Faraday's Law of Induction Calculator
Enter turns, magnetic field, coil area and angular velocity to compute the induced EMF in a rotating coil.
Input Data
Results
At a glance:Faraday's law of induction states that the induced electromotive force in a circuit equals the negative rate of change of magnetic flux through it: ε = −N·dΦ/dt, where N is the number of turns and Φ the flux. The minus sign is Lenz's law, indicating the induced EMF opposes the change. For a coil of area A rotating at angular velocity ω in a uniform field B, Φ(t) = N·B·A·cos(ωt), so ε(t) = N·B·A·ω·sin(ωt) with peak ε_peak = N·B·A·ω and frequency f = ω/(2π), period T = 2π/ω. This is the operating principle of AC generators.
Formula
ε = −N·dΦ/dt
Rotating coil: ε(t) = N·B·A·ω·sin(ωt)
Peak: ε_peak = N·B·A·ω
f = ω/(2π), T = 2π/ω
$$\varepsilon = -N\frac{d\Phi}{dt}$$$$\varepsilon_{\text{peak}} = N B A \omega$$$$f = \frac{\omega}{2\pi}$$How to Use
- Enter turns N, magnetic field B, coil area A and angular velocity ω.
- The calculator returns induced EMF, peak EMF, frequency and period.
Case Studies
Bicycle dynamo coil
N = 200, B = 0.1 T, A = 0.01 m², ω = 31.4 rad/s (~5 Hz).
ε_peak = 200×0.1×0.01×31.4 ≈ 6.28 V.
AC output, frequency 5 Hz.
FAQ
What does the minus sign mean?
Lenz's law: the induced EMF drives a current whose magnetic field opposes the original change in flux, conserving energy.
How does a generator use this?
Rotating a coil in a field produces a sinusoidal EMF; more turns, stronger field, larger area or faster rotation all increase the peak voltage.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.