A loop of wire spins steadily in a fixed magnetic field — the world's recipe for electricity. The voltage it makes alternates. Spin it faster and you obviously get more cycles per second — but does the PEAK voltage rise too, or is it fixed by the field and the loop?
▶ Launch the interactive simulationRotate a loop (N turns, area A) at angular velocity ω in a uniform field B, so the flux linkage Φ(t) = N B A cos ωt sweeps a full cosine each turn. The lab traces Φ(t) against the induced EMF = −dΦ/dt, marks the loop's face-on (Φ extremum) and edge-on (Φ = 0) instants, and overlays the SAME loop spun at 2ω. A real generator — N=100, A=0.02 m², B=0.25 T, f=50 Hz — is also read with 2% noise on its peak.
EMF = N B A ω sin ωt — a SINE 90° behind the cosine flux, so the voltage is exactly ZERO when the loop is face-on (flux MAXIMUM, conductors sliding along the field) and PEAKS when the loop is edge-on (flux zero, conductors cutting fastest): the rotating, steady-state form of 'rate, not flux'. And the peak ε₀ = N B A ω is PROPORTIONAL to ω — double the spin, double the frequency AND double the amplitude (why a bicycle dynamo brightens, not just flickers); inverting a real ε₀ ≈ 157 V weighs the field B = ε₀/(N A·2πf) ≈ 0.25 T