Solving Limits on Homework: Stuck on x's Range

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The discussion revolves around calculating the electric potential at point A from a half sphere with a uniform volume charge distribution. The user initially breaks the problem into disks but struggles with determining the limits for the variable x, which changes with each disk. Clarifications reveal that the potential is indeed electric, and the setup involves integrating the contributions from each disk along the x-axis. Suggestions include separately integrating the disks and then summing them, with specific formulas provided for the radius of the disks and the distance to point A. The conversation emphasizes a methodical approach to solving the integral for clarity.
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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.


Homework Equations





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asi123 said:

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?
 
LowlyPion said:
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.
 
asi123 said:
Oh, sorry.
Electric potential.

... and it's an insulator with uniform volume charge distribution perhaps? Or is it a half conducting sphere?
 
LowlyPion said:
... 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.
 
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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