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Calculate the electrostatic energy of a homogeneously charged sphere

  1. Oct 13, 2009 #1
    QUESTION:

    Calculate the electrostatic energy of a homogeneously charged sphere of Volume V and
    compare the result with 2 times the electrostatic energy of a homogeneously charged
    sphere of V/2.

    SOLUTION:

    OK, so we have a charge Q which is uniformly distributed within a sphere of radius, R.

    We know:
    q(r) is the charge in the sphere when it has
    attained radius, r.
    q(r)= [tex]\rho[/tex](4/3)[tex]\Pi[/tex]r3

    the work done in bringing a charge dq to it is dW
    dW= (q(r) dq)/(4[tex]\Pi[/tex]r[tex]\epsilon[/tex]0

    dq= [tex]\rho[/tex]4[tex]\Pi[/tex]r2dr

    so, we plug in the knowns:

    dW= ([tex]\rho[/tex](4/3)[tex]\Pi[/tex]r3 * [tex]\rho[/tex]4[tex]\Pi[/tex]r2dr )/ (4[tex]\Pi[/tex]r[tex]\epsilon[/tex]0)

    and integrate.

    Is this correct thus far?
    What are the limits?

    Thanks!
     
  2. jcsd
  3. Oct 13, 2009 #2

    G01

    User Avatar
    Homework Helper
    Gold Member

    Your bounds would be 0 to R as that covers the whole sphere.
     
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