Electric field in the vicinity of long thin conducting rods

We report on the results of numerical and analytical calculations of distributions of potentials and electric fields in the vicinity of thin conducting rods that model the leader channel of lightning and lightning rods. We consider rods represented in the form of a uniformly charged filament, a conducting ellipsoid with a free charge on its surface, as well an ellipsoid or a cylinder in a uniform external electric field. The effect of parameters of conducting rods modeling the leader channel of lightning and lightning rods, as well as the region containing a space charge around the tip of the leader channel, on the distribution of potentials and field strengths are analyzed. The conditions for the propagation of the counter leader from the lightning rod are specified.