(a) Write an expression for the volume charge density ρ(r) of a point charge q at r′. Make sure that the volume integral of ρ equals q.
(b) What is the volume charge density of an electric dipole, consisting of a point charge −q at the origin and a point charge +q at a?
(c) What is the volume charge density (in spherical coordinates) of a uniform, infinitesimally thin spherical shell of radius R and total charge Q, centered at the origin? [Beware: the integral over all space must equal Q.]