Consider the two-dimensional wedge-shaped region of Problem 2.26, with β=2π. This corresponds to a semi-infinite thin sheet of conductor on the positive x axis from x=a to infinity with a conducting cylinder of radius a fastened to its edge.
(a) Sketch the surface-charge densities on the cylinder and on the top and bottom of the sheet, using the lowest order solution.
(b) Calculate the total charge on the cylinder and compare with the total deficiency of charge on the sheet near the cylinder, that is, the total difference in charge for a finite compared with a=0, assuming that the charge density far from the cylinder is the same.