emhw07 - Electromagnetic Theory I Problem Set 7 Due: 10...

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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 z-plane to the interior of the figure in the w-plane, with the real axis of the z-plane 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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emhw07 - Electromagnetic Theory I Problem Set 7 Due: 10...

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