# Stuck integral (electric potential)

## Homework Statement

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:

$$\int_{\mathcal{S}} \frac{d^2x'}{|\vec{x}-\vec{x'}|}$$

Where $\vec{x}$ 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), $\vec{x'}$ 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?

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dx
Homework Helper
Gold Member

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.

dx
Homework Helper
Gold Member
You have to specify what the surface is more precisely.

You have to specify what the surface is more precisely.
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.