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## Homework Statement

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?

## Homework Equations

## 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.)