10 ELECTRICAL ENGINEERING 



where ri, r 2 , r 3 , etc. are the distances from the various charges to 

 the point. Fig. 7. 



Potential at a Point Due to a Charged Surface. In Fig. 8 AB 

 is a surface with a non-uniform distribution of charge over it; 



TI 

 FIG. 8. Potential due to a charged surface. 



if dq is a small element of charge at a distance r cm. from the 

 point P, the potential at P due to the charge dq is 



, dq 

 de = , 



and the potential due to the total charge on the surface is 



16. Equipotential Surfaces. Surfaces of which all points are 

 at the same potential are called equipotential surfaces. 



In Fig. 9 A is an isolated sphere of radius R, charged with 

 Q units of electricity. Any spherical surface drawn about the 

 centre of A is an equipotential surface. The potential of surface 



(1) is - , that of (2) is - and that of the sphere A is ^ 

 T\ r% t\j 



The difference of potential between surfaces (1) and (2) is 

 - - and is the work that must be done in taking a unit charge 



from any point on (2) to any point on (1). It makes no differ- 

 ence what path the charge follows, because its path can always 

 be resolved into two displacements, one along the equipotential 

 surface and the other normal to it; no work is done in moving 



