If a and b are constant vectors, (r) = (a r) (b r) is the electrostatic potential in some region of space.

If a and b are constant vectors, ϕ(r) = (a × r) · (b × r) is the electrostatic potential in some region of space. Find the electric field E = −∇_ϕ and then the charge density ρ = ε₀∇ · E associated with this potential.