Faraday’s law of electromagnetic induction
A changing magnetic flux through a conducting loop induces an electromotive force. For N identical tightly coupled turns, the average EMF magnitude over a finite interval is N|ΔΦ|/Δt.
This calculator reports magnitude only. The minus sign in Faraday’s law expresses Lenz’s law: the induced effect opposes the change in magnetic flux. Direction requires a defined loop orientation and flux sign convention.
How to calculate induced EMF
- Choose the unknown: Select EMF magnitude, turn count, flux change, or time interval.
- Use per-turn flux: Enter the magnetic flux change through one representative turn, not total flux linkage.
- Enter a positive interval: Use seconds and a positive integer turn count where entered.
- Interpret direction separately: Apply a loop normal and Lenz’s law if polarity or current direction is needed.
Formula and variables
ΔΦ is the magnetic flux change through one turn. Multiplying by N assumes each turn has the same flux linkage.
|εavg| = N|ΔΦ|/Δt- |εavg| — Average induced EMF
- Magnitude of induced voltage over the interval (V)
- N — Coil turns
- Positive integer number of equally linked turns (turns)
- |ΔΦ| — Flux change per turn
- Magnitude of final minus initial magnetic flux through one turn (Wb)
- Δt — Time interval
- Positive duration of the flux change (s)
One hundred-turn coil
Flux through each of 100 turns changes by 0.02 Wb in 1 second.
- Turns
- 100
- Flux change per turn
- 0.02 Wb
- Time
- 1 s
- |εavg| = 100 × 0.02 / 1
Result: Average induced EMF magnitude is 2 V.
Polarity is not specified by the magnitude calculation; it depends on the chosen orientation and direction of flux change.
Understanding your results
Finite interval means average EMF
If flux changes nonlinearly with time, instantaneous EMF can differ throughout the interval.
- Shorter time for the same flux change produces a larger average magnitude.
- More equally linked turns produce proportionally more EMF.
- A solved noninteger turn count is a mathematical requirement; a physical coil design needs an integer and recalculation.
- Resistance and load current are outside this calculation.
Assumptions
- Every turn has the same magnetic flux change.
- The entered flux is per turn and the time interval is positive.
- The finite-difference average form adequately represents the requested quantity.
Limitations
- Does not calculate instantaneous waveforms, polarity, current, resistance losses, inductance, back EMF, saturation, leakage flux, or mutual coupling.
- Does not derive flux from field strength, area, or orientation.
- Turn-count solutions may be noninteger and require engineering adjustment.
Common mistakes
- Entering total flux linkage NΦ as though it were flux per turn and multiplying by N again.
- Ignoring the difference between average and instantaneous EMF.
- Using milliseconds without conversion to seconds.
- Treating magnitude as a polarity or current direction.
Practical use cases
Electromagnetic induction education
Explore how turn count, flux change, and time affect average induced voltage.
Coil calculation screening
Check a simplified ideal flux-linkage requirement before a complete circuit or magnetic design.
Frequently asked questions
Why is there no negative sign in the result?
The calculator reports magnitude. The negative sign in the signed law encodes Lenz’s-law direction relative to a chosen orientation.
Is ΔΦ for one turn or the whole coil?
Enter flux change through one turn. The calculator multiplies it by the number of turns.
Does this calculate induced current?
No. Current also depends on circuit impedance and any connected load.
Sources and review
- Faraday’s Law — OpenStax University Physics Volume 2. Accessed 2026-07-13.
- Lenz's Law — OpenStax University Physics Volume 2. Accessed 2026-07-13.
Reviewed 2026-07-13.