This example examines characteristics of electrostatic quadrupole configuration. Configurations such as these can frequently be found in electron optics instrumentation (electrostatic lenses), particle accelerators and beam transport lines (beam focusers).
Configuration consists of two pairs of electrodes, blue ones on -1000V and red ones on 1000V.
After solving for charge densities it is interesting to see various characteristics of electrostatic field structure on main sections. The picture below shows absolute field strength on the section which cuts electrodes configuration at the middle. One can clearly see that total electrostatic field strength vanishes in the middle of the quadrupole configuration, as the result of the symmetry of the problem.
Following calculation shows absolute field strength on one section.
If desired, a few characteristic points (points of minimal and maximal field strength) can be identified by analyzing x and z field components into more details.
Results of these calculations can be exported into a friendly formated text files and analysed in other powerful programming and calculating environments such as Matlab, Wolfram Mathematica, R, etc.