Theory of charge on an enclosed globe 407 



and the potential due to the whole shell is therefore 



Integrating with respect to (/> from o to 2ir, 



...... (10) 



Differentiating (6) with respect to 9, 



rdr = absinOdO. (n) 



Hence, V == \ f (r)dr = \ ^ {/ (r z ) -f (,,)} (12) 



the upper limit r 2 being always a + b, and the lower limit r l being a b when 

 a > b, and b a when a < b. 



Hence, for a point inside the shell 

 for a point on the shell itself 



and for a point outside the shell 



-)}- (15) 



We have next to determine the potentials of two concentric spherical shells, 

 the radius of the outer shell being a and its charge a, and that of the inner 

 shell being b and its charge /?. 



Calling the potential of the outer shell A, and that of the inner B, we find 

 by what precedes, 





B = A/ (26) + JL {/(fl + b} _ f(a _ b)} ....... (iy) 



In the first part of the experiment the shells communicate by the short 

 wire and are both raised to the same potential, say V. 



Putting A = B = V and solving equations (16), (17), we find for the charge 

 of the inner shell 



B - 2 Vb - -- lflffl 



t) f(2a)f(2b} - {/(+'6) -f(a - b}}* ' 



In the original experiment of Cavendish the hemispheres forming the outer 

 shell were removed altogether from the globe and discharged. The potential 

 of the inner shell or globe would then be 



B l =^J(2b). ...... (19) 



In the form of the experiment as repeated at the Cavendish Laboratory, 

 the outer shell was left in its place, but was connected to earth, so that A -= o. 



