102-105] 



Coefficients of Potential 



93 



As a special case, let us reduce conductor (2) to a point P, and suppose 

 that the system contains in addition only one other conductor (1). Then 



The potential to which the conductor is raised by placing a unit charge 

 at P, the conductor itself being uncharged, is equal to the potential at P when 

 unit charge is placed on the conductor. 



For instance, let the conductor be a sphere, and let the point P be at a 

 distance r from its centre. Unit charge on the sphere produces potential 



- at P, so that unit charge at P raises the sphere to potential . 



Coefficients of Potential, Capacity and Induction. 



105. The relations jo 12 = > 21 , etc. reduce the number of the coefficients 

 PU, Pi*> Pnny which occur in equations (32), to %n(n + l). These coeffi- 

 cients are called the coefficients of potential of the n conductors. Knowing 

 the values of these coefficients, equations (31) give the potentials in terms 

 of the charges. 



If we know the potentials V lt F 2 , ..., we can obtain the values of the 

 charges by solving equations (32). We obtain a system of equations of 

 the form 



etc. 



(34). 



The values of the qs obtained by actual solution of the equations (32), are 



P^Pzz ...p m 



Pr 



where 



A = pnPn-'Pm - 



.(35), 



PinPzn Pnn 



Thus q rs is the co-factor of p rg in A, divided by A. 



The relation q r8 q gr 



follows as an algebraical consequence of the relation p rs =p sr , or is at once 

 obvious from the relation 



and equations (34), on taking the same sets of values as in 104. 



