{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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 = 0 ) 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 π (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 z =
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern