(a) Suppose the potential is a constant V0 over the surface of the sphere. Use the results of Ex. 3.6 and Ex. 3.7 to find the potential inside and outside the sphere. (Of course, you know the answers in advance—this is just a consistency check on the method.)
(b) Find the potential inside and outside a spherical shell that carries a uniform surface charge σ0, using the results of Ex. 3.9.
Reference 3.6
The potential V0(θ) is specified on the surface of a hollow sphere, of radius R. Find the potential inside the sphere.
Reference 3.7
The potential V0(θ) is again specified on the surface of a sphere of radius R, but this time we are asked to find the potential outside, assuming there is no charge there.
Reference 3.9
A specified charge density σ0(θ) is glued over the surface of a spherical shell of radius R. Find the resulting potential inside and outside the sphere.
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