ELECTRIC CIRCUITS 99 



and the flux equivalent to the flux inside the whole section is 



S*R r R 2I 



02 = I d<j> = I -^-.x 3 dx 

 Jo Jo -ft 



i 



and the inductance per centimeter due to the flux inside the con- 

 ductor is 



X 2 = ^ = i c.g.s. units (136) 



The inductance of each wire per centimeter is therefore 



X = Xi + X 2 = 2 log p - +^ c.g.s. units, . . (137) 



and the inductance per mile of wire is 

 L= 2.54 X 12 X 5280^2 X 2.303 logw ^^ + 0.5^10- 9 henrys 



(138) 



71. The Sine Wave of Electromotive Force and Current. If 



the coil abed in Fig. 73 rotates with a constant angular velocity 

 in a uniform magnetic field between the poles N and S, an alter- 



Rotation 



FIG. 73. Generation of an alternating e.m.f. 



nating e.m.f. will be generated between the terminals t and t'. 

 Referring to the figure it can be seen that in position (1) the e.m.f. 

 generated in the coil is zero, since the conductors forming it are 

 moving parallel to the lines of magnetic flux and therefore are 

 not cutting them; in position (2) it is positive and increasing; in 



