Near-zone electric field computation of a horizontal semi-infinite wire above earth

Abstract

Asymptotic expressions are obtained for the electric field due to a current propagating on a horizontal semi-infinite wire above the earth. First, exact integral representations are derived for the electric field due to a current on a semi-infinite wire in a general multi-layered medium. The resulting integral expressions are then specialized for the problem of a semi-infinite wire above the earth. The resulting expressions involve a semi-infinite integration over an integrand containing the incomplete Lipschitz-Hankel integrals. The steepest descent technique is applied to the direct and reflected terms separately, thereby providing a far-zone approximation for the field (E α r⁻¹). A recurrence relationship is then developed which allows the r⁻² term in the asymptotic expansion to be computed from the previously computed r⁻¹ term. A numerical comparison between the following three methods is carried out: numerical integration, one-term (1/r) approximation, and two-term (1/r²) approximation. It is shown that two-term solution yields more accurate results than that of the one-term solution, especially when the problem of a finite length wire above the earth is considered. The two-term expansion provides accurate results for the fields when 0.1 λ < r < ∞ and it consumes much less computation time than the numerical integration solution.