This simulator rotates a rectangular multi-turn coil at constant speed between opposed magnetic pole shoes, connecting it through slip rings and brushes to a series resistor-inductor load. It tracks flux linkage, induced emf, circuit current and energy transfer as the coil's orientation — and therefore the flux through it — changes continuously.
• A real-time 3D generator with a magnetic yoke and pole shoes, a rotating rectangular coil, shaft bearings and drive, slip rings and brushes, a series R-L load circuit, and field/coil-normal arrows — with home view, focus-selected-part, auto-rotate, expand and toggleable labels. • Seven live controls: series coil turns (20–200), magnetic flux density (0–1 T), coil area (0.002–0.02 m²), shaft speed (0–600 rpm, prescribed constant rotation), total circuit resistance (1–100 Ω), total circuit inductance (0–0.2 H) and a switch to connect or disconnect the load circuit. • Eleven live metrics: coil angle, flux through one turn, flux linkage, induced emf, circuit current, resistive load voltage, mechanical-to-electrical power, resistive energy, inductive stored energy, net converted energy and electromagnetic resisting torque. • A Curves & measurements tab charting voltage/current and energy accounting, the full model equations and snapshot measurements. • An Experiments tab with four guided scenarios (open-circuit generator, pure resistive load, inductive lag, stopping the flux change), a model-verification bench of independent automated checks, and a timestamped event log with a copyable trial report. • A Learn & assess tab with guided lessons, a two-question knowledge-check quiz and a written scope/reference statement.
Flux linkage is λ = NBA cosθ, and induced emf is the negative time derivative of that linkage: emf = −dλ/dt = NBAω sinθ. Because the coil rotates at constant angular speed ω, this produces a sinusoidal emf even though the applied magnetic field itself never changes — the changing geometry, not a changing field, is what induces the voltage. Lenz's law shows up in the electromagnetic resisting torque: the induced current creates its own magnetic effect that opposes the flux change, so under a resistive load the mechanical drive must supply positive average power to keep the coil turning at constant speed.
With the load switch open, the coil still develops emf — flux linkage keeps changing as it rotates — but current stays at zero, so electrical output power is zero even though voltage peaks near 3 V in the open-circuit experiment. Closing the switch into a pure resistance puts current exactly in phase with emf. Adding inductance changes that: the R-L circuit obeys L di/dt + Ri = emf, and after the starting transient the current lags the emf by arctan(ωL/R) — about 51.5° in the inductive-lag experiment — while an inductor can also briefly return stored energy back to the circuit. Two continuous slip rings (not a split-ring commutator) preserve this alternating current rather than rectifying it.
At the fastest rate of change of flux linkage, not at maximum flux linkage. Since emf = −dλ/dt and flux linkage varies sinusoidally, its magnitude peaks when flux linkage crosses zero (fastest change) and is zero when flux linkage is at its maximum or minimum (momentarily not changing).
No. The simulator uses two separate continuous slip rings, which preserve the alternating voltage generated by the rotating coil. A split-ring commutator is a different component that reverses connections each half-turn to produce pulsed DC — that is not what is modeled here.
Because the circuit obeys L di/dt + Ri = emf, an inductor opposes changes in current, delaying its response to the sinusoidal emf. After the starting transient settles, the current lags the emf by a phase angle of arctan(ωL/R) — the inductive-lag experiment sets this up so the lag is about 51.5°.
It is a uniform-field lumped-parameter generator with prescribed constant rotation: mechanical inertia, spin-up, magnetic saturation, brush voltage drop, parasitic capacitance and iron losses are all excluded. The closed R-L response uses the analytical sinusoidal solution starting from zero current, and geometry is representative rather than a manufactured machine specification.