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.

Using the magnetostatic potential can be extremely useful to calculate magnetostatic problems. In this example we use it to derive the magnetic field of a sphere with surface current.

The electrostatic potential of a dielectric sphere subject to an external field is calculated.