Question

from the plane, show that the total charge on the half-cylinder (actually charge per unit length in the z direction) is twice as large as would reside on a strip of width 2a in its absence. Show that the extra portion is drawn from regions of the plane nearby, so that the total charge on a strip of width large compared to a is the same whether the half-cylinder is there or not. 2.27 Consider the two-dimensional wedge-shaped region of Problem 2.26, with B = 27. This corresponds to a semi-infinite thin sheet of conductor on the positive x axis from r = 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 defi- ciency 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.

2.27 classical electrodynamics 3rd edition jackson

Answer 1