Mutual Impedance of Grounded Wires Lying on the Surface of the Earth*

This paper presents a formula for the mutual impedance between two insulated wires of negligible diameter lying on the surface of the earth and grounded at their end-points. The formula holds for frequencies which are not too high to allow all displacement currents to be neglected. For any two elements dS, ds of the two wires the mutual impedance is obtained from their direct-current mutual impedance by introducing the complex factor2(γ r)² [1-(1 + γ r ) e^-γ r]in the reactance term, γ being the propagation constant in the earth, and r the distance between the elements dS and ds.