Confirmation of understanding of electrodynamics

[polomeister]

Hi

I'm trying to get my head round why Maxwell's equations fail for the electron going round the atom.

The common sentence I see is along the lines of:

"Accelerating charges emit electromagnetic radiation (EMR), and a point electron orbiting a point nucleus would continually accelerate, therefore emit radiation, lose energy and fall into the atom"

However I can't find a derivation of this (could someone provide a link?)

What I have found is:
- a point charge has an electric field emanating from it
- if you vary an electric field then (via maxwells equations) this sets up waves throughout the field, to which we ascribe the interpretation of EMR

Is this correct?

If so, why do the waves carry energy away from the point charge, why can't they just be changes in the electric field without draining energy from the charge?

Thanks

 

[marcusl]

Look up synchrotron radiation (in Wikipedia, e.g.) for a discussion of how charges radiate during acceleration. The power density of EMR is given quantitatively by integrating the Poynting vector over a closed surface surrounding the charge. Thus energy is continually carried away by radiation.

 

[WannabeNewton]

Hi there! See the figure in this PDF: http://www2.astro.psu.edu/~niel/astro485/derivations/baker-larmor.pdf