Hi Faizan!
You may find what you are looking for by following the link or just downloading the attachment
Hope it helps (If it did, please upvote)
Best!
https://mbourget.wikispaces.com/file/view/Back+EMF+in+a+Motor+Notes.pdf
http://www.electrical4u.com/torque-equation-of-three-phase-induction-motor/
Rotor induced EMF, the SE2 is responsible to control the rotor current, could be considered as back EMF, and would be equal to E2 at stand still, when slip S=1. For D.C motor V=Eb+IaRa, or Eb=V-IaRa.
Study Dr. Bimal K. Bose book : "Modern Power Electronics and AC Drives", the answer to this question is way more complicate than you expect...
Induced EMF in the rotor of the Induction motor can be called as Back EMF, which is analogous to back EMF of the DC motor.
The equation of induced voltage in the rotor is Eb = s*E
Where is E = stator emf
s = slip of the induction motor
However there is a difference in the effect of back emfs of Induction motor and DC motor.
In DC motor at the starting the back emf is zero, while in Induction machine Back emf is maximum.
In DC motor, if speed is high back emf is also high but in case of induction motor it is completely reverse. Means if rotor emf is more speed is less and if rotor emf is approaching towards zero speed approaches towards synchronous speed.
An induction machine is a very non-linear 5th ode system, when using Clarke and Park transformations, where you will obtain two equivalent circuits for d and q axis. The use of vector control make it possible to control as an equivalent dc machine, however the dynamics are very complicate to explain in a post like this. In addition to Dr. Bose's book, there are many others, many IEEE papers also cover this subject. My recommendation for you is, do not try to find an equivalent back-EMF, but study hard the d-q modeling of induction machines.
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