EQUI POTENTIAL SURFACES. II 



The work done by a mass x ?# of electricity in passing from the 

 equipotential surface S x to the surface S 2 , is ;// (V 1 - V 2 ). Electrical 

 work, like that of gravity on a falling body, appears as a product of 

 two factors, one m, which corresponds to the weight of the body, and 

 the other, V l - V 2 , to the height of the fall. 



When a mass of positive electricity is left to itself, it tends to move 

 along a line of force towards the points where the potential is lower ; 

 negative electricity would move towards high potentials. 



If the electrical masses are distributed on dielectrics, they can only 

 be displaced by carrying along with them the dielectric itself. Con- 

 ductors, on the contrary, are characterised by the property of allowing 

 a free passage to electrical masses, which go to the surface, and 

 distribute themselves there so as to produce equilibrium. 



In all cases, the difference of potential V t - V 2 may be considered 

 as producing the motion of electrical masses ; it is often called the 

 electromotive force. 



24. EXPRESSION OF FORCE AS A FUNCTION OF POTENTIAL. 

 Consider two infinitely near equipotential surfaces S and S', whose 

 potentials are V and V (Fig. i). At the point M of the former 

 surface the force is F ; if dn is the distance of the two surfaces 

 measured along the perpendicular, the work done by this force on unit 

 mass in going from M to M' is equal to ~dn. We have then the 

 equation 



which gives 



"-- 



Thus, the force at a point is equal, and of opposite sign, to the 

 differential of the potential, in reference to the perpendicular to the 

 equipotential surface which passes through this point. 



