Find the primitive, Cartesian monopole, dipole, and quadrupole moments for each of the following charge distributions. Use the geometrical center of each as the origin.

(a) Two charges +q at two diagonal corners of a square (±a,±a, 0) and two minus charges −q at the two other diagonals of the square (±a ∓a, 0).

(b) A line segment with uniform charge per unit length λ which occupies the interval −ℓ ≤ z ≤ +ℓ.

(c) An origin-centered ring in the x-y plane with uniform charge per unit length λ and radius R.