Free particle in a uniform external magnetic field

[espen180]

Assume we have a particle lying in the xy-plane with an initial velocity in the x-direction. If an external, constant and uniform magnetic field is applied in the z-direction, the particle, assuming it has a positive charge, will begin to do circular clockwise laps.

However, it seems to me that this negliges energy loss from radiation, and that the trajectory of the particle should decay in an exponential fashion.

I have never seen a derivation of this, and a search on the forum and google did not provide any results. Am I mistaken?

 

[Born2bwire]

That's correct and it was one of the big problems when considering the classical electron orbital. Take a look at the Larmor formula which provides an expression for the radiated power of an accelerating charge.

 

[espen180]

Thank you very much! :)

 

[technician]

You are correct and the effect is made use of in particle accelerators. In a synchroton electrons travel in a circular path and the resulting radiation is called synchroton radiation. It is one way to produce X-rays.

 

[chrisbaird]

I should mention that you have the get a charged particle to travel at a very high speed before you notice the radiation emitted due to its circular trajectory. An every-day-sized DC current through a circular loop of wire, like in a small motor, is not going to fry you with gamma rays.