Surface magnetic charge distribution of a long, thin cylinder and its edge singularity

The surface magnetic charge distributions with edge singularities are studied for a half-infinite circular cylinder with uniform permeability. The cylinder is placed in an axially uniform magnetic field. The subject of this study is the charge densities around the edges on both side and end surfaces. The charge densities over a certain distance from the edge on the side surface are regarded as constant. It is shown that an integral equation can be found for the charge density around the edge on the side surface. The unknown quantity in the integral equation is expressed as a product of a bounded function and an edge-singular power function depending on the relative permeability. The charge density on the end surface is expressed as a function of the charge densities on the side surface. Numerical calculations are carried out for various values of the relative permeability and are illustrated to clarify the surface magnetic charge densities. The charge densities around 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 singularity power factor increases with the relative permeability μ and is equal to the same on the right-angled wedge of the same μ