68 STATIC ELECTRICITY 



system of measurement. The numerical relation obtained depends 

 on the units employed. Whatever be the unit of charge, if \u- 

 define strain as on p. 52, the strain is ql^-jrd 2 , but the intensity 

 is only q/d? when a particular unit is chosen. We shall see here- 

 after that with this particular unit, but with a medium other than 

 air, the relation is KE = 4?rD, where K is a constant for each 

 medium. When we discuss the relation between intensity and 

 strain in media other than air we shall be able to show that \\ e 

 may interpret the intensity as analogous to elastic stress and the 

 strain as analogous to elastic strain. 



The outward pull per unit area on a charged con- 

 ducting surface. Since the intensity is always outwards from a 



positively electrified surface and in- 

 wards to a negatively electrified one, 

 it is evident that in each case an 

 actual element of the surface, if lc> 

 would tend to move outward- \\ I 

 shall now find the amount of the pull 

 outwards per unit area. NNV 1 

 seen in Chapter III that the intensity 

 at a point P p Fig. 59, just outside a 

 conductor is normal to the surface 

 and is equal to 47nr. Also we found 

 that it may be regarded as made up 

 FIG. 69. of two equal parts, one due to the 



charge on the area a i tn media t< 1\ 



under it, and the other due to the rest of the charges of the 

 system. Each is therefore 2x0-. 



Now consider an element da of a just under P,. The 

 outwards on this element is not due to the re.st of , B fa 



practically all in the same plane as da. It mu>t thei due 



to S alone, and its value is : intensity due to S x charge on da 



= %7rar X ordu 



The pull outwards per unit area is therefore 



F = 27TC7 1 . 



If, then, we know the distribution of charge on a condiu 

 body, we know all the forces acting upon it, and the resultant force 

 is the resultant of all the elementary pulls outward-. 



Note on the method of investigating the field in 

 Chapters III-V. The mode of analysing the total strain at a 

 point into the actions of the separate elements each supposed to 

 act directly, and without regard to the intervening medium, is that 



