176 ADVANCED ELECTRICITY AND MAGNETISM. 



Therefore, substituting the value of Q from equation (4) of Art. 

 104, we get: 



Electrical stress at surface of f \ 



wires of a transmission line j f D R\ \ R D R 



2 log e 



This expression gives the electrical stress in volts per centimeter 

 at the surface of either wire in Fig. 115, E being the electro- 

 motive force between the wires in volts, R the radius of the 

 wires in centimeters, and D the distance between the wires in 

 centimeters. 



1 06. Distribution of electric potential in the neighborhood of 

 a line charge. The electric field at a point distant r centimeters 

 from the axis of a uniformly charged cylinder in air is: 



e= '7 (I) 



according to equation (2) of Art. 94, and evidently the field does 

 not depend upon the diameter of the cylinder if the charge per 

 unit length Q is given. Therefore we may suppose the charged 

 cylinder to have an indefinitely small diameter, and we thus 

 arrive at the notion of what is called a line charge, namely, a 

 charge of Q coulombs per centimeter distributed uniformly 

 along a straight line. Equation (i) expresses the electric field 

 intensity in the neighborhood of a line charge. 



To find the electric potential distribution in the neighborhood 

 of a line charge it is not permissible to choose the infinitely 

 distant region (r = oc) as the region of zero potential because 

 to do so leads to infinite values of potential everywhere; it is 

 most convenient to choose the region which is at unit distance 

 (r = I centimeter) from a line charge as the region of zero 

 potential. 



The dot A in Fig. 116 is an end view of a line charge of Q 

 coulombs per centimeter, and is the chosen region of zero 

 potential; and it is desired to find the potential at the point p 



