This is the code used to create the dipole gif. To avoid singularies you notice a displacement of .0001 and .0000001. Essentially, I created a table for various values of y and z, for each value of wt as wt goes from 1 to tnum (24 here). Notice that the expression El has a "reduced wt" so that the time really cycles from 0s to 1s, one complete cycle for a 1rad/s (~.16hz) oscillator, though multiplying all values of wt by A will give resutls for an A rad/s oscillator. The table is then exported to a gif file with a time delay per frame of .042 (1/24 second). Note: mathematica wouldn't let me copy paste without picking up strange formatting characters, so this is a screen shot.