Frequency of Radiating EM Waves from a Moving Electron on a Unit Circle

[qoqosz]

Let's assume that electron is moving around the unit circle. Using Maxwell equations show what is the frequency of radiating EM waves.
How to start with it? What's the form of known variables - current density and charge density?

 

[Meir Achuz]

If all you want is the frequency, calculate omega from the electron's velocity and the radius.

 

[qoqosz]

I know that, but I'd like to derive it somehow.

 

[GRDixon]

An electron can travel in a circle, at a constant speed, only if it is driven by a tangential force that points in the same direction as the instantaneous velocity. The power expended by that force is constant, and thus the radiation can only be circularly polarized. You can solve for the electric field at some point above the circular orbit's center and will find that E spins about that line with the same frequency as the frequency of electron revolution.

 

[conway]

Well, it's circularly polarized only if you look at it directly along the axis of the loop. The radiation in the plane of the loop is of course linearly polarized.

 

[qoqosz]

Ok, thanks.

 

[GRDixon]

Well, it's circularly polarized only if you look at it directly along the axis of the loop. The radiation in the plane of the loop is of course linearly polarized.

It's "elliptically polarized" (if you prefer) everywhere. In the orbital plane the minor axis goes to the minimum limit of zero.