When a charge is accelerated it brakes because it emits radiation. If a carge is accelerated with costant acceleration and the traiectory is a line what is the frequency of the emitted radiation? (I think 0Hz but i am not sure)

mfb
Mentor
0 Hz is not radiation. The charge will emit some frequency spectrum, the shape depends on the acceleration and the speed (=it changes over time).

The acceleration law in this case is:
ax=k
ay=0
Where k is a costant parameter and a is acceleration on the axis x and y

ChrisVer
Gold Member
??? I don't get the question...
if the charged particle is accelerated, it's going to radiate (and decelerate until "stopped" or somehow keep getting accelerated).

ZapperZ
Staff Emeritus
When a charge is accelerated it brakes because it emits radiation. If a carge is accelerated with costant acceleration and the traiectory is a line what is the frequency of the emitted radiation? (I think 0Hz but i am not sure)
I'm with @ChrisVer . This is very puzzling.

If the charge is accelerating due to some external field, then the charge will radiate due to that acceleration. Without that external agent, the charge won't be accelerating.

Braking radiation happens when the charge is slowing down (decelerating), such as when it enters a material. It is "braking", thus the name.

Your post appears to mix the two, which is very odd.

Zz.

Thank you

vanhees71
Gold Member
It may sound simple, but in fact it isn't. Constant acceleration means hyperbolic motion (it's hopeless to solve this problem in the non-relativistic limit since then you get faster-than-light motion of the charge, which simply makes no sense in electrodynamics), and the Bremsstrahlung of this motion is mathematically very delicate, because the worldline is asymptotically lightlike. The mathematical solution is physically well understandable: There is no way to really realize this motion but only for a finite time (e.g., approximately by running an electron through a plate capacitor, which always is of finite extent). So you first consider the problem where the particle is at constant proper acceleration for a long but finite time interval and assume that the particle runs as a free particle before and after this time interval and at the end make this time intervall going to the whole real axis. You find the careful analysis in the paper

J. Franklin, D. J. Griffiths, The fields of a charged particle in hyperbolic motion, Am. J. Phys. 82, 755 (2014)
https://dx.doi.org/10.1119/1.4875195
Erratum: American Journal of Physics 83, 278 (2015)
https://dx.doi.org/10.1119/1.4906577

mfb
tech99
Gold Member
When a charge is accelerated it brakes because it emits radiation. If a carge is accelerated with costant acceleration and the traiectory is a line what is the frequency of the emitted radiation? (I think 0Hz but i am not sure)
According to my book, Electromagnetic Vibrations, Waves and Radiation, by Bekefi and Barrett, for the case of braking radiation, or Bremsstrahlung, there is a pulse of radiation lasting for the duration of the event, t, and by Fourier analysis it has a uniform spectrum extending from zero frequency to 1/t Hz.
The same must presumably happen with an accelerating particle.
My own query is that the radiated E field appears to be unidirectional and extends to DC, and we cannot have radiation at zero frequency.