CAPACITY OF SINGLE-PHASE LINE 85 



to the wire exerted by the charge on the element dl will be 

 q^ cos 6 =%- cos OdO, 



r\ 

 since dl cos = r dd 



r\ 



and 



COS0 



The total force exerted by the wire will be 



The potential of the point (Fig. 19) midway between 

 the wires, will be zero, since the effect of the positive charge 

 on A will be equal to the effect of the negative charge on B. 

 The potential difference between P and O is the work done 

 in moving a unit charge from one point to the other. The 



/y /7 



force due to the wire A on a unit charge at any point is * , 



acting directly away from A. Therefore the work done 

 in moving a distance dr toward A is 



and thus the total work in moving from P to O against the 



force due to A is 



t_ 



2? log^. 



Similarly, the work against the force due to B is equal to 



i 



