Solving Limits on Homework: Stuck on x's Range

In summary, you are trying to find the electric potential at a point on a half-sphere with a uniform volume charge distribution.
  • #1
asi123
258
0

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

 

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  • #2
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?
 
  • #3
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.
 
  • #4
asi123 said:
Oh, sorry.
Electric potential.

... and it's an insulator with uniform volume charge distribution perhaps? Or is it a half conducting sphere?
 
  • #5
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.
 
  • #6
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.
 

1. What are limits in mathematics?

Limits in mathematics refer to the value that a function or sequence approaches as the input (x) approaches a certain value. It is used to describe the behavior of a function near a specific point.

2. How do I know if a limit exists?

A limit exists if the left-hand limit (approaching the value from the left side) and the right-hand limit (approaching the value from the right side) are equal. If they are not equal, then the limit does not exist.

3. What is the purpose of solving limits?

Solving limits helps us understand the behavior of a function at a specific point, which is important in many mathematical and scientific applications. It also helps us determine the continuity and differentiability of a function.

4. How do I solve limits on homework?

To solve limits on homework, you can use algebraic manipulation, substitution, or graphing methods to evaluate the limit. It is also important to check for any restrictions on the domain of the function and to consider the behavior of the function near the limit point.

5. What should I do if I am stuck on the range of x for a limit?

If you are stuck on the range of x for a limit, you can try graphing the function to get a visual representation of its behavior. You can also try using different values for x and see how the output changes. If you are still unsure, it is best to consult your teacher or a tutor for guidance.

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