Dipole Moments and Flux

The net force that the electric field produces on these charges is zero. However, the direction of these forces creates a torque about the midpoint of the distance between these two objects. The moment of this dipole is the product of the distance between these two charges and their charge. 

The work performed on the dipole by the torque is the negative of the change in potential energy of the dipole. At 90 degrees, there is zero potential energy and the dipole is in a stable position.

This is our prediction of what a given code written in python will produce.

These field lines help to describe the features of an electric field. The higher the maginude of the the charges, or the closer the charges are, the more dense the shading will be. Also, the lines flow away from positive charges, and toward negative charges. The 3 dimensional shapes at the bottom depict flux. Electric fields flow out a surface containing a
positive charge, and produce a positive flux. Electric fields flow out of a surface of containing a negative charge and produce a negative flux.

Flux is zero when the area vector is directed perpendicularly to an electric filed. Here the only two sides witnessing flux are the sides shaded green. The net flux through a closed surface is zero.