1 82 



ADVANCED ELECTRICITY AND MAGNETISM. 



produced by A and a fictitious line charge at B' which is 

 called the electric image of A with respect to the metal cylinder 

 BB. 



1 08. Another important example of the method of images. 

 A uniform electric field as modified by a cylindrical conductor. 

 Figure 123 shows the trend of the lines of force in the neighbor- 



\U-axi8 



X-OX18 



Fig. 123. 



hood of a metal cylinder of radius R in a region which would 

 be a uniform electric field parallel to the #-axis if it were not 

 for the presence of the metal cylinder. The mathematical formu- 

 lation of the field distribution in any case is greatly simplified by 

 using the idea of potential. We will proceed therefore to find an 

 expression for the potential at any point p in Fig. 123 of which 

 the polar coordinates with respect to are r and 6, 6 being 

 the angle between r and the #-axis of reference. 



The finding of this mathematical expression depends upon the 

 combining of two potentials, namely, (a) the potential due to the 

 original undisturbed uniform field e parallel to the x-axis, and 

 (b) the potential due to what is called a line doublet. 



Potential due to a uniform field of intensity e parallel to the 

 x-axis. Let V be the potential which is associated with e; 



