42 ADVANCED ELECTRICITY AND MAGNETISM. 



the lines of force in Fig. 35, Z is the number of wires lying length- 

 wise on the outside surface of the armature, and n is the speed 

 of the armature in revolutions per second. This equation applies 

 to the direct-current dynamo having a two-pole field magnet.* 

 While one of the armature wires moves from a to b in Fig. 35 



Fig. 35. 



it cuts all of the magnetic flux <i> which enters the armature core 

 from the north pole of the field magnet. The time of one revolu- 

 tion of the armature is I/nth of a second, and the time required 

 for a wire to move from a to b in Fig. 35 is i/2nth of a second. 

 Therefore, dividing $ (the amount of flux cut) by i/2wth of a 

 second gives 2n$ as the average rate of cutting of flux or the 

 average electromotive force induced in an armature wire while it 

 moves from a to b. But the average electromotive force in a 

 given wire while it is moving from a to b, is the same as the 

 average electromotive force in all of the armature wires between 

 a and b at any instant. Therefore 2w<i> is the average induced 

 electromotive force in the wires (\Z in number) on the half- 

 armature acb; but the wires on the half-armature are all in series, 

 and therefore the electromotive force available at the brushes is 

 2, 

 - X 2n$ from which equation (i) follows at once. 



The induced electromotive force E in equation (i) may be 



* The general form of the equation is discussed on pages 99-100 of Franklin and 

 Esty's Dynamos and Motors, The Macmillan Co., New York, 1909. 



