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Stuck integral (electric potential)

  1. May 26, 2009 #1
    1. The problem statement, all variables and given/known data

    When one calculates electric potentials, it involves integrating over the charge distribution, and for a surface with a uniform charge distribution, you encounter an integral of the form:

    [tex]\int_{\mathcal{S}} \frac{d^2x'}{|\vec{x}-\vec{x'}|}[/tex]

    Where [itex]\vec{x}[/itex] is the vector from the origin (in whatever coordinate system you choose) to the field point (the point at which you want to determine the potential), [itex]\vec{x'}[/itex] is the vector from the origin to a point on the surface containing the charge distribution, and the integration is over the source points.

    Now I want to calculate this integral but in the following situation:

    Here S is a surface which is bounded by two planes.

    Here's a picture which illustrates the situation:

    http://www.ccbm.jhu.edu/doc/presenta...sisDefense.pdf

    Page 41, picture D. You can see the two planes I was referring two. Here "S" is the surface which is exactly in the middle. Now x is a point OUTSIDE of S and x' is a point in S (of course at least one of them must be outside S otherwise the denominator is not defined).

    How can you approach this calculation?
     
    Last edited by a moderator: Apr 24, 2017
  2. jcsd
  3. May 26, 2009 #2

    dx

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    Your link doesn't work.
     
  4. May 26, 2009 #3
    Sorry. Here it is:

    After /doc it should be /presentations/pdf/ScollanThesisDefense.pdf

    That is: /doc/presentations/pdf/ScollanThesisDefense.pdf

    It is working, just checked it.
     
  5. May 26, 2009 #4

    dx

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    You have to specify what the surface is more precisely.
     
  6. May 26, 2009 #5
    That's all I'm given, I forgot to state that also S is assumed to be of infinite extent, basically S represents a part of the ventricular tissue which is separated by two walls: the epicardium and the endocardium.
     
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