  In this paper it is shown that the equations of electric field lines of an
arbitrarily moving charged particle in the general case are reduced to
homogeneous, linear differential equations with variable coefficients. For
trajectories where the expression b=Zeta/(Gamma*Kappa) is a constant (Zeta -
orbit torsion, Kappa - orbit curvature, Gamma - Lorentz factor of a particle)
these equations are reduced to homogeneous, linear differential equations with
constant coefficients. This case, in particular, includes all planar
trajectories. This paper presents solutions of the equations of electric field
lines and corresponding illustrations both in the orbital plane and outside it
for a charge moving in a flat monochromatic linearly polarized wave.
