Back EMF (electromotive force) is the voltage generated in the armature of a DC motor (or any electric motor or generator) due to its rotation within a magnetic field. It’s called "back" because it opposes the applied voltage that drives the motor, acting as a counterforce to the current flow. This phenomenon arises from Faraday’s law of electromagnetic induction, which states that a changing magnetic field (or motion through a magnetic field) induces an electromotive force in a conductor.
Back EMF naturally regulates the motor’s speed. If the load decreases, the motor speeds up, increasing, which reduces armature current and torque until equilibrium is reached. It limits the current drawn by the motor, preventing overheating once it’s running. At startup, with no back EMF, the current is limited only by armature resistance, which is why motors often need starters or controllers.
Back EMF Formula |
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\( V_a \;=\; E_b \cdot \Phi_B \cdot \omega \) (Back EMF) \( E_b \;=\; \dfrac{ V_a }{ \Phi_B \cdot \omega }\) \( \Phi_B \;=\; \dfrac{ V_a }{ E_b \cdot \omega }\) \( \omega \;=\; \dfrac{ V_a }{ E_b \cdot \Phi_B }\) |
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| Symbol | English | Metric |
| \( E_b \) = Back EMF | - | \(V\) |
| \( k \) = Motor Constant (Depends on the Design) | - | - |
| \( \Phi_B \) (Greek symbol Phi) = Magnetic Flux per Poll | - | \(Wb \;/\; mm^2\) |
| \( \omega \) (Greek symbol omega) = Angular Speed of the Rotor | - | \(rad \;/\; s\) |
