Forces and Movement
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.
The theoretical description of the movement of a particle in some curved 3D-space and the movement of it on a 2D-surface are equivalent. Both entities are described by a metric and the equation of motion is the geodesic equation. Further giving the particle a charge lets it further interact with an electric field. In this problem you can learn to derive the corresponding geodesic equation.