ELEMENTARY THEORY OF ELECTROMAGNETISM. 49 



Example. A coil is made by winding a layer of insulated wire 

 on a very long wooden or paper cylinder. The length of the coil 

 is / centimeters, its radius is r centimeters and the number of 



turns of wire is Z. What is its inductance in abhenrys? The 



2j 

 number of turns of wire per centimeter is y [ = z of equation 



(2) of Art. 17]. Therefore, according to Art. 17, the intensity of 



Z 



the magnetic field inside of the long coil is H = 4* X y X /. 



Therefore the amount of magnetic flux passing through the middle 



g 

 part of the coil is irr 2 H or 47r 2 r 2 X y X / But this flux is 



encircled by Z turns of wire. Therefore Z<' is equal to 



-, X I, and this is equal to LI according to equation (2) 

 I 



above. Therefore we have : 



I.-**? (3) 



which expresses the value of L in abhenrys. This equation is 

 only approximate because the flux Trr z H which passes through 

 the middle part of the coil spreads out and does not all pass 

 through the turns near the ends of the coil as shown in Fig. 42. 



Fig. 42. 



32. Self-induced electromotive force. When the current in 



a circuit increases, the flux through the opening of the circuit 



also increases, according to equation (i) of Art. 31. Let us base 



our discussion, however, on equation (2) of Art. 31, where Z 



5 



