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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?

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How fast is it moving compared to $c$? –  ja72 Nov 17 '12 at 1:58
    
If it makes much difference, suppose two speeds: one slow, and one that is a significant fraction of c. –  Kaz Nov 21 '12 at 0:21

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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 21_B_movingproton.py and run it in VPython. Note that this particular program uses a relativistic field transformation to calculate the moving proton's magnetic field. If you want it, I'll post a similar program that calculates the moving proton's magnetic field from the Biot-Savart law.

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