Indexing the archive…
Your Universe of Digital Possibilities
The rack had everything but electromagnetism — so here is the law that runs it, F = q(E + v×B), made visible. A charge is launched into fields you control and a Boris integrator traces where the Lorentz force takes it: a helix in a pure magnetic field, a sideways E×B drift in crossed fields, a mirroring, drifting shell in Earth's dipole. Drag to orbit; flip the charge and watch the gyration reverse while the drift stays exactly where it was.
The whole instrument in one line. E pushes a charge straight; the v × B term pushes it sideways, always perpendicular to motion — so it does no work and can only turn. Magnetism curves; electricity accelerates.
In a pure magnetic field the charge circles forever at the Larmor radius rL, turning at the cyclotron frequency ωc — which depends on the field and the charge-to-mass ratio, not on speed. Faster particles just trace bigger circles in the same time.
Cross an electric field with a magnetic one and the gyrating charge slides sideways at a steady drift — and the drift velocity is the same for every charge, positive or negative, light or heavy. The plasma moves as one; that’s the “aha”.
Everywhere else on the rack a field is a backdrop; here it is the whole subject. The magnetic part of the Lorentz force does no work — it is always perpendicular to the velocity — so it can only curve a path, never quicken it, and a free charge in a uniform field circles forever. Cross that field with an electric one and something stranger happens: the orbit drifts sideways at E×B/B², and the drift is identical for electrons and ions alike, which is why a magnetised plasma moves as a single fluid. Swap the uniform field for a dipole and you have the magnetosphere — the same three motions (gyration, mirror bounce, azimuthal drift) that paint the aurora and trap the Van Allen belts. Maxwell wrote the fields; The Cone on this rack is what they forced — relativity fell out of taking these equations seriously.