CHAP, iv.] ELECTRICITY AND MAGNETISM. 201 



ductor exhibit induced charges of opposite kinds. The 

 explanation of the paradox is that in the space round the 

 charged body the potential is not uniform. Suppose the 

 body to have a + charge, the potential near it is higher 

 than the space farther away. The end of the insulated 

 conductor nearest to the charge is in a region of high 

 potential, while its farther end is in a region of lower 

 potential. It will, as a whole, take a mean potential, 

 which will, relatively to the potential of the surrounding 

 medium, appear negative at the near end, positive at the 

 far end. 



245. Law of Inverse Squares. An important 

 consequence follows from the absence of electric force 

 inside a closed conductor ; this fact enables us to de- 

 monstrate the necessary truth of the " law of inverse 

 squares " which was first experimentally, though roughly, 

 proved by Coulomb with the torsion balance. Suppose 

 a point P anywhere inside a hollow sphere charged with 

 electricity (Fig. 98). The charge is uniform all over, 

 and the quantity of electricity 

 on any small portion of its 

 surface will be proportional 

 to the area of that portion. 

 Consider a small portion of | 

 the surface AB. The charge 

 on AB would repel a + unit 

 placed at P with a certain 

 force. Now draw the lines 

 AD and BC through P, and 

 regard these as mapping out 

 a small conical surface of 

 "two sheets, having its apex at P ; the small area CD 

 will represent the end of the opposed cone, and the 

 electricity on CD will also act on the + unit placed at P, 

 and repel it. Now these surfaces AB and CD, and the 

 charges on them, will be directly proportional to the 

 squares of their respective distances from P. If, then 



