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Electro-static energy

  1. Jun 23, 2007 #1
    1. The problem statement, all variables and given/known data
    I have a question,it's not homework related..I know the electro-static energy of a sphere is:(3/5)kQ/R

    I tried to calculate it today using the expression:
    U = 1/2 * integral (phi * rho dV)
    where: phi is the potential, rho is charge density(uniform), dV is the volume element.

    it's not hard to calculate the potential everywhere in space,but my problem is when I integrate over volume elements (4*pi*r^2 dr) should I integrate over:
    r=0 to r=infinity? it doesnt seem reasonable because rho=0 outside the sphere.

    anyway I tried to do that,i.e integrating over r=0 to r=R using the potential inside the sphere,but I didnt get the correct answer.

    I would love to get some help with this.

  2. jcsd
  3. Jun 23, 2007 #2
    You're right: the integral should go over all of space (r = 0 to r = infinity), but since rho is 0 outside of the sphere, all of the integration that goes on outside the sphere amounts to 0. That's why it's OK to only integrate inside the sphere (r = 0 to r = R). So you should be set. If it's not coming out, check your math and your equations again. Is the sphere uniformly charged? Is it a hollow shell with the charge just on the outside? Make sure you know which situation you're looking at.

    P.S. I'm guessing that you're equation for the energy in the sphere ( (3/5)kQ/R ) is off. There should be a Q^2 term in there to make the units work...right now you have the units of an electric potential...which is potential energy per unit charge...they're closely related, but there's a distinct difference.
    Last edited: Jun 23, 2007
  4. Jun 23, 2007 #3
    of course I meant (3/5)kQ^2/R :)

    and you were right,I had a stupid math mistake(I really hate those)

    thanks alot.
  5. Jun 23, 2007 #4
    Those will get you every time! Gotta love it :tongue2: Glad it worked out though!
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