THE INDUCTION MOTOR 239 



is a maximum when the conductor is in the field of greatest flux 

 density, the current will be a maximum at practically the same 

 instant. The current is then in time-phase with the emf. and 

 hence in space-phase with the flux. Under these conditions the 

 current in the particular conductor which is under the center 

 of the pole, Fig. 227 (a), is a maximum, and that in the other 

 luctors is less, decreasing sinusoidally as indicated. 



Figure 227 (6) shows both the flux distribution in the gap and 

 the current distribution in the conductors of Fig. 227 (a), the 

 current in each conductor being proportional to the flux density 

 of that part of the field in which the conductor finds itself. 

 (For simplicity a smooth current-distribution curve is shown. 

 This would hold true only with a uniform metal sheet about the 

 rotor). The force acting on each conductor is proportional to 

 its current and to the flux density of that part of the field in which 

 the conductor finds itself (see Vol. I, page 310, equation 106). 

 The force due to each conductor, Fig. 227 (a), is indicated hi 

 direction by an arrow attached to that conductor. The torque 

 curve is obtained by taking the product of the current and flux at 

 each point, multiplied by a constant. The torque curve for the 

 conductor belt shown in Fig. 227 (a) is given in Fig. 227 (6). 

 This curve is obtained by multiplying the current at each point 

 by the flux density at that point. That is, the ordinate of the 

 torque curve, at any point Fig. 227 (6), is equal to the product of 

 the ordinates of the flux and the current curves at that point, 

 multiplied by a constant. It will I>e noted that this torque curve 

 is of double frequency, that it is always positive, reaches /. r<> 

 t\vi< < every cycle, and is similar to the power curve of page 22, 

 19. 



As the value of the slip increases, the react a nee of the rotor 



ises, the reactance being proportional to the rotor frequency 



and hence to the slip, and the an^le a by which the current 



lags its induced emf. increases, since tan a = 2irfsL*l\;. The 



current in any conductor will not reach its maximum value until 



a tiin -s after the induced emf. has reached its maximum 



value. In the interval between the time when the induced emf. 



tl maximum and the current reached its maximum, the 



maximum point of the flux wave has moved aloim by tin- 



ductor by a electrical spao a, as shown in I IL:. 'J'jsjo). As 



'lit, some conductors, as o, Fig. 228 (a), find themselves in a 



