More on Maxwell and Twist Rings

Continuing to delve into Maxwell’s for the Twist Ring, I realized there should be several symmetries that will make this derivation easier, I think. The E-field component magnitude on the ring is constant, and the change in phase is also constant, so since the B field will be a derivative of this, its magnitude should also be constant around any circumference. I briefly looked into getting a Maxwell’s eqn solver on the web–no open source ones yet, and it looks like the commercial ones do not necessarily handle moving situations (they solve things like antenna problems where the antenna does not move). It might be worth trying to write one (iterative Maxwell’s solver for the twist ring), but I’d rather get an analytic solution if possible.

I’m a little worried that the symmetry of the E and B fields are such that you cannot get a 1/r^3 – 1/r^2 differential equation, and that got me to thinking–did I make a wrong turn concluding that the twist ring solution is of this form? It’s a perfectly legitimate solution to only use the magnetic portion of the Lorentz force equations, it will generate curvature as well (but haven’t yet derived whether it is stable like the 1/r^3 – 1/r^2 case–it might be better since the 1/r^3 – 1/r^2 has 3D direction dependencies). I had wondered about this before, since I was worried about the 1/r^2 component. You can’t have E field components attracting each other, only particles. If I only have the magnetic part to worry about, this might simplify the derivation, and could get rid of some nagging problems with the 1/r^2 attraction business. I’m starting to think that there’s no way an attraction can be part of the electron model, instead a single normal force due to the twist in a magnetic field at constant speed c should also generate a fixed radius ring.

Whatever the right model, I need to be able to answer the question why doesn’t a photon path get bent by an applied magnetic field (or an E field, for that matter), since I’m proposing that the same magnetic field within the twist ring is bending the ring. It’s got to either be the effect of a twist moving through a specific ring E field, or perhaps the locality and intensity of the B field in the vicinity of the ring path that isn’t duplicated by a global B (or E) field.



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