Liénard-Wiechert Scalar Potential of Oscillating Particle (Classical Electrodynamics)
This is an animated plot of the Liénard-Wiechert potential due to a particle that was at rest before the video begins, but then starts oscillating in the horizontal direction with frequency 3E9 Hz, amplitude 8 cm.
The Liénard-Wiechert potential can be thought of as the relativistically correct version of the Coulomb potential; it reduces to the Coulomb form when the particle is stationary - which is what we see in the beginning of the video.
As soon as the particle starts moving, the potential field around it is effected; however, this disturbance spreads at a finite speed (the speed of light). In fact such disturbances in the potential field, spreading out over great distances, are what constitutes light!
The Liénard-Wiechert potentials can be found here:
http://en.wikipedia.org/wiki/Li%C3%A9...
I have written a C++ program that calculates these potentials for user-supplied particle motion. Computing the so-called "retarded time" was done using a binary search algorithm with accuracy on the order of the machine precision.
I created a series of bitmap images using my C++ program; I then used the excellent VirtualDub to create the video (virtualdub.sourceforge.net).