Electrostatic fields of point charges studied on the computer

Abstract

An integrated software environment has been produced and used for the study of electrostatic fields created by point charges. The program allows modeling and visualizing arbitrarily complex systems of charges in a plane. Results include: geometric description and classification of field lines; methods that can be employed for arbitrary fields; sample field images, including all possible two-charge configurations. For all simple systems rigorous mathematical expressions are given. A correlation between electric flux and aspect of field lines is established.

Purpose of this paper

Assuming that we have obtained an image of the field, one would want to know why field lines behave the way they do. Take the field generated by two charges of opposite signs and different magnitudes q1 and q2; we can see that:

• some lines of force run from one charge to another; others escape to infinity before reaching the second charge
• some equipotentials close around q1, some around q2, and some around both charges.

These aspects are discussed in section 2.

Computer modeling

2 Description of field lines

2.2 Two charges in a plane

2.2.2 Lines of force

2.2.3 Equipotentials

2.3 Colinear charges

2.4 Arbitrary systems of charges -- conclusions

2.4.1 Four equal charges on a square

2.4.2 "Uniform" field

2.4.3 A random configuration

2.4.4 Composite dipole -- three charges

Miscellanea

Copyright 1996, 2004 Dan Alin Muresan