# Homework Help: Electric potential 3

1. Dec 27, 2008

### asi123

Electric potential 3 :)

1. The problem statement, all variables and given/known data

Hey guys.
Look at this question, I'm suppose to find how much energy does it take to build this sphere with the new formula.
The answer suppose to be (3/5) * (kQ^2/R), instead I got (1/10) * (kQ^2/R).
I tried to solve it again and again but nothing, I couldn't find the problem.
Any idea where I got this wrong?

Thanks.

2. Relevant equations

3. The attempt at a solution

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2. Dec 27, 2008

### Defennder

Re: Electric potential 3 :)

I don't think $$d^3x = d^3 r$$. In this case it should have been $$dV=dxdydz$$, a triple integral in rectangular coordinates. So in spherical coordinates, where this problem is best solved, it should be $$dV=r^2dr \sin \theta d\phi d\theta$$.

3. Dec 28, 2008

### asi123

Re: Electric potential 3 :)

Thanks a lot.

Last edited: Dec 28, 2008
4. Dec 28, 2008

### asi123

Re: Electric potential 3 :)

I'm still getting the same answer, look at that.
Any idea?

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5. Dec 29, 2008

Re: Electric potential 3 :)

I have used symbol e for epsilon.
The formula you have used requires integration over all of space - not only over the sphere.
But the equation for electric field E will be different for inside sphere and outside sphere.
So you should break the integral into two parts. One from 0 to R and the other from R to infinity.
You have already done the first part. Do the second part and add the two.
For the second part,
E = KQ/r^2 (point is outside the sphere)

6. Dec 29, 2008

### Defennder

Re: Electric potential 3 :)

I think you need to tell us more about how the problem is set up. Is it a insulating charged spherical shell? Or a conducting shell? And yes you have to integrate over all space for r, visharad said.