40 



STATIC ELECTRICITY 



by Gauss's theorem 4^1 = 4-TrQ or I = -~, that is, it is the same as 



if Q were all concentrated at the centre. 



It is obvious that for a gravitating sphere arranged in Con- 

 centric shells, each of uniform density, the same result hold-, and 



the attractive intensity at a point 

 outside the sphere is the same a< it 

 the whole mass were collected at the 

 centre. 



Intensity inside the shell. 

 Now draw a concentric sphere S 2 of 

 radius r 2 inside the shell S. The 

 intensity I overS 2 is from symmetry 

 everywhere normal to S 2 and every- 

 where the flame in magnitude. Then 

 4?r? 2 a l = 4?r x = 0. nnce then- is no 

 charge within S 2 . Hence 1=0 e\ i \ 

 \vhere within S,. 



It is obvious that if S is the 

 face of a gravitating sphere arranged 



in concentric shells, each of uniform density, the shells outside 

 S 2 produce no intensity at S 2 , while the -lulU \\ithin art as if all 

 collected at the centre. 



Intensity at any point in the axis of a uniformly 

 charged circular disc. I^et AB, Fig. 34, be a diameter of tin- 

 disc, and CP its axis. The intensity at P will, from symmetry, ! 

 along CP. Let the charge per unit area of the disc be <T. Tnil is 



FIG. 33. 



Fio. 34. 



termed the surface density of charge. To find the contribution 

 of any element to the intensity we need only consider the resolved 

 part along CP. Take an element of surface dS with section 

 EF and let FPC = 0. The intensity due to it along CP is 



But if we draw a cone with P as vertex and dS as 



