# How to Calculate Back Emf

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Back emf (electromotive force) is the emf exerted by a magnetic field created by the initial emf. For example, if an emf induces a current through a coil that produces a magnetic field, by Lenz's law, the increasing magnetic field creates its own emf that opposes the emf inducing the magnetic field. It can be shown that this is a result of the conservation of energy. Back emf also goes by the names "self-induced emf," "counter-emf" and "cemf."

### Things You'll Need

• Circuit with an inductor (coil) and emf source
• Ammeter (optional)
• Calculate the resistance (R) of the circuit by running the circuit with an ammeter in place of the inductor (coil). Use V=iR to solve for R (i is the current reading on the ammeter and V is the emf inducing the magnetic field in the inductor and driving the initial current).

• Read the inductance (L) off of the side of the inductor, if the coil was commercially purchased. If you made it and don't know L, take it to an electrician to have L found, since the measurement equipment required is a little complex.

• Solve for the instantaneous rate of change of the current (di/dt) as follows: di/dt=V/L---exp[-Rt/L], where exp uses Euler's number as the base of the exponent in brackets.

• Multiply di/dt by -L to get the back emf. The negative ensures that the back emf is in the opposite direction of the inducing emf (V) regardless of whether the current is increasing or decreasing. If V is decreasing, the back-emf opposes the decrease.

## References

• Argonne National Lab
• R.P. Feynman; Feynman Lectures on Physics; Vol. 2; 1964
• Halliday & Resnick; Fundamentals of Physics; 1989
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