Consider the Dirac expression

For the vector potential of a magnetic monopole and its associated string L. Suppose for definiteness that the monopole is located at the origin and the string along the negative z axis.(a) Calculate A explicitly and show that in spherical coordinates it has components

(b) Verify that ? = ? x A is the Coulomb-like field of a point charge, except perhaps at ? = ?.

(c) With the ? determined in part b, evaluate the total magnetic flux passing through the circular loop of radius R sin ? shown in the figure. Consider ? ?/2 separately, but always calculate the upward flux.

(d) From ? ? ? dl around the loop, determine the total magnetic flux through the loop. Compare the result with that found in part ?. Show that they are equal for 0

dl x (x - ') A() |x ' 4 .