Using the charged ring potential we derive the potential and field for a homogeneously charged disk. Limiting cases and generalizations are discussed.

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.

We will study the movement of charged particles in a so-called Paul trap by solving the equations of motion using approximative methods.

The potential of a dipole in front of a flat metallic surface is calculated. A Taylor expansion is used to understand the resulting electric field.

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

We find the solution to the electrostatic problem of a homogeneously charged sphere. The electrostatic potential and fields are calculated.

We solve the problem of a spherical capacitor with (almost) arbitrary permittivity of the dielectric.

The movement of a charged particle along a surface subject to an external electric field is considered. We find the same equations of motion as for geodesic movement in general relativity.

A derivation of the boundary integral equation in electrostatics. The relation to the Boundary Element Method is explained.