Stuck integral (electric potential)

In summary, when calculating electric potentials, one encounters an integral of the form \int_{\mathcal{S}} \frac{d^2x'}{|\vec{x}-\vec{x'}|}, where \vec{x} is the vector from the origin to the field point and \vec{x'} is the vector from the origin to a point on the surface containing the charge distribution. For a surface with a uniform charge distribution bounded by two planes, such as the surface in the middle of the ventricular tissue with epicardium and endocardium walls, the approach for calculating this integral is not specified and further clarification is needed.
  • #1
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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:

[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?
 
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  • #2
Your link doesn't work.
 
  • #3
dx said:
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.
 
  • #4
You have to specify what the surface is more precisely.
 
  • #5
dx said:
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.
 

1. What is a "stuck integral" in relation to electric potential?

The term "stuck integral" refers to a situation where the value of an electric potential function becomes constant or "stuck" at a certain point in space. This can occur due to various factors such as the boundary conditions of the system, the behavior of the electric field, or the presence of charges in the vicinity.

2. How does a "stuck integral" affect the overall electric potential of a system?

A "stuck integral" can significantly affect the overall electric potential of a system by altering the behavior of the electric field. This can result in changes to the distribution of charges and the flow of currents, ultimately impacting the behavior and functioning of the system.

3. Can a "stuck integral" occur in both electric and magnetic fields?

Yes, a "stuck integral" can occur in both electric and magnetic fields. In both cases, it refers to a situation where the value of the potential function becomes constant or "stuck" at a certain point in space, affecting the behavior of the fields and the overall system.

4. What are some possible causes of a "stuck integral" in electric potential?

There are several possible causes of a "stuck integral" in electric potential, such as the presence of conductors or insulators, the boundary conditions of the system, the behavior of the electric field, and the presence of charges or current sources. These factors can influence the distribution of charges and the overall behavior of the electric potential in the system.

5. How can a "stuck integral" be identified and resolved in a system?

A "stuck integral" can be identified by analyzing the behavior of the electric potential and the electric field in the system. If the value of the potential function becomes constant at a certain point, it is likely a "stuck integral." To resolve this issue, the factors causing the "stuck integral" must be identified and addressed, such as adjusting boundary conditions, altering the behavior of the electric field, or modifying the presence of charges or current sources in the system.

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