Calculation of the electric field distribution in the vicinity of the conductive rod

The article reviews the methods of mathematical modeling of electric fields in the vicinity of conducting rods and presents a method developed for calculating the distribution of the electric field strength and potential in systems with conducting rods. This method allows to use a computational spatial grid with a step proportional not to the radius of the rod, but to its length, which is relevant when the ratio of the rods length to its radius is large. The method is applied to the calculation of rods EF, for which this ratio is of the order of 10–10. The proposed method is based on the finite integration method. At the same time, the nonlinear decrease in the levels of strength and potential when moving away from the rod in directions perpendicular to its axis is taken into account. The difference coefficients at the nodes surrounding the rod were obtained by integrating over the computational grid cell surfaces of expressions describing the strength and potential of the electric field for an elongated conducting ellipsoid under potential. With this representation of the conducting rod, it was possible to achieve the greatest accordance of calculations with the analytical solution. In practice, the application of the presented method allows for a more accurate calculation of the electric field in the vicinity of a conducting rod, which is either under potential, or in a homogeneous electric field, using a computational grid with a step proportional not to the radius of the rod, but to its length. The non-linear character of the decrease in the strength and potential of the electric field near the rod is taken into account using analytical expressions for a conductive ellipsoid under potential. In the area surrounding the rod and above its top, when using a spatial grid step proportionate with the length of the rod, and not with its radius, the relative errors in calculating the strength decreased from 27 % to 3 %. The results of calculating the electric field of a lightning rod are presented in order to analyze the conditions for the occurrence of upward leaders.