The diagrams I'm able to find online only show the concentric field lines in the particle's plane, perpendicular to the motion, which of course generalizes to the cylindrical shape around a conductor. Can someone share a nice representation of the three-dimensional magnetic field all around a moving point charge?
I highly recommend you look at the VPython programming environment. You can get it free for Windows, Mac, and Linux. Then go to this page on the Matter & Interactions support site and get the file named