110 STATIC ELECTRICITY 



Let electrification, density p, be distributed uniformly within the 

 sphere centre O, radius a, Fig. 77. At any point P within the 

 sphere the intensity due to this is along OP and since the shell 



FIG. 76. 



external to P has no effect and the sphere within P may be regarded 



4 ( )l u 4 

 as collected at its centre it is equal to ^ irp Tjp^a 71 "/ ^' *""' 



let electrification density p be uniformly distributed within 



FIG. 77. 



a sphere, radius a, centre O' close to O, O'O being in the dinrtion 

 of E. The intensity at P due to this second sphere is | -jrp PO' 

 along PO', since the electrification is negative. The two distribu- 

 tions superposed will have resultant | irpOO' through P parallel 



to OO'. The result of this superposition is zero density, or no 

 charge m the overlapping part of the spheres, a + layer on the 

 hemisphere towards A, and a - layer on the hemisphere towards B. 



rv^A* C K neSS f the layer at an y P oint Q in a Direction with 



OA is GO cos 0, and therefore the surface density is p OO' < 

 Now adjust p and OO' so that 



