"INVERSE SQUARE" SYSTEMS 83 



be represented on a larger scale in Fig. 24-, in which AHBK repre- 

 sents dS. The intensity at dS may be taken as q/OA 2 outwards 

 along the axis of the cone, and if is the angle which the axis 



makes with the normal to AHBK, then N = ? and 



OA 2 

 But if we draw ALCM, a section of the cone dw, through A 



B 



FIG. -Jl. 



and perpendicular to the a\i>, the angle between AHBK and 



A I. CM is fJ, and since die i^ ><> -mall that BC is practically parallel 

 to AO, ALCM = dScos0. 



Hence NWS ~ 



If we now >um up for every element of the surface, the 

 contribution of fj i> 



J SdS =f qd(t) = qj du = 4nrq 



since the total solid angle round q is 4?r. 



The normal intensity at any point of S due to any number of 

 elements of charge is equal to the sum of the normal intensities due 

 to the separate elements. Hence for the whole charge Q within S 

 we shall have to add up all the quantities such as 4^^, and so 



Now let (] be outside the surface at O, Fig. 25, and let an elemen- 

 tary com- (Its cut. S in r/Sj at A, and JS 2 at B. Let the intensities at A 

 and B normal to the surface be ^ N 2 respectively. Then, as we have 

 just proved, NjCfSi^^w, while at B, N being in wards and negative, 



f/dw. The two, therefore, neutralise each other. Tins 



