Electric potential, solution to Laplace's Eq.

[nsatya]

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.

 

[gabbagabbahey]

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