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Energy of uniformly charged sphere watch

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    The nucleus of an atom can be considered to be a charge +Ze uniformly distributed
    throughout a sphere of radius a. Show that the potential energy of a nucleus due to its
    charge is \frac{3{Z^2}{e^2}}{20PEa} (where P is pi and E is the permittivity of free space) What would the potential energy be if the charge was spread uniformly
    over the surface of the nucleus?

    I'm guessing this is going to be similar in some way to the energy of a system of point charges, probably involving integrating up over small "pieces" of volume, but i'm at a loss with where to start, mainly due to a massive lack of sleep. A push in the right direction would be much appreciated.
 
 
 
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Updated: February 14, 2010
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