In certain transmission problems principally those relating to induction and interference phenomena, it is necessary to know the transmission characteristics of a circuit composed of an underground wire with earth return. These can be evaluated by well known engineering formulas provided the ground return impedance is known. The present paper gives the mathematical solution of this problem and shows that the ground return impedance is substantially independent of the depth of the wire below the surface.
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John R. Carson (1929) studied this question.