A turbine uses the movement of a fluid (wind or water, for example) to rotate a magnet within a loop of wires (or rotate the wires in a magnetic field). The electrons in the wire experience a changing magnetic field which forces them to flow down the wire as electricity. Conventional power generation methods, such as burning coal or nuclear fission, also use turbines. The heat from the reaction is used to heat up water, and the steam is used to drive the turbine.
A very famous scientist called Michael Faraday showed that if you move a magnet close to a metal wire, you make an electric current in the wire. So a turbine contains magnets, and as it turns the magnets move past lots of copper wire. This makes an electric current, which is how we make electricity.
Turbines contain magnets and when you turn those magnets near an electrical wire the force of electromagnetism pushes electrons down the wire, making electricity! Its an amazing thing and something we rely on not just for all our electricity generation but also for how we convert our electricity into other things like motion and movement (because the process can also happen in reverse).
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