# Back EMF

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

EMF back is the instantaneous EMF induced = 2NlvBsinθ

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

### AC motors

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