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Electric potential, solution to Laplace's Eq.

  1. Feb 14, 2009 #1
    1. The problem statement, all variables and given/known data

    Prove that the potential outside of any radially symmetric charge distribution of total charge q, given by,

    V = q/(4*pi*epsilon_0*r)

    is a solution to Laplace's Equation.

    Hint: Only a masochist would solve this problem by solving Laplace's Equation. It is much easier to demonstrate that this solution is a solution to Laplace's equation.



    2. Relevant equations



    3. The attempt at a solution

    I first tried to plug V into Laplace's Equation del^2 V = 0. Since V only depends on r in this case, I thought I could just take the 2nd derivative of V and show that it is 0. I got to this point but could not go much further with it. Any help would be appreciated.
     
  2. jcsd
  3. Feb 14, 2009 #2

    gabbagabbahey

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    Hint: what is the Laplacian of any scalar function [tex]f[/tex] in spherical coordinates? Is the radial component really just [tex]\frac{\partial^2 f}{\partial r^2}[/tex] ? :wink:
     
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