86 TRANSMISSION LINE FORMULAS 



Therefore the potential difference between P and is 

 equal to the total work, and is 



Fig. 21. 



At P (Fig. 21) make the angle APD equal to the angle 

 PBD. Then the triangle PBD is similar to the triangle 

 APD, and therefore 



AP r^ 

 _DB 



P 



If we draw a circle of radius p about the fixed point D, 

 then at any point on this circle similar triangles are formed 

 by p, ri, and r 2 , as in Fig. 21, and therefore 



r 2 DB 



= = constant, 



ri P 



where r\ and r 2 are the distances of the point on the circle 

 from A and B respectively. Therefore, the potential 



will be the same at all points on this circle. 



Now let a solid cylindrical conductor fill all the space 

 inside the circle of radius p. All points on its surface will 

 be at the same potential. The distribution of potential 

 outside of the cylinder will not be altered from the previous 

 condition when all points on the circle of radius p were 



