IDEA OF POTENTIAL. 167 



temperature and the negatively charged cylinder is at a low tem- 

 perature, the intervening region being filled with a heat conductor. 

 Then the heat-flow through the surrounding region would be 

 along the fine lines with arrow heads, and the heavier lines 

 would be lines of equal temperature. The heavier lines represent 

 surfaces at right angles to the plane of the paper, and each of 

 the surfaces so represented would be an isothermal surface. 

 Let V be the value of the electric potential at a point, then 



dV 



is the gradient or slope of V in the direction of the x-axis 



dx 



of reference, and therefore, in accordance with the above defini- 

 tion of potential, we have: 



-*. 

 -' 



*. 



where X, Y and Z are the components (parallel to the x, y 

 and z-axes respectively) of the electric field at a point. Also 

 it is evident that dV = X dx, that is the increment of poten- 

 tial along dx is found by multiplying the x-component of the 

 electric field by dx. 



A clear understanding of electric potential may be obtained 

 by considering the electric field between the two plates in Fig. 90 

 or Fig. 91. Let E be the electromotive force between the 

 plates, then E/x is the field intensity or slope of the potential 

 hill, and if we multiply this slope, E/x, by the distance x 

 between the plates we get the total rise E of the potential hill 

 from one plate to the other. That is to say, the electromotive 

 force between any two points is the difference in level of the poten- 

 tial hill at these two points or simply the potential difference 

 between these two points. Let q coulombs be an amount of 

 charge which is transferred from one point to another, and 



