TY - JOUR

T1 - Potential and field singularity at a surface point charge

AU - Silbergleit, Alexander

AU - Mandel, Ilya

AU - Nemenman, Ilya

PY - 2003/10/1

Y1 - 2003/10/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0142136727&partnerID=8YFLogxK

U2 - 10.1063/1.1605497

DO - 10.1063/1.1605497

M3 - Article

AN - SCOPUS:0142136727

VL - 44

SP - 4460

EP - 4466

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 10

ER -