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Stuck on the limits

  • Thread starter asi123
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1. Homework Statement

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. Homework Equations



3. The Attempt at a Solution
 

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LowlyPion

Homework Helper
3,079
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1. Homework Statement

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.
Calculate what potential? Gravity, electric potential of a uniform charge distribution in an insulator, on a conductor ... What are you trying to do?
 
258
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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?
Oh, sorry.
Electric potential.
 

LowlyPion

Homework Helper
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Oh, sorry.
Electric potential.
... and it's an insulator with uniform volume charge distribution perhaps? Or is it a half conducting sphere?
 
258
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... and it's an insulator with uniform volume charge distribution perhaps? Or is it a half conducting sphere?
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.
 

LowlyPion

Homework Helper
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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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