Faraday's Law and Generators

Move a magnet through a coil of wire and a voltage appears across the coil's terminals. Move it faster and the voltage increases. Use a stronger magnet and the voltage increases. Add more loops to the coil and the voltage increases. Michael Faraday discovered this in 1831, and it remains the operating principle of nearly every power plant on Earth.

Faraday's Law states that a changing magnetic field through a coil induces a voltage proportional to the rate of change. More precisely: the induced voltage equals the number of coil turns multiplied by the rate at which the magnetic flux changes. Faster change, more voltage. More turns, more voltage.

In a generator, the "changing magnetic field" comes from a rotor (magnet or electromagnet) spinning inside a stator (set of stationary coils). Each rotation sweeps the magnetic field through the coils, inducing voltage that drives current through the external circuit. The mechanical energy spinning the rotor (from steam, water, or wind) converts to electrical energy in the coils. The frequency of the output AC matches the rotational speed: 60 rotations per second (3,600 RPM for a 2-pole generator) produces 60 Hz AC.

Worked Example

A generator has 100-turn coils. The magnetic flux through each turn changes at a rate of 2 webers per second (2 Wb/s).

• Apply Faraday's Law. Induced voltage = N x (dΦ/dt) = 100 x 2 = 200 V.

If the generator operator doubles the rotation speed, what happens to the induced voltage (approximately)?

The rate of flux change doubles, so the voltage roughly doubles to 400 V. This is why generator output voltage depends on rotational speed, and why maintaining precise speed (and therefore precise frequency) is critical for grid stability.

Faraday's Law is the quantitative link between mechanical rotation and electrical output in every generator on the grid.

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