58 ELECTRICAL ENGINEERING 



(r 2 + z 2 )* = r 3 (1 + cot 2 0)' = r 3 cosec 3 = - 



rd6 



dx = r cosec 2 dd = 



sin 2 



if the solenoid is assumed to be very long the limits of may 

 be taken as and TT, and, therefore, 



2<jrr z nl ro s in 3 ,_ / r dd \ 



efl, = I x I ' I 



2-irnI 



I 



2 wnl T . l0 

 = [cosfl; 



(93) 



If the current is expressed in amperes 



. 0.4 irnl , 



cH: = - dynes, ...... (94) 



and the field intensity on the axis of a long solenoid is proportional 

 to the product of amperes and turns or ampere turns and is in- 

 versely proportional to the length of the solenoid. 



The field intensity throughout the volume enclosed by the 

 solenoid is practically uniform except near the ends and can be 

 expressed by equation 94. 



45. Magnetomotive Force of a Solenoid. The m.m.f. of a 

 solenoid is the line integral of the magnetic forces along any 

 closed path through it and is measured by the work done in 

 carrying a unit magnetic pole around the closed path. (Fig. 48.) 



The work done is equal to the product of the current and the 

 flux cut, and thus 



m.m.f. = 4 7rn7, where I is in absolute units, 

 or 



m.m.f. = 0.4 TrttJ, where I is in amperes. 



The magnetomotive force is proportional to the ampere turns 

 of the coil. It does not make any difference whether it is a small 

 current in a large number of turns or a large current in a small 

 number of turns. 



