The mutual impedance between short earth-return circuits

Formulae are derived for the mutual impedance between short earth-return circuits separated by distances which are electrically large. For parallel circuits this condition is shown to be satisfied when the separation in kilometres is greater than about 0.08 ¿(¿/f), where ¿ is the earth resistivity (ohm-cm), and f is the frequency (c/s). In the range in which the formulae apply, the mutual impedance is independent of frequecny, inversely proportional to the cube of the separation, and directly proportional to earth resistivity. Experimental results are given for two test site, one on clay subsoil of resistivity about 750 ohm-cm, and the other on coal-bearing lime-stone of resistivity about 4000 ohm-cm. The measured values at both sites show good agreement with theory.