Mutual impedance of grounded wires lying on or above the surface of the earth
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This paper presents a formula for the mutual impedance of any insulated wires of negligible diameter lying in horizontal planes above the surface of the earth and grounded by vertical wires at their four end-points. The formula holds for frequencies which are not too high to allow all displacement currents to be neglected. Tables and curves are given to facilitate numerical computation by means of the formula. In the expansion of this formula for low frequencies and for any heights the first two terms give the direct-current mutual impedance; the third term is independent of the heights, thus being identically the same as that previously found for wires on the surface. The mutual impedance for wires at any heights H and h, with separations large in comparison with these heights, is found to be approximately equal to the mutual impedance for wires on the surface multiplied by the complex factor [1 + Γ(H + h)], where Γ is the propagation constant in the earth.