1 86 ADVANCED ELECTRICITY AND MAGNETISM. 



109. The production of any desired field distribution in a 

 region by the creation of proper potential values everywhere 

 over the boundary of the region. The distribution of electric 

 field in a region depends upon two things; namely, (a) Upon the 

 distribution of electric charge over the boundary of the region, 

 and (b) upon the distribution of electric charge throughout the 

 region itself. When there is no charge in the region, the boundary 

 distribution alone determines the field throughout the region. 

 In practice it is much easier to produce assigned potential values 

 than to produce assigned distributions of charge. Therefore for 

 practical purposes the following proposition may be used instead 

 of the above. When there are no free electric charges in a region, 

 the potential values over the boundary of the region completely 

 determine the field distribution in the region. 



Example i. Figure 125 represents the lines of force sur- 

 rounding a line charge, the line charge being perpendicular to 



Fig. 125. 



the plane of the paper. The dotted circle in Fig. 125 represents 

 a cylinder with its axis parallel to the line charge. Imagine this 

 cylinder to be made of narrow insulated strips of metal as repre- 

 sented by the separate dots of the circumference, and imagine 



