Horace Heffner wrote:
At 3:05 AM 12/4/4, Harry Veeder wrote:
Since it is acceptable to question conservation laws on this forum, perhaps CF is possible because the charge on subatomic particles is not conserved in all contexts.
Note: This is different from the concept of 'charge shielding'.
There are various concepts in which charge might not be conserved. Here is an example I posted here a while back that indicates apparent charge moving in a circle may vary depending the angle of observation.
Planar Circular Currents
BACKGROUND AND ASSUMPTIONS
It is well known that special relativity predicts changes in the observed field of a particle due to the flattening of the field in the direction of motion. This flattening is due to application of the Lorentz contraction due to relative motion. This relativistic effect of flattening the apparent field is called the "pancaking" of the Coulombic field. It is the intent here to discuss the effects of pancaking with respect to planar circular direct currents.
On p.492 of *The Electromagnetic Field*, Albert Shadowitz provides the equation for relativistic (Coulombic) field pancaking...
I had three comments on this analysis (which I snipped -- hope that's OK).
First, watch out for Shadowitz -- I've seen an instance where he messed up an analysis by using the "motion" of the EM field relative to a particle, which has no role in relativistic EM. Rindler, Jackson, and Griffiths seem more reliable, to name some I'm aware of. I don't know any reason to doubt Shadowitz's formula for pancaking, but you should definitely double check any general assertions he makes about how fields transform.
Second, pancaking of the field for a point charge is derived from evaluating the 4-vector potential for the charge using the retarded integral. Pancaking isn't really "fundamental"; the representation in terms of retarded integrals is. So, to see what's really going on in a complex situation involving accelerated charges, it's probably safer to use the retarded integrals directly.
Finally, let's do just that. For simplicity, assume a rotating ring of uniform negative charge density, with a fixed positive charge in the middle of the ring. Let's look at the axial field.
Since the ring is uniform, the 4-current density is not varying in time, and we can forget about the "retarded" part. The motion of the ring affects the spacelike parts of the integral but not the timelike part. So, the timelike part of the 4-vector potential will be identical to the timelike part of the 4-vector potential for a STATIONARY ring of charge.
The E field measured in the lab frame depends on the timelike part of the 4-vector potential, and on its time derivative. We already noted that the situation is time invariant, so the time derivative of the 4-vector potential is zero. So, the actual E field we measure is going to be IDENTICAL to the E field for a stationary ring of negative charge with a single positive charge in the center of the ring.
This field is well understood and it's certainly conservative.
It's got a nonzero dipole moment but the far field on axis goes rapidly to zero (1/r^3, I think?).
