# Stuck on the limits

## 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.

## The Attempt at a Solution

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LowlyPion
Homework Helper

## 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?

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

... 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
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.