Trajectory of an electron passing through the deflection plattes of an oscilloscope

Description:

The package PlattenC.tgz serves for the computation of the non-relativistic trajectory of an electron passing through a charged plate capacitor with square plates. The influence of the field at the rim of the capacitor has been of special interest for a lecture on the basics in electrostatic field theory by Prof. Schwarz (IEE, TU-Dresden).

The electrostatic field of the capacitor is computed by a simple boundary element method (method of moments) implemented in plattenC.cc. The dynamical interaction of the electron charge and the charge on the capacitor plates is not regarded.

The non-relativistic trajectory of the electron is computed by an explicite Runge-Kutta method implemented in Maths/tobiRungeKutta.cc.

Note, that the package was not realy intented for a release. Up to the moment it lacks any concise description. Maybe, you can gather some useful information from the Makefile. If the Makefile fails, you have bad luck.

Author: Tobias Nähring
License: GPL (http://www.gnu.org/)
Version: 0.0.1
Requirements: Linux; g++ ≥ 2.95; gnuplot ≥ 3.7; gnu-make ≥ 3.8; a recent latex distribution
Download: PlattenC.tgz

Results


Figure 1: At first the setup of the model:

setup


Figure 2: The iso-potential lines of the electrostatic potential of the plate capacitor and the trajectory of the electron

trajectory


Figures 3 and 4: The speed of the electron in x- and y-direction

speed in x-dir. speed in y-dir.


Figure 5: The absolute value of the speed.

speed

Here, we see that finally the electron looses all its kinetic energy gained while dropping into the potential pot of the positive capacitor plate. Please take a further look on figure 2 and note that at the rim of the capacitor the electron runs up the potential barrier almost perpenticular to the iso-potential lines. So, the velocity vector of the electron changes mainly in absolute value and (almost) not in direction.


Figure 6: The x-component of the electrical field strength at the momentary position of the electron. (vs. x-position of the electron).

Ex


Figure 7: The y-component of the electrical field strength at the momentary position of the electron. (vs. x-position of the electron).

Ey