Solving Electric Potential 3: (kQ^2/R)

[asi123]

Electric potential 3 :)

Homework Statement

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.

Homework Equations

The Attempt at a Solution

 

[Defennder]

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 $$dV=r^2dr \sin \theta d\phi d\theta$$.

 

[asi123]

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 $$dV=r^2dr \sin \theta d\phi d\theta$$.

Thanks a lot.

 

[asi123]

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

 

[visharad]

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)

 

[Defennder]

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.