ELEMENTARY THEORY OF ELECTROMAGNETISM. 41 



the north pole. Therefore the magnetic flux inside of the bar 

 at b is 4irM lines.* 



27. The electromotive force in abvolts which is induced in the 

 moving wire be in Fig. 31 is equal to the rate at which the wire 

 cuts magnetic flux. Consider the sidewise distance A* moved 

 by the wire be in Fig. 31 during the short time interval A/. Then: 



Ax = v-At (i) 



The area swept over by the wire during the time interval At is 

 I -Ax, and the amount of flux crossing this area is A$ = HI -'Ax, 

 or, using the value of Ax from (i), we have: 



A$ = Hlv -At (2) 



and, of course, this is the amount of flux which is "cut" by the 

 wire during the time interval At. Therefore, dividing A3> by 

 At we have the rate at which the wire cuts flux [in lines of force 

 (or maxwells) per second], and from equation (2) we have: 



f-Bfo (3) 



That is the rate at which the wire "cuts" flux is equal to Hlv, 

 but Hlv is the electromotive force in abvolts induced in the mov- 

 ing wire, according to equation (i) of Art. 24. Therefore the 

 electromotive force in abvolts induced in the moving wire be in Fig. 

 31 is equal to the number of lines of force (maxwells) cut by the wire 

 per second. 



28. Fundamental equation of the direct-current dynamo. 

 The electromotive force induced in the armature winding of a 

 direct-current dynamo is : 



E (in abvolts) = $>Zn (i) 



in which $ is the magnetic flux which enters the armature core 

 from the north pole of the field magnet and leaves the armature 

 core to enter the south pole of the field magnet as indicated by 



* The bar magnet being very long and slim so that the small portion of the 

 sphere which is inside of the bar at b may be neglected. 



