How a spinning coil makes alternating current

A coil of wire turns between the poles of a magnet. As it turns, the amount of magnetic field passing through the loop keeps rising and falling, and that change pushes electrons along the wire. Each half turn the push reverses, so the output is alternating current whose frequency matches how many turns the coil makes per second.

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Coil speed

Turns of wire in the coil

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A steady magnetic fieldTwo opposite poles face each other, so a steady field runs straight across the gap from north to south.
The turning coilA loop of many turns spins in that gap. When its face points at the poles it holds the most field; edge on, it holds none. The changing field through the loop induces a voltage.
Slip rings and brushesEach end of the coil connects to its own ring. Brushes ride on the rings, so the output keeps reversing direction along with the coil instead of being straightened out.
Faster means more voltsDoubling the speed doubles both the peak voltage and the frequency. Watch the lamp flicker brighter.
More turnsEach turn of wire adds its own share of voltage, so more turns give a higher peak at the same speed and frequency.

Faraday's law for a spinning coil

For a flat coil of N turns and area A spinning at angular speed omega in a uniform field B, the voltage is EMF = N x B x A x omega x sin(omega x t). The peak value is N x B x A x omega, and the RMS value a meter shows is the peak divided by the square root of 2.

This model assumes a 0.2 tesla field and a 10 cm by 10 cm coil, which is 0.01 square meters. The coil is drawn much larger, and its spin is slowed so the motion is visible.

Try it: set 50 turns at 300 rpm, then move to 500 turns at 3600 rpm. The peak voltage grows from a few volts to over 370 volts, while the frequency only depends on speed.

Grid frequency

A two pole machine makes one cycle per turn, so frequency = rpm / 60. Power plants that spin two pole generators at 3600 rpm produce 60 hertz. Machines with more poles can turn slower and still match the grid.

Sources

Electric Generators (College Physics 2)Michigan State University Libraries
DOE Fundamentals Handbook: Electrical Science, Volume 3 (AC generators)U.S. DOE Office of Scientific and Technical Information
How electricity is generatedU.S. Energy Information Administration

How to cite this model

Avid Solutions International. (2026, November 11). How a spinning coil makes alternating current [Interactive 3D model]. Avid Field Lab. https://avidsolutionsintl.com/explore/ac-generator

Last updated November 11, 2026

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