EASA / CAR Part-66 · Module 3 · 3.13 AC Theory · Cat A · B1/B2

AC Generation, the Rotating Coil

Objective: a coil rotating in a magnetic field induces a sinusoidal EMF, e = N·B·A·ω·sin(ωt). Spin the loop between the poles and see why the voltage peaks when the coil is edge-on to the field and falls to zero when it lies flat across it.

Coil rotating between the poles

Induced EMF & phasor

Rotation speed 600 rpm

Flux density B 0.6 T

Turns N 20

Coil area A 100 cm²

Frequency f

0Hz

Peak EMF Ê

RMS EMF

EMF now

e = N·B·A·ω·sin(ωt) · Ê = N·B·A·ω · ω = 2πf · E_rms = Ê/√2

As the coil turns, the magnetic flux through it changes and induces an EMF e = −N·dΦ/dt. With flux Φ = B·A·cos(ωt), that rate of change is a sine wave. The EMF is greatest when the coil is edge-on to the field, its sides sweep across the flux fastest, and zero when the coil lies flat facing the poles, where the flux is momentarily at a maximum and not changing. Spinning faster raises the frequency and the peak voltage together, because ω appears twice: once as the rate of rotation and once inside Ê = N·B·A·ω. The slip rings and brushes carry the alternating current out to the load.

Try this: Double the speed, watch BOTH the frequency and the peak EMF double.
Try this: Freeze the moment the waveform crosses zero, the coil is lying flat across the poles.
Try this: Raise the turns N, only the amplitude grows, the frequency is unchanged.
Try this: Note E_rms ≈ 0.707 × Ê, the value an AC meter would show.