Formula and Method for Faraday's Law of Electromagnetic Induction
Faraday's Law of electromagnetic induction, published by Michael Faraday in 1831, describes how a changing magnetic field through a loop of wire induces an electromotive force (EMF) — a voltage capable of driving a current around the loop. The law states that the induced EMF equals the negative rate of change of magnetic flux through the circuit, multiplied by the number of turns in the coil: ε = -N(ΔΦ/Δt). This calculator finds the change in magnetic flux, the induced EMF, and the resulting current from the coil's number of turns, the magnetic field before and after, the coil's area, the time interval, and the circuit's resistance.
How the calculation works
Magnetic flux through a single loop is Φ = B × A, where B is the magnetic field strength (in teslas) and A is the loop's area (in square meters) measured perpendicular to the field. When the field changes from B₁ to B₂ over a time interval Δt, the flux changes by ΔΦ = (B₂ - B₁) × A. Faraday's Law scales that rate of change by the number of turns N in the coil, since each turn contributes its own induced EMF and the turns are wired in series: ε = -N(ΔΦ/Δt). Once the coil is connected in a closed circuit with resistance R, Ohm's law converts that EMF into a current: I = ε / R.
Common mistakes
- Forgetting the number of turns: a single loop and a 200-turn coil experiencing the same field change produce very different EMFs — always multiply by N.
- Mixing area units: convert the coil's area to square meters before combining it with a field in teslas, since Φ = B × A only comes out in webers when A is in m².
- Ignoring Δt: the same flux change induces a much larger EMF if it happens in 10 ms than if it happens over 10 s — the rate of change matters, not just the total change.
Real-world applications
- Electric generators and alternators rotate a coil through a magnetic field (or vice versa) to continuously change flux and produce alternating EMF.
- Transformers use a changing current in a primary coil to induce a changing flux, which induces an EMF in a secondary coil.
- Induction cooktops and wireless chargers use rapidly alternating magnetic fields to induce currents in a nearby conductor.
- Metal detectors and induction sensors detect conductive objects by sensing how they distort a coil's magnetic flux.