Potential Energy of a Finite Proton

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Homework Statement


This was in a problem set I found. Suppose that the proton in a hydrogen atom is not a pointlike object, but instead described by a uniform spherical charge distribution with charge e and radius R = 8.7 x 10^-16 m. Using Gauss's law and the definition for the electric potential, derive an expression for the potential energy of this finite sized proton.

Homework Equations


CodeCogsEqn (1).gif

CodeCogsEqn (1).gif

The Attempt at a Solution


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I tried to solve this but got lost in it. Any help?
 
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