ELEMENTARY LESSONS ON [CHAP. iv. 



Induction. In the case of the single electrified sphere 

 the lines of force would be straight lines, radii of the sys- 

 tem of equipotential spheres. In general, however, lines 

 of force are curved ; in this case the resultant force at 

 any point would be in the direction of the tangent to the 

 curve at that point. Two lines of force cannot cut one 

 another, for it is impossible ; the resultant force at a point 

 cannot act in two directions at once. The positive 

 direction along a line of force is that direction in which 

 a small body charged with + electricity would be im- 

 pelled by the electric force, if free to move. A space 

 bounded by a number of lines of force is sometimes 

 spoken of as a tube of force. All the space, for example, 

 round a small insulated electrified sphere may be re- 

 garded as mapped out into a number of conical tubes, 

 each having their apex at the centre of the sphere. The 

 total electric force exerted across any section of a tube 

 of force is constant wherever the section be taken. 



244. Potential -within a Closed Conductor. 

 The experiments related in Arts. 29 to 32 prove most 

 convincingly that there is no electric force inside a closed 

 conductor. Now we have shown above that electric 

 force is the rate of change of potential per unit of length. 

 If there is no electric force there is no change of 

 potential. The potential within a closed conductor (for 

 example a hollow sphere) is therefore the same all over 

 the interior ; the same as the potential of the surface. 

 The surface of a closed conductor is therefore necessarily 

 an equipotential surface. If it were not at one potential 

 there would be a flow of electricity from the higher 

 potential to the lower, which would instantaneously 

 establish equilibrium and reduce the whole to ofte 

 potential. 



An apparently paradoxical contradiction of this will 

 probably at once occur to the student, namely, the fact 

 that when an electrified body is placed near an insulated 

 conductor the nearer and farther portions of that con- 



