Suppose that there is a distribution of electric charge given by the charge density $\rho(\mathbf{x})$. Develop the multipole expansion, up to quadrupole terms, for the electrostatic potential $\phi$ and define the dipole and quadrupole moments of the charge distribution.

A tetrahedron has a vertex at $(1,1,1)$ where there is a point charge of strength $3 q$. At each of the other vertices located at $(1,-1,-1),(-1,1,-1)$ and $(-1,-1,1)$ there is a point charge of strength $-q$.

What is the dipole moment of this charge distribution?

What is the quadrupole moment?