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Complex analysis of electrostatic problem

  1. Jul 23, 2008 #1
    I'm not sure whether to post this in the Mathematics or Physics forums, but I figure this problem is easily reduced to its transformation irrespective of the physics it describes.

    Consider a semi-infinite sheet of (infinitely thin) conductor charged to a potential [tex]V[/tex]. It is placed at a distance [tex]h[/tex] perpendicular to a perfectly screening bulk conductor (so the electric field is always perpendicular to the surface). See the attachment below. I want to investigate the charge density on the surface of both sheets. I'm struggling to determine the transformation that can describe the electrostatic field.

    graphene1.jpg

    Now, I have calculated a similar problem with a semi-infinite conducting plane paralell to an infinite conducting plane at a distance [tex]h[/tex]

    graphene2.jpg

    I have transformed it into the upper half-plane (so it looks like a capacitor), and I found the transformation
    [tex]
    z = h \left( \frac{w}{V} - \frac{1}{\pi} \left(1+ e^{-\frac{\pi w}{V}} \right) \right)
    [/tex]
    determines this electrostatic field. How can I transform my problem with perpendicular planes into something similar? Can I use this result, with another transformation? Any help would be greatly appreciated.
     
    Last edited: Jul 23, 2008
  2. jcsd
  3. Jul 25, 2008 #2
    You should have posted this in the Physics boards, because not all the Math students are familiar with electrostatic concepts (sigh).
     
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