Magnetism
Induced voltage: changing flux
- where
- induced voltage (V)
- number of turns
- flux change per turn (Wb)
- time taken (s)
Explain this equation
Gives the average voltage induced in a coil when the magnetic flux through it changes. It is the basis of transformers and generators, and explains the voltage kick when an inductive load is switched off.
N is the number of turns. ΔΦ is the change of flux through each turn, in webers. Δt is the time that change takes, in seconds. |e| is the size of the average induced voltage; the vertical bars mean magnitude only, with no polarity.
Each turn develops a voltage equal to the rate of change of flux through it, and turns in series add up, so N multiplies. A faster change, meaning a smaller Δt, gives more voltage. The induced voltage opposes the change (Lenz's law), which is the minus sign left out of this magnitude form.
100 turns with a 0.02 Wb change in 0.1 s gives 20 V. Make the same change ten times faster and you get 200 V, which is why interrupting current in an inductor can cause a large spike.
Watch out: ΔΦ is the change per turn, not for the whole coil. The answer is an average over Δt, not the peak.
A changing magnetic flux induces a voltage in a coil. More turns or a faster change gives a larger induced voltage.
The magnitude formula does not state polarity. Lenz’s law gives the opposing direction, represented by a minus sign in the signed Faraday equation.
Enter your values to see the result.
Common mistake
Forgetting that flux change is per turn.
Limits
Magnitude of the average emf for the stated flux change; each turn links the same flux. It is not the average of the absolute emf if polarity reverses during the interval.
Sources
The tools calculate the displayed equation. They do not automatically choose cable sizes, approve installations, supply current regulatory tables, certify equipment or replace inspection and testing.