The quadrupole moments of a homogeneously charged ellipsoid are calculated. The result will help us to understand how and why the quadrupole moments of an ellipsoidal charge distribution changes if it gets into an excited state.

We will calculate the first three multipole moments of a deformed charged sphere. Such a charge distribution is often used to model nuclei and understand their stability.

Starting from specific examples, we find the general form of the multipole moments for charge distributions with rotational symmetry.