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The behavior of the magnetic potential near a point charge (fluxon) locatedat a curved regular boundary surface is shown to be essentially different fromthat of a volume point charge. In addition to the usual inverse distancesingularity, two singular terms are generally present. The first of them, alogarithmic one, is axially symmetric with respect to the boundary normal atthe charge location, and proportional to the sum of the two principalcurvatures of the boundary surface at this point, that is, to the local meancurvature. The second term is asymmetric and proportional to the difference ofthe two principal curvatures in question; it is also bounded at the chargelocation. Both terms vanish, apparently, if the charge is at a planar point ofthe boundary, and only in this case. The field in the charge vicinity behavesaccordingly, featuring generally two singular terms proportional to the inversedistance, in addition to the main inverse distance squared singularity. Thisresult is significant, in particular, for studying the interaction of magneticvortices in type II superconductors.Comment: 5 pages, 1 figure, RevTeX

Potential and field singularity at a surface point charge