ELECTRIC CHARGE. THE CONDENSER. 1 87 



point. Let the plane of the paper in Fig. 1 14 be a horizontal 

 plane, and imagine a hill built upon this plane in such a way 

 that its slope lines as seen projected upon the base plane coin- 

 cide with the lines of force in Fig. 1 14. If the height of this hill 

 is measured in volts then its slope may be expressed in volts per 

 centimeter at each point, in fact its slope will be a complete rep- 

 resentation of the electric field in the plane of Fig. 1 1 4. The 

 height, at a point, 'of an- imagined hill whose slope is everywhere 

 equal to the electric field is called the electric potential at that 

 point. The heavy curved lines ppp in Fig. 114 are the contour 

 lines, or lines of equal level, on the potential hill which is im- 

 agined to be built as described above. The potential is there- 

 fore the same at every point along each of the heavy curved lines 

 and these lines are therefore called lines of eqnipotential. 



The above example refers to the distribution of electric field in 

 two dimensions, and in this case the potential hill may be actually 

 constructed as a geometrical hill. In general, however, this is 

 not possible, that is to say, it is not possible to construct a geo- 

 metrical representation of the potential hill. A clear idea of po- 

 tential in this general case may be obtained as follows : Imagine 

 any given distribution of electric field, the electric field surround- 

 ing a charged sphere, for example, and imagine the region sur- 

 rounding the sphere to vary in temperature from point to point in 

 such a way that the temperature gradient (degrees per centimeter) 

 at each point may be equal to the electric field (volts per centime- 

 ter) at that point. Then the temperature at each point represents 

 what is called the electric potential at that poiitjt. In this ex- 

 ample of the field surrounding a charged sphere, the lines of force 

 are radial straight lines and any surface drawn so as to be at 

 each point at right angles to the lines of force is a surface of equi- 

 potential. 



In order to completely establish the value of the electric poten- 

 tial at different points in space, a region of zero potential must be 

 arbitrarily chosen. Then the potential at any other point is 

 equal to the electromotive force E between the arbitrarily chosen 



