D.4 · IB Physics
AC generator
Spin a coil in a magnetic field. The flux swings as cosθ and the EMF is its negative gradient, so the EMF peaks where the flux is zero. Change speed, field, turns and area.
Predict first
Start from the default settings (120 rpm, 0.5 T, 50 turns). If you double the rotation speed to 240 rpm, what happens to the peak EMF and the frequency?
ε₀ = NBAω and f = ω ÷ 2π are both proportional to ω, so doubling the speed doubles both (6.28 V to 12.6 V, 2 Hz to 4 Hz).
Check it in the model: Move the Rotation speed slider from 120 to 240 rpm and compare the Peak EMF ε₀ and Frequency f readouts.
Traces show the last 2.00 s. Flux (green, normalised) and EMF (navy, in volts).
ε = −dΦ/dt = N B A ω sinωt
ε₀ = N B A ω , ω = 2π f
ε(rms) = ε₀ ÷ √2
- Peak EMF ε₀
- rms EMF
- Frequency f
- Period T
- Coil angle θ
- Flux linkage NΦ now
- EMF now
Try this
- Run the baseline (120 rpm, 0.5 T, 50 turns, 0.020 m²) and note ε₀ and f. Double the rotation speed to 240 rpm. What happens to ε₀ and to f?
- Press Pause when the EMF trace is at a maximum. What are the coil angle θ and the flux linkage at that moment, and why?
- Return to the baseline and double N from 50 to 100. Compare ε₀ and f with what you got by doubling the speed.
Exam tip: when asked to sketch the new EMF graph after the speed changes, double the peak and halve the period together, since both ε₀ and f are proportional to ω, and the peaks sit where the flux is zero.