In the following problems we will be concerned with the movement of charged particles under the influence of an electrostatic field. Depending on the question we will have to solve Euler-Lagrange equations of motion or use similar approaches. A lot of the problems are historically motivated to which we shall refer in the respective background sections.
We will study the movement of charged particles in a so-called Paul trap by solving the equations of motion using approximative methods.
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.
The movement of a dipole-like molecule in a constant electric field is derived using the Euler-Lagrange equations.