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An electric guitar pickup uses the same principle of operation as an electric generator.
A generator or dynamo consists of a coil of wire and a magnet. The coil is made to move in the field of the magnet and, thanks to the wonders of the natural laws of physics, an electric current is induced in the coil.
So the electric guitar pickup consists of a magnet and a coil. But they do not move - both are in firmly fixed positions. The only thing that moves is the guitar string, which vibrates when picked.
It would in theory be possible simply to have a magnet beneath the strings and then pick up the current induced in the strings themselves. Doubtless this has been tried and obviously not found to work sufficiently well. Plainly, a guitar string is a poor imitation of a coil. If connected as part of an electric circuit then it would effectively be a coil, but a coil of only one turn.
So the action of a guitar pickup is a little more complex...
When the string moves in the magnetic field then, since it is made of a magnetic material, it disturbs that field. The disturbance of the field, which acts with the same frequency as the vibration of the string, is physically equivalent to actually moving the magnet. So a current is induced into the coil with the same frequency as the vibration of the string.
The resulting output is moderate in voltage but low in available current. So the electric guitar must be plugged into a specially designed input circuit, which all guitar amplifiers have, that does not require much current. Such an input is called a high impedance input.
Electric guitar strings are made from steel. If they were made from nylon, aluminum, silver, gold or any other non-magnetic material, they simply would not work.