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Published October 1, 2003 | public
Journal Article Open

Potential and field singularity at a surface point charge


The behavior of the magnetic potential near a point charge (fluxon) located at a curved regular boundary surface is shown to be essentially different from that of a volume point charge. In addition to the usual inverse distance singularity, two singular terms are generally present. The first of them, a logarithmic one, is axially symmetric with respect to the boundary normal at the charge location, and proportional to the sum of the two principal curvatures of the boundary surface at this point, that is, to the local mean curvature. The second term is asymmetric and proportional to the difference of the two principal curvatures in question; it is also bounded at the charge location. Both terms vanish, apparently, if the charge is at a planar point of the boundary, and only in this case. The field in the charge vicinity behaves accordingly, featuring generally two singular terms proportional to the inverse distance, in addition to the main inverse distance squared singularity. This result is significant, in particular, for studying the interaction of magnetic vortices in type II superconductors.

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©2003 American Institute of Physics. Received 14 May 2003; accepted 13 June 2003. We thank Leonid Bakaleinikov, David Gross, Lev Kapitanski, Akakii Melikidze, Andrei Ruckenstein, Andrey Shytov, and Robert Wagoner for discussions and valuable references. A.S. and partly I.M. were supported by NASA Grant No. NAS 8-39225 to Gravity Probe B. I.N. was supported by NSF Grant No. PHY99-07949 to Kavli Institute for Theoretical Physics.


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September 13, 2023
September 13, 2023