Back EMF

emf figure

In the above figure,

  • EMF applied produces a current in the rod
  • Current interacts with field, producing a force to the right (F = IlB)
  • Speed of rod (v) increases
  • However, the rod is cutting through field lines
  • Therefore, an EMF is induced (Faraday’s law)
  • This EMF is induced in the opposite direction to the applied EMF!
  • EMF back = lvB


  • Hence, the EMF pushing current is equal to: EMF applied – EMF back
  • As v and EMF increase, EMF current decreases, and so therefore I and F decrease, so acceleration of the rod stops at max velocity.

Back EMF in DC motors

  • As a DC motor spins, EMF back is produced, since the coil is cutting through field lines.
  • Therefore, the voltage available to produce current in the coil, and therefore torque, is equal to

EMF applied – EMF back

 back emf graph

EMF back is the instantaneous EMF induced = 2NlvBsinθ

  • If motor speed increases, current in coil decreases, and so the applied torque decreases

backemf graph2 back emf graph3

AC motors

  • Simple AC motors are simple AC generators in reverse
  • All usual equations apply.




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