Faraday's Law Calculator
Enter number of turns, magnetic flux change and time to compute the induced EMF ε = −N·ΔΦ/Δt.
Input Data
Results
At a glance:Faraday's law of induction: the induced electromotive force around a closed loop equals the negative rate of change of magnetic flux through the loop, times the number of turns: ε = −N·dΦ/dt. Flux Φ = B·A·cosθ (field × area × orientation). The magnitude is N·|ΔΦ|/Δt. The minus sign (Lenz's law) means the induced EMF drives current opposing the flux change. A transformer works because the changing flux in the primary induces an EMF in the secondary; an inductor stores energy in its field.
Formula
Magnitude: ε = N·|ΔΦ|/Δt
Signed: ε = −N·ΔΦ/Δt
$$\varepsilon = -N\frac{d\Phi}{dt}, \quad \Phi = \int \mathbf{B}\cdot d\mathbf{A} = BA\cos\theta, \quad \nabla\times\mathbf{E} = -\frac{\partial\mathbf{B}}{\partial t}$$How to Use
- Enter the number of turns N.
- Enter the magnetic flux change ΔΦ (Wb) and the time interval Δt (s).
- The calculator returns the induced EMF and rate.
Case Studies
Inductor kick
N = 500, ΔΦ = 0.002 Wb in 0.01 s.
ε = 500×0.002/0.01 = 100 V.
Large transient EMF when current is interrupted.
FAQ
Why the negative sign?
Lenz's law: nature opposes the change. The induced current creates a field that resists the flux change, so energy is conserved.
What units is flux in?
Webers (Wb); 1 Wb = 1 T·m². EMF is in volts (Wb/s).
Related Tools
References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.