LOW-FREQUENCY INDUCTION 579 



In the type of problem we are considering the telephone wires 

 comprise one side of a long loop, the other side of which is the earth. 

 Likewise, the power wires comprise one side of a loop, the other side 

 being the earth. It is a well known fact that the magnetic coupling 

 between two parallel loops at a given separation increases as the sizes 

 of the loops increase. The sizes of the loops in the case being con- 

 sidered are determined by the distribution of the return current in 

 the earth. 



A great deal of theoretical and experimental work has been done in 

 connection with the analysis of the distribution of current in the earth, 

 and it has been found that one of the important factors is the "re- 

 sistivity" of the earth. The efifect of resistivity of the earth can be 

 briefly summarized as follows: 



(a) Considering the outgoing and return paths for residual current on a 



power line, the mutual induction between the current in the 

 wires and the return current in the earth tends to pull the earth 

 currents together and to concentrate them under the line as 

 near the surface as practicable. This action tends to decrease 

 the coupling to an adjacent circuit by decreasing the effective 

 separation of the sides of the loop. 



(b) The resistance which the current encounters in flowing through 



the earth tends to make it spread out because, by so doing, the 

 current density is reduced and the voltage drop is consequently 

 reduced. This spreading out tends to increase the coupling to 

 an adjacent circuit. 



(c) The net distribution of the current in the earth is a balance 



between these two opposing tendencies and this distribution will 

 be different for difi^erent resistivities of the earth. Generally 

 speaking, the greater the resistivity of the earth, the more the 

 current will spread and the greater will be the coupling to an 

 adjacent circuit. 



Figure 3 is a graphical representation of how the return current in 

 the earth tends to spread with an increase in earth resistivity. While 

 this figure shows only the vertical spread, a similar spreading also 

 takes place horizontally. 



The effect of the sizes of the primary and secondary loops on the 

 coupling is greater when the loops are widely separated than when 

 they are close together. For this reason, the effect of earth resistivity 

 on coupling is much greater for wide separation exposures than for 

 exposures where the lines are close together. Consequently, with 

 high resistivity earth, the coupling not only is higher at all separations 



