Induced Emf⚠ unverified
Physics / Electromagnetics · Compute the induced electromotive force from Faraday's law
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| dPhi | dPhi | Wb | 1.0 | Change |
| dt | dt | s | 1.0 | Time interval over which the flux changes |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | emf | V | Induced EMF, in volts (V). Returns 0.0 when ``dt`` is not positive |
The science & history
Understanding the Parameters
-
$\Delta\Phi$ — flux through the circuit, $\Phi = \int\mathbf{B}\cdot d\mathbf{A}$ (see Magnetic Flux Density page — that card computes $\Phi$).
-
$\Delta t$ — shorter time for the same $\Delta\Phi$ → larger EMF (fast switching spikes).
- Sign — Lenz’s law: induced current opposes the flux change (the minus sign).
Derivation (Approaching a Proof)
Maxwell–Faraday equation $\nabla\times\mathbf{E} = -\partial\mathbf{B}/\partial t$ integrated around a loop via Stokes’ theorem yields
$$\oint\mathbf{E}\cdot d\mathbf{l} = -\frac{d\Phi_B}{dt}.$$
The left side is the induced EMF. For $N$ turns, $\mathcal{E} = -N\,d\Phi/dt$.
History
Michael Faraday (1831) discovered electromagnetic induction; it is the basis of generators, transformers, and inductors.
Related Concepts: Magnetic Flux Density, Self Inductance, Mutual Inductance, Inductance Solenoid, Lorentz Force
Notes: Registry calculator induced-emf (unverified). Single-turn finite-difference form; multiply
flux by $N$ for multi-turn coils if $\Phi$ is per-turn.