1. The problem statement, all variables and given/known data Taking the proton to be a uniformly charged sphere of radius 1 fm, ﬁnd an expression for the change in potential experienced by the muon as compared with that in the case of a point-like proton. Use ﬁrst order perturbation theory to calculate the ground-state energy shift in muonic hydrogen 2. Relevant equations E=-grad(V) 3. The attempt at a solution The electric field due to a uniformly charged sphere is exactly the same as the field due to a point charge of the region outside the sphere (by a simple application of gauss's law). For this reason I see no need for the potential to change. What am I missing?