Explain the multipole expansion in electrostatics, and devise formulae for the total charge, dipole moments and quadrupole moments given by a static charge distribution $\rho(\mathbf{r})$.

A nucleus is modelled as a uniform distribution of charge inside the ellipsoid

$$\frac{x^{2}}{a^{2}}+\frac{y^{2}}{a^{2}}+\frac{z^{2}}{c^{2}}=1$$

The total charge of the nucleus is $Q$. What are the dipole moments and quadrupole moments of this distribution?

Describe qualitatively what happens if the nucleus starts to oscillate.