114, 115] Coefficients for Spherical Condenser 99 



outside this conductor ; for charges outside this " screen " cannot affect the 

 screened system. The principle of electric screening is utilised in electro- 

 static instruments, in order that the instrument may not be affected by 

 external electric actions other than those which it is required to observe. As 

 a complete conductor would prevent observation of the working of the 

 instrument, a cage of wire is frequently used as a screen, this being very 

 nearly as efficient as a completely closed conductor (see 72). In more 

 delicate instruments the screening may be complete except for a small 

 window to admit of observation of the interior. 



Spherical Condenser. 



115. Let us apply the methods of this Chapter to the spherical con- 

 denser described in 79. Let the inner sphere of radius a be taken to be 

 conductor 1, and the outer sphere of radius b be taken to be conductor 2. 



The equations connecting potentials and charges are 



A unit charge placed on 2 raises both 1 and 2 to potential 1/6, so that on 

 putting E l = 0, E 2 = 1, we must have V l = F 2 = l/b. Hence it follows that 



1 



If we leave 2 uncharged and place unit charge on 1, the field of force is that 

 investigated in 79, so that F x = I/a, F 2 = l/b. Hence 



= 1 = 1 



These results exemplify 



(i) the general relation > 12 => 2 i> 



(ii) the relation peculiar to electric screening, p 12 = p&. 

 The equations now become 



1 ~~ a b ' 



Solving for E l and E z in terms of F x and F 2 , we obtain 



ab v ab v 



y 1 ~ 7, '2> 



J - J \ ' 1 7 



b a b a 



T? _ ab y b 2 y 



2 ~~ b-a l b -a 2 ' 



ab ab 6 2 



so that ?n = j^> V = V* =: -b^i i q * 2 = b^~a' 



72 



