Radiation emitted by an accelerated charge

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

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 refering 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).

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

Last edited:
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

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

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