QO TRANSMISSION LINE FORMULAS 



Effect of the Earth on Capacity of Line. The effect of 

 bringing a conducting plane, such as the earth, near to two 

 charged wires is to change their electrostatic field and in- 

 crease their capacity. 



Consider two long parallel wires, A and A (Fig. 23), of 

 infinitesimal section and carrying + q and - q units of 



electricity per centimeter 

 respectively. As in Fig. 

 19, the point midway 



M / o N between the two wires 



will be at zero potential. 

 All points having the same 



potential must have equal 



?2 



to a constant. It is evi- 

 dent that all points at the same potential as lie in the 

 plane MON, perpendicular to AA^ since for all such 

 points 



r\ = r z . 



Therefore, the wire A[ may be replaced by a solid con- 

 ducting plane MTV, which will be at zero potential. Thus, 

 when the conducting plane is the earth, its effect is the same 

 as that of a charged wire at a depth below the surface 

 equal to the height of the original wire.* The assumed 

 wire is called an image wire, since it occupies the same 

 position as the image of the real wire, considering the 

 surface of the ground as a mirror. 



In the case of a single-phase transmission line, image 

 wires A' and B' must be assumed for both wires A and B 



* See " Elements of Electricity and Magnetism," by J. J. Thomson, page 

 138. 



