Problem — The electric guitar

Problem

The electric guitar uses magnetic pickups placed beneath the strings. How do they convert the vibration of a metal string into electrical voltage? Discuss in five lines and explain why they only work with ferromagnetic strings.

Solution

A pickup consists of a permanent magnet around which a coil of many turns is wound. The magnet magnetises the section of ferromagnetic string above it: the string thus becomes a small magnet.

When the plucked string vibrates, it moves closer to and further from the pickup: the magnetic flux linked with the coil varies in time. By Faraday-Neumann’s law an induced EMF $E=-N\,\dd\Phi/\dd t$ arises, an electrical signal that reproduces the vibration frequency of the string and is then amplified.

A ferromagnetic string (steel, nickel) is required: only a material that magnetises enough produces an appreciable flux and modulates its variation. Nylon or other non-magnetic strings do not alter the flux, so they generate no signal.

$\ev{\text{magnetised string vibrates}\to \dd\Phi/\dd t\neq 0\to \text{induced }E\text{; ferromagnetic materials only}}$

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Topics: Induzione elettromagnetica Concepts: Legge di Faraday-Neumann-Lenz · Flusso magnetico · Induttanza e autoinduzione