Solving Limits on Homework: Stuck on x's Range

[asi123]

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

The Attempt at a Solution

 

[LowlyPion]

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?

 

[asi123]

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]

Oh, sorry.
Electric potential.

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

 

[asi123]

... 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]

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.