354 THE -INDUCTION MOTOR. 



the direction of the main flux at the instant under con- 

 sideration. The rotor is assumed to have no magnetic 

 leakage, and the circuits formed by the conductors 

 are consequently without self-induction. 



P is the position of a conductor, O P making an 

 angle a with the vertical 



. B = maximum field density. 



b = field density at P. 



s = slip. of rotor. 



a = radius of rotor. 



v = rate of motion of field relatively to conductors = 

 2 TT sa. 



I = length of rotor core. 



N = number of rotor conductors. 



r = resistance of each conductor. 



c 1 = current induced at given moment in conductor 

 at P. 



c = virtual value of current induced in conductor. 



e 1 = E.M.F. induced at given moment in conductor 

 at P. 



e = virtual value of E.M.F. induced in conductor. 



Then 



e 1 = lines cut per second by conductor = Ib v. 



Since distribution of field round the armature is 

 sinusoidal and the maximum density is along X ( =B). 



b = B sin a 

 hence e 1 = IvB sin a = 2 TT sal B sin a 



e 1 2 Trsal B sin a 

 and c 1 = - (2) 



The maximum value of c 1 will be 



r 



Consequently the virtual current = c = ,-~ (maxi- 



%irsalB A/IT T sal B 

 mum value ot c 1 ) = 7 ~- 



A/2. r r. 



Instead of B it is more useful to state the flux in 

 terms of the total number of lines forming the rotating 

 field ( = Z). 



2 B 

 The average value of b or B sin a is - - since the 



7T 



average value of sin a = - 



7T 



