A point charge q is located in free space a distance d from the center of a dielectric sphere of radius a (a<d) and dielectric constant ϵ/ϵ0.
((a)) Find the potential at all points in space as an expansion in spherical harmonics.
((b)) Calculate the rectangular components of the electric field near the center of the sphere.
((c)) Verify that, in the limit ϵ/ϵ0→∞, your result is the same as that for the conducting sphere.