ELEMENTARY THEORY OF ELECTROMAGNETISM. 59 



for the same strength of current in the wire; from which it follows 

 that the magnetic flux through each turn of wire in Fig. 45 is 

 twice as great as the magnetic flux through the corresponding 

 turn of wire in Fig. 44 for the same current in the wires. There- 

 fore the value of Z3>' (= LI according to Art. 31) in Fig. 45 

 is twice as great as in Fig. 44 for the same strength of current 

 in the wire. Therefore L in Fig. 45 is twice as great as L in 

 Fig. 44. 



The inductance of a coil of given size and shape is proportional 

 to the square of the number of turns of wire. To understand 

 this proposition consider Figs. 46 and 47. These figures represent 



OOO 

 000 

 OOP 



OOO 

 000 

 OOO 



Fig. 46. 



Fig. 47. 



a spool of given size and shape wound full of coarse wire and of 

 fine wire respectively. In fact, the diameter of the wire in Fig. 

 47 is half as great as the diameter of the wire in Fig. 46. There- 

 fore there are twice as many turns in each layer of wire, and 

 twice as many layers; and consequently four times as many 

 turns of wire in Fig. 47. Therefore, according to the above 

 proposition, the coil in Fig. 47 has sixteen times as much induc- 

 tance as the coil in Fig. 46. 



The above proposition may be established as follows: Let the 

 coil in Fig. 47 contain n times as many turns of wire as the coil 

 in Fig. 46. Then each particular turn of wire in Fig. 46 corre- 

 sponds to a bundle of n wires in Fig. 47, and lo have a current 



