I UNIVERSITY ) 



CHAP, iv.] ELECTRICITY AND 5$AGNETISM. ~i\K*97 



zero, just as it is convenient to consider " sea-level " as 

 a zero from which to measure heights or depths. 



240. Difference of Potentials. Since potential 

 represents the work that must be done on a + unit in 

 bringing it up from an infinite distance, the difference 

 of potential between two points is the work to be done on 

 or by a + unit of electricity in carrying it from one point 

 to the other. Thus if V P represents the potential at P, 

 and V Q the potential at another point Q, the difference 

 of potentials V P V Q denotes the work done in moving 

 up the + unit from Q to P. It is to be noted that since 

 this value depends only on the values of the potential 

 at P and at Q, and not on the values of the potential at 

 intermediate points, the work done will be the same, 

 whatever the path along which the particle moves from 

 Q to P. In the same way it is true that the expenditure 

 of energy in lifting a pound against the forces of gravity 

 fro-i one point, to another on a higher level, will be the 

 same whatever the path along which the pound is lifted. 



241. Electric Force. The definition of " work " is 

 the product of the force overcome into the distance 

 \br/yirjji w.birh. the, force .is, owrcnnaf^ cy: marls: = force 



x distance through which it. is overcome. 



Hence, if the difference of potential between two 

 points is the work done in moving up our 4- unit from 

 one point to the other, it follows that the average electric 

 force between those points will be found by dividing 

 the work so done by the distance between the points : 



or p ~ Q =f (the average electric force along the line 



PQ). The (average) electric force is therefore the rate 

 of change of potential per unit of length. If P and Q 

 are near together the force will be practically uniform 

 between P and Q. 



242. Bquipotential Surfaces. A charge of elec- 

 tricity collected on a small sphere acts on external 

 bodies as if the charge were all collected into one point 



