Radiation emitted by an accelerated charge

[menachem]

I would need to know what is the state of the art about the study of the radiation emitted by an accelerated charge. According to classical EM theory, does a uniformly accelerated charge emit radiation? Or is the radiation proportional to the 3rd time derivative of position (so that a non-uniformly accelerated charge radiates..). When a charged body radiates (= loses energy) how can one observe the energy loss of the body? Is it still an open point in today's physics or has it been sorted out?
Thanks
Menachem

 

[vertices]

I would need to know what is the state of the art about the study of the radiation emitted by an accelerated charge. According to classical EM theory, does a uniformly accelerated charge emit radiation? Or is the radiation proportional to the 3rd time derivative of position (so that a non-uniformly accelerated charge radiates..). When a charged body radiates (= loses energy) how can one observe the energy loss of the body? Is it still an open point in today's physics or has it been sorted out?
Thanks
Menachem

No I don't think so - Bremstrahhlung radiation (is that what you are referring to?) is given off when electrons deflect off charged particles - if there is deflection, the acceleration isn't uniform.

One can measure the energy loss by using a scintillation counter (I think that's what you call it).

 

[Bob S]

Uniformly accelerating charges do emit radiation*. The acceleration can be either parallel to, or perpendicular to, the direction of motion of the charge. Are you interested in accelerating charges (currents) in wires, like an antenna, or accelerating charges in a vacuum like in an x-ray tube?
Bob S

*See Panofsky and Phillips, "Classical Electricity and Magnetism", Addison Wesley, page 302, Eq 19.22

 

[menachem]

thanx for your quick replies!
I don't know about x-ray tubes, but in antennas charges are not uniformly accelerating (they are subjected to a sinusoidal electric field).
Excuse my naivetè but i'll try to make an example: if I have an electrically charged iron ball (so a macrscopic charged body, which should act according to classical EM theory) and I drop it from the top of a tower, does it radiate?
(as soon as possible I'll try to have a look at the reference you Bob point me at)
Thanks
Menachem

 

[vertices]

thanx for your quick replies!
I don't know about x-ray tubes, but in antennas charges are not uniformly accelerating (they are subjected to a sinusoidal electric field).
Excuse my naivetè but i'll try to make an example: if I have an electrically charged iron ball (so a macrscopic charged body, which should act according to classical EM theory) and I drop it from the top of a tower, does it radiate?
(as soon as possible I'll try to have a look at the reference you Bob point me at)
Thanks
Menachem

Yes it would, although the amount of energy would be miniscule. This link might be useful:

http://hyperphysics.phy-astr.gsu.edu/HBASE/Particles/synchrotron.html

 

[Bob S]

if I have an electrically charged iron ball (so a macrscopic charged body, which should act according to classical EM theory) and I drop it from the top of a tower, does it radiate?

Yes. According to Panofsky and Phillips "Classical Electricity and Magnetism" Eq 19.22, the radiated power for a uniformly accelerating charge parallel to its velocity is proportional to

-dW/dt = ~[du/dt]² where u is velocity

Yes it would, although the amount of energy would be miniscule. This link might be useful:

http://hyperphysics.phy-astr.gsu.edu/HBASE/Particles/synchrotron.html

This link is for acceleration perpendicular to velocity (synchrotron radiation).

Bob S

 

[menachem]

ok thank u guys.. things are getting clearer in my mind.
The link provided by vertices is actually about a uniformly accelerating charge (what I was looking for), and the formula provided there agrees with the proportion given by Bob: -dW/dt = ~[du/dt]2 (the minus sign is negligible here, being due to a convention). The first formula given in this link is presented as valid for any accelerated charge. I would like to know if this is a "unifying formula" that works for (uniformly and not uniformly) accelerated charges, and not only and not only acceleration perpendicular to velocity. And secondly again I'd like to know what kind of energy loss happens in an accelerating charged macroscopic body that radiates? Is it energy loss of electrons going from a higher-energy to a lower-energy level?
Thanks
Menachem

 

[Rajini]

there is no change of electron state! but electron losses may be due to poor vacuum, losses due to electrons hitting the wall, and so on..usually in synchrotron additional external electric field (in the for of radio freq.) is supplied for keep the electrons running permanently..