Determination of Critical Atmospheric Electric Field around Franklin’s Lightning Protection Rod That Leads to Break-down

In this paper atmospheric electric field distribution is determined in the vicinity of the Franklin’s lightning protection rod top which is modeled by half-spherical ending. Special emphasis is given to determination of critical atmospheric electric field that leads to break-down at the top of the rod. For the values of external atmospheric electric field that overcome critical value at the rod top, the corona occurs, so linear analysis is not valid any more. In this paper the first Laplace equation for potential is solved, for Franklin lightning protection rod approximated with one half of the prolate rotational ellipsoid in homogeneous earth atmospheric electric field, and the equation itself is solved in the coordinate system of prolate rotational ellipsoid. For that case, electric field along z-axis is determined and especially at the top of the rod. As numerical methods, method of subsections and finite element method are used and the comparison of these two methods is given.