From Griffiths Third Edition: "Introduction to Electrodynamics" p.p. 81 ex. 2.6
"Find the potential inside and outside a spherical shell of radius R, which carries a uniform surface charge. Set the reference point at infinity.
V(r) = -∫E⋅dl
The Attempt at a Solution
The electric field inside the spherical shell is 0, so I'm looking at
V(r) = 0∫dl = 0 which attacks this problem by working from the center of the sphere outward. The issue is that, and this is what is confusing to me, something the author mentions: "It is tempting to suppose that you could figure out the potential inside the sphere alone but this is false: The potential inside the sphere is sensitive to what's going on outside the sphere as well" p.p 82 because what is going on outside the sphere in this situation? absolutely nothing except that the field generated by the charge distribution on the surface of the sphere radiates uniformly away from the sphere not towards it...so what is having an effect on the inside of the sphere?