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Stuck on the limits

  1. Feb 24, 2009 #1
    1. The problem statement, all variables and given/known data

    Hey guys.
    So I've got half a ball from 0 to point A as you can see in the pic and I need to calculate the potential of the ball at point A.
    So what I did is to break it into disks.
    I found the differential potential of a volume ring which is inside the disk at point A and now I need to sum it up.
    I know that I need to take r from 0 to R, my problem is with x, what are its limits? I mean it keep changing from disk to disk.
    I hope the problem is clear.
    Thanks a lot.


    2. Relevant equations



    3. The attempt at a solution
     

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  3. Feb 24, 2009 #2

    LowlyPion

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    Calculate what potential? Gravity, electric potential of a uniform charge distribution in an insulator, on a conductor ... What are you trying to do?
     
  4. Feb 24, 2009 #3
    Oh, sorry.
    Electric potential.
     
  5. Feb 24, 2009 #4

    LowlyPion

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    ... and it's an insulator with uniform volume charge distribution perhaps? Or is it a half conducting sphere?
     
  6. Feb 24, 2009 #5
    Well, it's half a sphere with a uniform volume charge distribution (p). I used it in the formula.
    Sorry again, my English kind of sucks.

    Thanks.
     
  7. Feb 24, 2009 #6

    LowlyPion

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    I would figure the integrals separately to avoid confusion, doing first the disks and then summing the little disks along the x-axis.

    The radius of each little disk is (R² -x²)1/2 such that at x = 0 the circumference of the rings are 2π*R and that distance from around the rings to A is ((A-x)² + y²)1/2.

    You would integrate that y from 0 to (R² -x²)1/2. I think that should give you the disks, that you then can integrate in x from 0 to R.

    I understand you can express it all as a double integral directly, but I'm a slow guy that likes to keep things straight.
     
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