This is a genuinely 2D mechanic, not a flattened 3D scene: you are looking straight down the generator's rotation axis, so the coil's two long sides appear as two dots orbiting a circle of radius r in a fixed uniform field B pointing "up" the page. Each dot moves with velocity v = ω×r tangent to the circle. The simulator computes the induced EMF two completely independent ways, every single frame, from real vectors — not from a memorized formula:
Motional EMF (per side): f = v × B (force per unit charge, along the axial wire)
ε_mot = N·L·(f₂ − f₁) integrated along both sides
Faraday's law (numeric): Φ(θ) = N·A·B·cos(θ)
ε_flux = −(Φ(t) − Φ(t−dt)) / dt (finite-difference derivative)
Both should converge to the same closed-form sinusoid ε₀ = N·B·A·ω·sin(θ), where A = 2·r·L is the loop area swept by the two moving sides. The "Method agreement" readout is the live percentage difference between the two independently-computed EMFs — it stays near zero (the small residual is the finite-difference step error in the flux method, which shrinks as the frame rate rises), which is exactly the cross-check that the motional-EMF picture and Faraday's flux-derivative picture describe the same physics.
- ω slider — spin rate of the coil; doubling ω doubles both the frequency and the peak EMF.
- B slider — the uniform field strength; scales the EMF linearly in both methods.
- N slider — number of turns; each turn contributes the same v×B force, so EMF scales linearly with N.
- R slider — load resistance; sets current I = ε/R for a given instantaneous EMF.
- The little ⊙ / ⊗ markers on the two orbiting dots show the instantaneous direction of the axial force qv×B — dot for out of the page, cross for into the page — so you can see directly why the two sides always push current the same way around the loop.
This is the same induction phenomenon as the 3D "AC Generator" simulation on this site, verified here from a different, independently-derived starting point (the motional-EMF integral along the physically moving wires) rather than the flux-through-the-loop bookkeeping alone.