69-71] 



Equipotentials and Lines of Force 



61 



the surface density is zero along the line of intersection, and is proportional 

 to the square of the distance from the line of intersection at adjacent points. 



If, however, a, b and c are all infinite, we have the electric intensity also 

 infinite, and therefore the surface density is infinite along the line of inter- 

 section. 



It is clear that the surface density will vanish when the conducting 

 surface cuts itself in such a way that the angle less than two right angles 

 is external to the conductor; and that the surface density will become 

 infinite when the angle greater than two right angles is external to the 

 conductor. This becomes obvious on examining the arrangement of the 

 lines of force in the neighbourhood of the angle. 



FIG. 24. Angle greater than two right angles external to conductor. 



71. 



FIG. 25. Angle less than two right angles external to conductor. 

 The arrangement shewn in fig. 25 is such as will be found at the 



point of a lightning conductor. The object of the lightning conductor is 

 to ensure that the intensity shall be greater at its point than on any part 

 of the buildings it is designed to protect. The discharge will therefore take 



