015Scopus ID: 2-s2.0-85052614069OAI: oai:DiVA.org:kth-237179DiVA, id: diva2:1258191
Note

QC 20181024

Available from: 2018-10-24 Created: 2018-10-24 Last updated: 2018-10-24Bibliographically approved

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Essén, Hanno

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