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Electric Potential energy

  1. Aug 23, 2010 #1
    A sphere of radius r contains a charge Q distributed uniformly throughout its volume. Charge dQ is brought in from infinity and deposited uniformly over the surface. The potential energy of the charge dQ is [tex]Q dQ/4\pi\epsilon0[/tex].

    This follows naturally from the result for the potential of 2 point charges after noting
    (a) E due to Q is the same as a point charge and
    (b) smearing dQ around the sphere (i.e., tangential to the radial direction) doesn’t change the energy.

    Why/how does "smearing dQ around the sphere (i.e., tangential to the radial direction) not change the energy"?

    Thanks in advance for any help!

    [N B : I am a first year physics undergraduate.]
     
  2. jcsd
  3. Aug 23, 2010 #2
    I am sorry for the poor latex code. The potential energy expression should read [tex]Q dQ/4\pi\epsilon_{0}[/tex]
     
  4. Aug 23, 2010 #3
    Mistaken for the second time now. The potential energy expression should read [tex]Q dQ/4\pi\epsilon_{0}r[/tex]
     
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