ROTATING FIELD 31 



and thoso for the currents forming a three-phase system 



ii = Ii sin pt 

 ta = I* sin (pt + 



t' 8 = I 8 sin (pt + 



It may be pointed out that the amplitudes of the currents forming 

 a polyphase system need not necessarily be equal ; if they are, the 

 system is said to be balanced. 



15. Rotating Field produced by Polyphase 



Currents 



Polyphase systems present several advantages * over the single- 

 phase system, one of the most important being the possibility of 

 producing a rotating magnetic field without the aid of any mechanical 

 rotation. 



In order to explain the production of such a field by means of 

 two -phase currents, we may consider two similar coils placed at right 

 angles to each other, as in Fig. 22 ; at any given point of space each 

 coil will produce, when conveying a current, a field proportional to 

 the current. Hence, if we suppose that the coils are traversed by the 

 two currents of equal amplitude 



ii = I sin pt 

 and 



ta = I cos pt 



respectively, the magnetic fields at the common centre of the two 

 coils due to the currents may be written (Fig. 22) 



x = M sin pt, along the horizontal axis, 

 and 



y = M cos pt, along the vertical axis, 



and since the fields are at right angles to each other, the resultant 

 field OR is given by the square root of the sum of their squares, i.e. 

 the magnitude of the resultant field is 



OR = 

 The magnitude of the resultant field is thus constant. In order to 



* These arc considered in 17. 



