We model the Hydrogen atom as a charge distribution in which the proton (a point charge) is surrounded by negative charge with the volume density of ρ = -ρ0 * exp (-2r/a0) where a0 is the Bohr radius. And ρ0 is a constant chosen such that the entire atomic distribution is neutral. What is the electrostatic energy contained within the electric field of outer region of the sphere of radius a0?
The Attempt at a Solution
I have tried reducing the sphere to a point charge, but it doesn't work for neutral distributions (Should've figured that sooner.) Generally, I've tried to apply everything I could as far as the formula W (energy) = ∫ φ * dq goes (where φ is the electrostatic potential, and dq is the charge.)