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As I navigate through physics stackexchange, I noticed Electron model under Maxwell's theory.

Electrons radiate light when revolving around nucleus? Why is it so obvious?

Note that I do not know anything about quantum mechanics - and I just want classical stories.

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3 Answers 3

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Because there is a changing configuration of charges with time, a time-dependent dipole moment. The electron's field is coming from a different center at different times, so that the field is oscillating in magnitude with a period the orbital period of the electron. When you have an oscillation of electric fields, it sets up oscillations of the entire electromagnetic field which goes out at the speed of light, and this is the radiation.

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  • $\begingroup$ Is it only the dipole? would a perfectly symmetric orbit not radiate classically? I have the impression it is the acceleration that is forcing radiation, and a rotating electron is continually accelerating ( giving brehmstrahlung in ring accelerators, getting worse with energy so that finally a linear collider is the only practical one at close to TeV energies). $\endgroup$
    – anna v
    Jun 26, 2012 at 5:39
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    $\begingroup$ If you make a classical ring of charge, and rotate it around a central nucleus, it will not radiate. $\endgroup$
    – Ron Maimon
    Jun 26, 2012 at 6:02
  • $\begingroup$ The electrons in the vacuum of the accelerators are guided by the magnetic fields to be in a perfect circle, but they do give off brehmstrahlung. Are you saying this radiation is not expected in classical electrodynamics? In addition then with your argument one could have an atom with several completely circular orbits around the nucleus, and the argument that classically you cannot have atoms will fail. $\endgroup$
    – anna v
    Jun 26, 2012 at 6:57
  • $\begingroup$ for example cv.nrao.edu/course/astr534/PDFnewfiles/LarmorRad.pdf $\endgroup$
    – anna v
    Jun 26, 2012 at 7:19
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    $\begingroup$ @annav: You need a uniform circular distribution, so that the current is steady, and then it is obvious that there is no radiation--- the current density is time independent as is the charge, so the equations settle down to a steady electric and magnetic field with no radiation. This doesn't invalidate anything, the field of orbiting point electrons don't settle down, and neither do bunched accelerator electrons. $\endgroup$
    – Ron Maimon
    Jun 26, 2012 at 7:36
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Any accelerated lectric charge radiates energy (bremsstrahlung). A circular orbit is accelerated (a=V^2/R) so the electron should radiates its energy. Rem: quantum mechanics does not explain the stability of the electron orbit because the Hamiltonian does not take into account the electromagnetic fields.One has to study the quantum electrodynamics to get the full picture right.

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First of all we all should know the meaning of the phrase "the electron is accelerating." It does not mean that $a=\mathrm{d}v/\mathrm{d}t$. The accelerating electron means that the electron is changing its electric field. Obviously no electromagnetic radiations will be produced during orbital motion of the electron because the electron doesn't radiate during orbital motion. Radiation will be emitted or absorbed only during transition between the energy states.

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