Electric potential, solution to Laplace's Eq.

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Homework Statement



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.



Homework Equations





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.
 

Answers and Replies

  • #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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