124 



Dielectrics and Inductive Capacity 



[CH. v 



A small charged particle placed at any point of this field will experience 

 a force of which the direction is along the tangent to the line of force through 

 the point. The force is produced by the point charge, but its direction will 

 not in general pass through the point charge. Thus we conclude that in 

 a field in which the inductive capacity is not uniform the force between two 

 point charges does not in general act aloog the line joining them. 



139. As an example of the action of a dielectric let us imagine a parallel 

 plate condenser in which a slab of dielectric of thickness t is placed between 

 the plates, its two faces being parallel to the plates and 

 at distances a, b from them, so that a + b + 1 = d, where 

 d is the distance between the plates. 



It is obvious from symmetry that the lines of force 

 are straight throughout their path, equation (71) being 

 satisfied by ej = e 2 = 0. 



Let a be the charge per unit area, so that the polari- 

 sation is equal to a everywhere. The intensity, by 

 equation (67), is 



in air, 



and 



R -= o- in dielectric. 



FIG. 44. 



Hence the difference of potential between the plates, or the work done in 

 taking unit charge from one plate to the other in opposition to the electric 

 intensity, 



4-7T 



= 47TO- . a + -= a . t + 47TO- . b 



and the capacity per unit area is 



Thus the introduction of the slab of dielectric has the same effect as 

 moving the plates a distance (1 ^) t nearer together. 



Suppose now that the slab is partly outside the condenser and partly 

 between the plates. Of the total area A of the condenser, let an area B be 

 occupied by the slab of dielectric, an area A B having only air between 

 the plates. 



