THE DIELECTRIC 



111 



I vp 00' = E. 

 o 



Then the two layers will give a uniform intensity E in the 

 overlapping region, which will neutralise the external field E in that 

 region, and the surface density of the layers is 



3 E cos 



4 7T 



Externally, and only externally, to the spherical space the two 

 distributions will act as if each were collected at its centre, and 



4 4 



therefore as if we had electrification ^7r/oa 3 at O and B-rr/oa 3 at O'. 



These two constitute what is termed an electric doublet, and they 



correspond to the two poles of a magnet. We define their moment 



4 

 to be M = 7r/oa 3 OO / = Ea 3 . Just as with a magnet, the in- 



ten-ity at distance d making with OO' is 



2Ea 3 cos S 

 d* 



along d, 



and -^ perpendicular to d (see Magnetism),* and this field is 



superposed on the uniform field E. It may be noted that just 



Fio. 78. 



outside the sphere at the ends of the diameter parallel to E where 

 d = a and = 0, the total field is E + 2E = 3E. 



The field in the neighbourhood of the sphere is shown in 

 Fig. 78. Since the field without is modified by the presence of the 



* These components may be obtained very easily by noting that the two 

 nearly equal forces -rpaa/rfa and jrpa3/(d + 5)2 acting at an angle differing from 

 r by the small angle <f> have resolutes along the two bisectors of the angle 

 respectively equal to the difference grpa. 3 & W3 and to ^irpa 3 (f>/d 2 . Here 5 is 

 O'O cos and 0Js OO r sin >l. 



