79-82] Cylindrical Condenser 73 



An examination of the expression for the capacity. 



ab 



b a ' 



will shew that it can be made as large as we please by making b a 

 sufficiently small. This explains why a condenser is so much more 

 efficient for the storage of electricity than a single conductor. 



81. By taking more than two spheres we can form more complicated 

 condensers. Suppose, for instance, we take concentric spheres of radii 

 a, b, c in ascending order of magnitude, and connect both the spheres of 

 radii a and c to earth, that of radius b remaining insulated. Let F be the 

 potential of the middle sphere, and let e and 2 be the total charges on its 

 inner and outer surfaces. Regarding the inner surface of the middle sphere 

 and the surface of the innermost sphere as forming a single spherical 

 condenser, we have 



Vab 



and again regarding the outer surface of the middle sphere and the outer- 

 most sphere as forming a second spherical condenser we have 



Vbc 

 e *- G -b' 



Hence the total charge E of the middle sheet is given by 



E = e l + e 2 



- V 

 " 



b a c b) ' 



so that regarded as a single condenser, the system of three spheres has a 

 capacity 



ab be 

 b a c 6* 



which is equal to the sum of the capacities of the two constituent condensers 

 into which we have resolved the system. This is a special case of a general 

 theorem to be given later ( 85). 



Coaxal Cylinders. 



82. A conducting circular cylinder of radius a surrounded by a second 

 coaxal cylinder of internal radius b will form a condenser. If e is the charge 

 on the inner cylinder per unit length, and if F is the potential at any point 

 between the two cylinders at a distance r from their common axis, we have, 



as in 75, 



V=C-2e\ogr, 



