Trajectory of charged particle in uniform gravitational potential

[jjustinn]

It sounds like an easy-enough problem, but even writing down the ridiculously nonlinear equation that would need to be solved is making my face hurt.

I'm talking classical/Newtonian gravitation, action-at-a-distance, constant-force. It could really be any external non-EM conserved force; gravity just seemed like the easiest.

However, the charge is NOT a test charge: e.g. its own self-field reactions are important.

Let's say it's a spherical marble, 1cm diameter, weighing 5g and charged to 1C, released from rest in a vacuum 50m above the surface.

Now I seem to recall that there is no "radiative braking" on a charge with uniform acceleration -- which is what the trajectory would be if there was no radiative braking...so you see why my face hurts.

Has anyone tackled this (or something similar) in he past? It seems like it should be about the simplest possible situation -- ye olde one-body problem -- but I can't find any references to it.

Thanks,
Justin

 

[haruspex]

Now I seem to recall that there is no "radiative braking" on a charge with uniform acceleration

My understanding is that a net acceleration of charge always has associated radiation, whether absorption or emission.

 

[cragar]

the question you ask is not simple at all. You want to know if a charged object in free-fall will radiate. Well we have Einsteins equivalence principle that says being in free fall is like floating in free-space. Try looking up radiation from objects in free-fall.

 

[jjustinn]

the question you ask is not simple at all. You want to know if a charged object in free-fall will radiate. Well we have Einsteins equivalence principle that says being in free fall is like floating in free-space. Try looking up radiation from objects in free-fall.

That's why I was hesitant to say "gravity" and tried to make clear that I was only talking about non-relativistic gravity; if you prefer, you can think of it as an unknown constant-potential field whose coupling has nothing to do with either force or mass; for instance, the great invisible pink unicorn stamps upon the particle so that it exerts a constant force upon it.

The problem you're talking about *is* very interesting, and there seems to be a lot of lively debate on the topic...which, unfortunately, makes finding discussion of the "simpler" problem nearly impossible ;).

My understanding is that a net acceleration of charge always has associated radiation, whether absorption or emission.

Right -- but just because there is power being radiated (Larmou formula-power proportional to acceleration) doesn't mean there's a net force on the particle (Abraham-Lorentz: force proportional to jerk). This link explains that part (http://books.google.com/books?id=Lh...orce on uniformly accelerating charge&f=false), but of course doesn't go into the consequences of this with respect to an unconstrained charge experiencing a net force; apparently the net energy flux out (Larmour formula) is exactly balanced by the energy flux in (work on the particle?)...