(a) Show that the charge density of a point quadrupole is (r) = Q ij i...

(a) Show that the charge density of a point quadrupole is ρ(r) = Q_ij ∇_i ∇_j δ(r − r₀).

(b) Show that the force on a point quadrupole in a field E(r) is Q_ij ^∂_i^∂_jE(r₀).

(c) Show that the torque on a point quadrupole in a field E(r) is N = 2(Q · ∇) × E + r × F where (Q · ∇)_iQ_ij ∇_j.

(d) Show that the potential energy of a point quadrupole in a field E(r) is V_E = −Q_ij ∂_iE_j (r₀).