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If the potential of a zero thickness spherical shell depends only on the `` polar angle...

If the potential of a zero thickness spherical shell depends only on the `` polar angle '' and is given by V (θ), being that inside and outside the sphere there is only empty space,
a) Show how to obtain expressions for the potential V (r, θ) inside and outside the sphere and how to obtain an expression for the electrical sources on the sphere.
b) Solve for V (θ) = V0cos2 (θ)
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