Actually, not even THAT is true. Farsight's radial plot might indeed be interpreted as electric field lines from a static charge; his bullseye plot might indeed be interpreted as magnetic field lines around a static line of current. (If he'd included an arrow, you would be able to make out the direction of the field which would break the symmetry you point out. But let's be generous and imagine such arrows was intended.)
I left out the arrows because in radial electric depictions they point outward for an electron and inward for a positron. See
this website which says "lines of force are also called field lines". But there isn't some outward force for an electron and some inward force for a positron. With no initial relative motion, the linear force depends on whether the particles have the same or opposite charge. And it either pushes them apart or pulls them together. It takes two to tango.
But in this case the spiral lines are NOT trajectories of charged particles...
No, think frame-dragging around a dynamical spinor. Think vorticial attraction and repulsion. Think cyclones. With no initial relative motion, two similar cyclones move apart, two opposite cyclones move together. It takes two to tango.
Magnetic field lines exert forces in the "cross" direction (F = v x B) which, no matter what the velocity is, is always perpendicular to B. Farsight's "spirals" have picked up a component parallel to B, in a direction where *neither* the radial nor the circumferential "lines" can exert a force. So those spirals are not force-directions, nor trajectories, nor anything else.
They depict the frame dragging around a dynamical spinor. If you throw an electron through a solenoid, its path is helical because it's a dynamical spinor moving through non-isotropic space.
I believe Farsight obtained them by just picturing "E + B", presumably believing that "electromagnetism" unification allows him to do this. He presumably was picturing "length of the little E arrow added to length of the little B arrow", which is how you graphically add vectors when the lengths represent magnitudes in the same units, but in this case is not true---in other words, it's precisely the "Shakespearean" crackpottery that you expected.
Clinger is a naysayer pumping out straw-man ad-hominem trash, and lots of it.
Also, as an aside, the "bullseye" pattern does NOT give the magnetic field lines of any actual static particle. That's the magnetic field of a line of current. Particles have magnetic dipoles...
So they aren't point-particles, are they? Hoist by your own petard, ben.
there is no slice of a dipole's field whose field lines look like Farsight's bullseye. Since Farsight comes right out and says this describes an "electron", we don't have to be generous: he's wrong.
The moot point is that the field concerned is the electromagnetic field, and you have to combine depictions of "the electric field" and "the magnetic field" to visualize it, whereafter you can understand it. Once you do understand it, you appreciate what Maxwell and Minkowski were talking about re the screw nature of electromagnetism, whereafter there's no going back.