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Unformatted text preview: Electromagnetic Theory I Problem Set 7 Due: 10 October 2011 25. J, Problem 3.23. Note that you are actually obtaining various representations of the Dirichlet Green function (just set q = ) for the interior of a cylinder when you do this problem. In particular, the form in part c) is an expansion of the Green function in a complete set of functions in all three coordinates as we discussed in class. 26. Consider 2 dimensional electrostatics on the interior of the figure shown. The width of strip 3 is L , and strips 1,2 are of equal width. We are interested in finding the Dirichlet Green function for this problem via conformal mapping. 1 2 3 A w=w w=w +i L w=w +i L/2 1 1 1 a) Show that the analytic function w = w 1 + iw 2 = f ( z ) L 2 (ln z + ln( z 1)) (1) maps the upper half zplane to the interior of the figure in the wplane, with the real axis of the zplane mapping to the boundary of the figure. Note that the points z = 0 , 1 map to the ends of strips 1 , 2 at w 1 = respectively, and that the point...
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 Spring '08
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