I am looking for a numerical simulation program which computes the trajectory of a charged particle moving in an electric field.
The electric field should be numerically determined by determining a geometry of charged conductors with defined electric potentials. In particular the following simple example should be possible:
In contrast to the picture above the program should work numerically with the "correct" inhomogenous electric field and not work with the simple infinite plate approximation.
The program should be free and run on linux, windows or via a browser interface.