SURFACE MAGNETIC CHARGE-DISTRIBUTION OF A LONG, THIN CYLINDER AND ITSEDGE SINGULARITY

The surface magnetic charge distributions with edge singularities are studied for a half-infinite circular cylinder with uniform permeabilit y. The cylinder is placed in an axially uniform magnetic field. The su bject of this study is the charge densities around the edges on both s ide and end surfaces. The charge densities over a certain distance fro m the edge on the side surface are regarded as constant. It is shown t hat an integral equation can be found for the charge density around th e edge on the side surface. The unknown quantity in the integral equat ion is expressed as a product of a bounded function and an edge-singul ar power function depending on the relative permeability. The charge d ensity on the end surface is expressed as a function of the charge den sities on the side surface. Numerical calculations are carried out for various values of the relative permeability and are illustrated to cl arify the surface magnetic charge densities. The charge densities arou nd the edge are proportional to a certain inverse power of a distance from the edge. It is clarified for the first time that the edge singul arity power factor increases with the relative permeability mu and is equal to the same on the right-angled wedge of the same mu.