THE DIELECTRIC 109 



of charge be or. We must suppose that the tubes of strain go 

 normally from plate to plate, and that the strain D = o- is the 

 same in air and in the slab. The intensity in the air is 4-Tro-, while 



that in the dielectric is -^. Then the potential difference 



A 



between the plates is 



The capacity per unit area is 



a- 1 



or is equal to that of an air condenser in which the plates are nearer 

 j _ 1 



together by ^- 1. 



If such a slab of dielectric is inserted between the plates of an 

 attracted disc electrometer maintained at a given potential, a layer 

 of air intervening between the slab and the attracted disc, the 

 charge a- is increased in proportion to the capacity. If then P is 

 the pull per unit area when air alone is between the plates, it 

 becomes with the insertion of the slab 



The effect of placing a dielectric sphere in a pre- 

 viously uniform field deduced from the effect of placing 

 a conducting sphere in the same field. If a sphere of 

 dielectric constant K is placed in a field in air, previously uniform, 

 the lines of strain crowd in upon the sphere, for it is more easily 

 strained than the air. The effect of a sphere with K about 1 '35 

 is shown in Fig. 76, where it will be seen that the strain within 

 the sphere is uniform and parallel to the original direction. 



\Ve shall not give a strict proof that this is the distribution, 

 but shall merely show that it will satisfy the conditions required 

 at the surface of separation. 



I-'irst, let us suppose that a conducting sphere occupies the 

 position. Then on one hemisphere a + charge is induced, and on 

 the other a charge. These two charges must be so distributed 

 tlmt they will produce a field within the sphere, just neutralising 

 the field E, which previously existed, for there is no field within the 

 conductor. We may find this distribution by the following device. 



