ELECTRICAL LEVEL OR POTENTIAL 



and ultimately X = -y- 



76 



or the intensity in any direction is the rate of fall of potential per 

 unit length in that direction. 



General nature of level surfaces. If the surfaces are 

 drawn at intervals such that the successive potentials differ by 

 unitv, it is evident that the surfaces crowd most closely together 

 where the intensity is greatest, for there the shortest distance will 

 be traversed with the unit charge in doing unit work. On 

 the other hand, where the intensity is less the surfaces open out. 

 Indeed, we can at once obtain a relation between the distance from 

 surface to surface and the cross-section of a unit tube of force. 



If E be the intensity at a point and d the distance between two 

 consecutive level surfaces there. 



.'. Ed = l. 



But if a be the area of the cross-section of the unit tube at the 

 point, Ea = 4-Tr (p. 67), 



d 



or the distance d is proportional to the cross-section a of the tube. 



When a conducting surface is charged entirely with one kind 



of electricity, the intensity is everywhere outwards if the charge be 



61. Charged sphere in the 

 middle of a cubical room. 



FlG. 62. Charged sphere inducing 

 opposite charge on a neighbouring 

 insulated sphere in the middle of 

 a cubical room. 



positive, and everywhere inwards if it be negative. Then in the 

 former ea-e the potential falls and in the latter rises as we go 

 outwards from the surface in all directions. In other words, 



