Magnetic charge densities around edges of circular cylinders

For a circular cylindrical magnetic body placed in a uniform axial magnetic field, the charge densities on the end and side surfaces are numerically calculated and illustrated for various cases of different aspect ratio and relative permeability. The results show that the charge densities are proportional to a certain inverse power of distance to the edge; this means that singularity occurs near the edge. The singularity is strongly dependent on the permeability but almost independent of the aspect ratio. Approximative formulas are given for the power indices