The text used Poisson’s equation to show that the charge density of a point electric dipole with moment p located at the point r₀ is ρ_D(r) = −p · ∇δ(r − r₀).
(a) Derive the given formula for ρ_D(r) using a limiting process analogous to the one used in the text to find its electrostatic potential.
(b) Show that the formula given above for ρ_D(r) is correct by demonstrating that it produces the expected dipole potential when inserted into the Coulomb integral for φ (r).