115-117] Coefficients for two distant Spheres 101 



Substituting these values in the equations 



we find at once that p n = - neglecting , 



GL 



Pl2 ~r c 3 ' 



and similarly we can see that 



P.& = j- neglecting . 

 o c 



Solving the equations 



Z7* ~E* 



Y = + 



2 ~ r b ' 



we find that, neglecting , 



c 



a 



ab 



_L *~" ~ 



ab ab f 1 



- 7 asfaras-, 



" c 2 



We notice that the capacity of either sphere is greater than it would be if 

 the other were removed. This, as we shall see later, is a particular case of a 

 general theorem. 



Two conductors in contact. 



117. If two conductors are placed in contact, their potentials must be 

 equal. Let the two conductors be conductors 1 and 2, then the equation 

 F! = F 2 becomes 



*+ = 0, 



or, say, a^ + ftE 2 + yE 3 + ... = 0. 



If we know the total charge E on 1 and 2, we have 



E\ + E 2 = E, 

 and on solving these two equations we can obtain E l and E 2 . We find that 



