About electric field lines of an arbitrarily moving point charge: https://arxiv.org/abs/1809.05868
We present an elementary derivation of a parametric equation describing electric field lines of an arbitrarily moving point charge. The found equation describes electric field lines as parametrized lines and occurs to be much simpler than the equation for the electric field which requires the solution of the implicit retarded-time equation. The found equation is generally valid and can be applied to arbitrarily complex and relativistic motions of a point charge. We exemplify this equation by considering four particular examples: an uniformly accelerated charge, an uniformly decelerated charge, a charge moving in a free electron laser, and a charge moving in a synchrotron.