ELECTRIC MOMENTUM. INDUCTANCE. 155 



(34), where / is the current in the solenoid in abamperes. 

 Therefore the total energy of the magnetic field inside of the 

 solenoid is equal to irr 2 x / x (^.irzlj 1 /Sir, according to equation 

 (27), that is, the energy of the magnetic field is given by the 

 equation 



but the energy of the magnetic field is equal to ^LP, accord- 

 ing to equation (48) so that L is equal to 4?rVr 2 /. 



Equations ($$a) and ($$&) are strictly true only for very long 

 coils with thin windings of wire. These equations are frequently 

 useful, however, in determining the approximate inductance of 

 comparatively short solenoids with thick windings of wire. 



82. Electric momentum. Flux-turns. The product of the mass of a moving 

 body and its velocity is called its momentum. The product of the inductance of a 

 circuit and the current is called electrical momentum. The term electrical momentum 

 is seldom employed, the term flux-turns being more usual. 



Proposition. The electrical momentum Li of a coil is equal to the product of 

 the flux through a mean turn of the coil and the number of turns of wire in the coil, 

 that is, 



Li = Z4> (56) 



in which L is the inductance of the coil in abhenrys, i is the current in the coil in 

 abamperes, 4> is the number of lines of magnetic flux passing through a mean turn 

 of the coil, and Z is the number of turns of wire in the coil. The truth of this 

 equation may be made evident as follows : The self-induced electromotive force in a 

 coil is due to the increasing flux produced by the increasing current, so that the self- 

 induced electromotive force is equal to Z-dfyjdt, according to equation (44), 

 where 4> is the magnetic flux through a mean turn of the coil due to the current in 

 the coil. The self-induced electromotive force is also equal to L difdt, accord- 

 ing to equation (5)- Therefore we have 



, di 7 d* 



L 7t= z Tt (') 



whence by integrating * we have Li = Z4>. 



83. The dependence of the inductance of a coil 04 the number of 







turns of wire in the coil and upon the size of the coil. The de- 



* This simple integration occurs so frequently in arguments of this kind that it is 

 worth while to consider its meaning as follows : In order to permit of a verbal ex- 

 pression of equation (i), divide both members by Z, giving dq>ldt-= LjZ X dijdt, 

 which means that the flux 4> increases always Lj Z times as fast as i, so that, if 

 4> and i start from zero together, then 4> must always be L / Z times as large as i. 



