quasar987,
A very interresting question. I found an answer by reading Landau-Lifchitz, field Theory.
Go back to the formula for the retarded potentials for a particle in motion, the so-called Liénard-Wiechert potentials.
A^i = e \frac{u^i}{R_k u^k}
where
R^k = [c(t-t'),\mathbf{r}-\mathbf{r}']
and where the prime coordinates are related by the light-cone condition:
R_k R^k = 0
t and r are the time and position of the observer and
t' and r' are those of the particle at the retarded time from the light-cone condition
From these expressions, the difference between constant velocity and variable velocity is rather obvious. Indeed, the fields are obtained by derivatives of the potential.
The calculation may be a little tricky, but the result to be expected must contain two terms:
one term where only coordinates and velocity will appear
a second term proportional to the time derivative of the velocity
It should be expected that the first term corresponds to static charges and currents and the second to waves.
The second term corresponds to the wave emission. It shows two clear wave-like features.
At large distance from the charge:
this electric field is perpenticular to the "line-of-sight" of the observer on the charge
this electric field varies as 1/R of 1/R² for a static potential
the Poynting vector is non-zero
These three features are markedly different from static fields and typical of electromagnetic waves in the vacuum. (sorry that the expression are a little bit too complicated for me to try writing them in Tex, this simple post took me already 30 minutes! See http://physics.usask.ca/~xiaoc/phys463/notes/note19.pdf" .)
Michel
Postscriptum:
This shows why we call the second term, proportional to the acceleration, a wave or radiative term.
However, the physical meaning still needs further clarification.
I would translate the missing link as such:
why does this electric field become perpendicular to the line-of-sight ?
why does the Poynting vector become non-zero ?
can these features be simply understood ? (picturaly, without algebra, ...)
Personally, thinking to ultra-sonic planes and how their bang occurs will help me a little bit to understand that. Indeed, fields "are emitted" with the speed of light, but the places where they are emitted from are not regularly spaced because of the acceleration. Therefore, the "emitted static fields" are deformed, sometimes compressed sometimes expanded depending on the actual motion. These distortions propagate as waves and carry their own energy.