36-38] The Potential 31 



The earth is a conductor, and is therefore at the same potential through- 

 out. In all practical applications of electrostatics, it will be legitimate to 

 regard the potential of the earth as zero, a distant point on the earth's 

 surface replacing the imaginary point at infinity, with reference to which 

 potentials have so far been measured. Thus any conductor can be reduced 

 to potential zero by joining it by a metallic wire to the earth. 



MATHEMATICAL EXPRESSIONS OF THE LAW OF THE INVERSE SQUARE. 



I. Values of Potential and Intensity. 



38. We now discuss the values of the potential and components of 

 electric intensity when the space between the conductors is air, so that 

 the electric forces are determined by Coulomb's Law. 



If we have a single point charge e 1 at a point P lt the value of R, the 

 resultant intensity at any point 0, is 



and its direction is that of PjO. Hence if 6 is the angle between OP t and 



FIG. 6. 



00', the line joining to an adjacent point 0', the work done in moving a 

 charge e from to 0' 



= -eRcos0. 00' 



= -eR(OP l -0'P 1 ) 

 = -eRdr, 



where OP l = r, 0'P 1 = r + dr. Hence the work done against the repulsion 

 of the charge ^ in bringing from infinity to 0' by any path is 



rr=O'P l rr^O'P, ^ 



-e Rdr = -e \dr = - 1 , 



J r =*> Jr=c r 2 r 1 i 



where r = O'Pj. 



If there are other charges e 2 , e s , ... the work^ done against all the 

 repulsions in bringing a charge e to 0' will be the sum of terms such as the 

 above, say 



