  Generation of electromagnetic fields by moving charges is a fascinating topic
where the tight connection between classical electrodynamics and special
relativity becomes particularly apparent. One can gain direct insight into the
fascinating structure of such fields by visualizing the electric field lines.
However, the calculation of electric field lines for arbitrarily moving charges
is far from trivial. Here, we derive an equation for the director that points
from the retarded position of a moving charge towards a specific field line
position, which allows for a simple construction of these lines. We
analytically solve this equation for several special but important cases: for
an arbitrary rectilinear motion, for the motion within the wiggler magnetic
field of a free electron laser, and for the motion in a synchrotron.

Classical Physics