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Electromagnetism · Induction

Faraday’s Law & Electromagnetic Induction Calculator

Calculate induced emf, magnetic-flux change, coil turns, or time interval and interpret the direction with Lenz’s law.

Formula shown Runs locally Reviewed Aug 11, 2026
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Equation guide

Average induction in an N-turn coil during a finite magnetic-flux change

Faraday’s law

εavg = −NΔΦ/Δt

Magnitude

|εavg| = N|ΔΦ|/Δt

Flux through a loop

Φ = BA cos θ
Faraday’s law

Solve electromagnetic induction

Enter positive magnitudes using at most three decimal places. A known N must be a positive whole number because it counts identical series turns. Displayed results are rounded to at most three decimal places.

|ε| = N|ΔΦ|/Δt

Choose the unknown and enter the other three positive quantities.

Using the model

Symbols, assumptions and limitations

Interpretation notes

The calculator uses the average induced emf magnitude for a coil whose linked magnetic flux changes uniformly during the selected interval. A known N is a positive whole-number turn count; a solved fractional N is a mathematical design requirement that must be converted to a practical whole number. The minus sign in ε = −NΔΦ/Δt expresses Lenz’s law: the induced effect opposes the change that produced it.

Worked examples

See the method in practice

01

Changing flux through a coil

A 200-turn coil experiencing a 0.020 Wb flux change in 0.500 s develops an average induced emf of 8 V.

02

Required switching time

For 500 turns and a 0.004 Wb change, limiting the average emf to 10 V requires 0.200 s.

Questions

Frequently asked

What does magnetic flux mean?

Magnetic flux measures the magnetic field passing through a surface. For a uniform field and flat loop, Φ = BA cos θ, where θ is measured from the surface normal.

Why does Faraday’s law contain a minus sign?

It encodes Lenz’s law: induced current creates a magnetic effect opposing the change in linked flux, conserving energy.

Is the result instantaneous or average emf?

It is the average emf over the entered time interval. Instantaneous emf requires the derivative ε = −N dΦ/dt.

Sources & review

Equations and examples are checked against the references below. Results are educational and should be independently verified for safety-critical work.

OpenStax University Physics — Faraday’s Law

Written by the STEM Hub editorial team · Reviewed August 11, 2026 · Review methodology