3D Visualization of Electric Fields of Point Charges

Tyrone Curtis

3DCharges.nb - Mathematica notebook

Summary of notebook contents

This is a Mathematica notebook for plotting electric field lines for a series of point charges in 3D.  Field lines are plotted by numerically solving the differential equations of the electric field.  Please note that this notebook has been created using Mathematica Version 5.1.  As such there may be incompatibilities with earlier versions of Mathematica.

Currently the notebook creates a random charge distribution, however it is possible to specify your own charge distribution.  Instructions on how this is done are included in the notebook.

Field lines may be generated starting around the charges, or starting from random positions in space (or you may specify the points to start the field lines at).  When the field lines are started from random positions, they are calculated both upfield and downfield.  The plotting method used will depend on the individual problem, for some situations it may be more informative to plot from random (or specified) positions rather than from around the charges.

Figures 1 shows the field lines for a dipole.   Figure 1 was generated starting the field lines around the charges. 

Figure 1 - Field lines for an electric dipole

There is also an option for generating an animation of the field lines so that you get a 360º view of the system - this uses the SpinShow command in Mathematica.

Unfortunately the field lines can look quite confusing and in a system with many charges it can be impossible to distinguish individual field lines.  This program may be more useful for viewing systems of charges from afar, to get an understanding of the system as a whole.

This notebook was created as a stepping-stone to plotting field lines for molecular data generated by Gromacs.  More information may be found on the 3D Visualization of electric fields of Charges from Gromacs page.