THE MAGNETIC FIELD IN THE POLYPHASE MOTOR. 



the field would be to set up an e. m. f. equal to 2.22 ~ z . <j> , 10"* volts; 

 however, through the distribution of the winding, only the parts of 

 the flux not covered with hrtchings can produce an e. m. f. expressed 

 by this formula, while the hatched parts of the field will have a con- 

 siderably smaller effect. The induced e. m. f. can be calculated as 

 follows : The width of the coil is 2b ; there are conductors in the coil 



spread over 2b. Per unit length there are, therefore, - conductors, 







hence the element d x contains d x . - conductors. The number of 



2b 



lines of induction threading the conductors in the element dx \t 

 equal to ** represented by the hatched area. We have, therefore, 



d e = 2.22 . ~ . . d x . ** . 10-8 volts. 

 2 b 



*, =<B.l_ aJ r.^~ = 

 2 2 



Hence n r&.^.. .. 



de = 2.22 . ~ . - --- I . io- 

 ib -L 2 26 



($,.x*.(tx-\ 



I . 

 26 J 



JL [jV^ - /B^lff I . I0 , 



2 ^L. o 2b J 



. _n . ,o 



6 J 



e = 2.22 . ~ . -" . ifi . -. . io- 

 2 3 



We have * = , therefore 

 2 



(4) <r = 2. 



This is in words, The e. m. f. induced by the field * upon a coil of 

 the width b is two-thirds as large as the e. m. f. which would be in- 



13 



