CAPACITY OF CONCENTRIC CYLINDERS. 



If the thickness is constant, then, putting V = V 1 -V 2 , we have 



M = 



v i-V 



VS 



47T 



The capacity of the jar in ether words, the charge which corre- 

 sponds to a difference of unit potential between the two coatings is 

 expressed in the same way as for spherical condensers; that is to say, 



The charge depends thus only on the difference of potentials, 

 and not at all on their absolute values : this result could be readily 

 foreseen, as the force itself only depends on this difference. 



80. CONCENTRIC CYLINDERS. Given two concentric cylinders 

 with circular bases of the radii Rj and R 2 , at the potentials V l and V 2 . 

 Consider the very small angle du formed by two planes passing 



Fig. 18. 



through the axis, and cut this by two planes perpendicular to the 

 axis, one of which we shall take for the plane of the figure (Fig. 

 1 8). All the lines of force being by symmetry perpendicular to 

 the common axis, the volume thus determined is a tube of force ; 

 the surfaces which it intercepts on the two cylinders are to each 

 other as the arcs ^S : and d 2 . If, then, F x and F 2 are the values 

 of the force at the distances Rj and R 2 , we have 



As, moreover, 



we obtain, by substitution, 



whence 



F 2 



