ELECTROSTATICS 



11 



along the equipotential surface, since there is no opposing force 

 and therefore all the work is done in the displacement along the 

 normal. 



The electrostatic force on an equipotential surface is normal to 

 the surface, therefore lines of induction pass normally through 

 equipotential surfaces. 



FIG. 9. Equipotential surfaces. 



Electric conductors not carrying current are equipotential sur- 

 faces, since if differences of potential did exist electricity would 

 flow from the points of high potential until the potential became 

 uniform throughout the conductor. 



17. Potential Gradient. The potential gradient at a point is 

 the space rate of change of potential at the point measured in 

 the direction of the electrostatic force. 



The difference of potential between two points is 



-jr 



(12) 



where ^ is the electrostatic force at any point and D is the distance 

 between the points. The potential gradient at any point is 



_ ^ gp 

 ^ ~~ dr 



and is equal to the electrostatic force at the point. 



(13) 



