AC Generation — the Rotating Coil

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.