Stuck integral (electric potential)

[Carl140]

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?

 

[dx]

Your link doesn't work.

 

[Carl140]

Your link doesn't work.

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]

You have to specify what the surface is more precisely.

 

[Carl140]

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.