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Physics of Stringed Instruments acoustic & electric

Physics of Electricity & Magnetism

Electromagnetism – The Basis of Pickup Operation

Electricity and magnetism are two major areas of physics describing the forces that mediate most of the energy transactions fueling physical existence.   In the study of physics they are frequently combined because they are intertwined to such an extent that one is seldom found without the other.  Although we do find electric fields without a magnetic component and magnetic fields without an electrical component, more often the two are found together in an electromagnetic field.  Common guitar and bass pickups are a form of electromagnetic transducer.

Electric Charge & The Electric Field

The concept of electric charge is based on the unit of charge, the electron (negative charge) and the proton (positive charge) which have equal but opposite values.  These are called charge carriers when they are in motion. There appears to be exact balance of charge throughout the universe—although more positive or negative charge may appear in a given area at some point in time, on a macroscopic scale the number of electrons and protons remains equal.

A fundamental property of these charged particles is that like charges repel and unlike charges attract each other.  Although a charged particle at rest exhibits only an electric field, when it is in motion it also exhibits a magnetic field component.  Charge carriers in motion within a conductor are called an electric current.  Electric currents are viewed as the movement of negative charge carriers, the electrons.  The direction of the current is the direction in which the electrons are moving.

Unfortunately this is confused by the persistence of the older concept of a so-called “conventional current,” positive charge carriers flowing in the opposite direction.  It is now understood that the positive charge carriers (protons) in a conductor cannot move; it is the negative charge carriers (electrons) that move.

In Direct Current or DC the charge carriers all move in one direction and their associated magnetic fields have a constant polarity oriented in a circular pattern around the direction in which the charge is moving.

In Alternating Current or AC the charge carriers are constantly reversing direction. Each time the charge carriers reverse direction their magnetic fields collapse and then expand with the opposite polarity.

Magnetism & The Magnetic Field

While magnetism and magnetic fields are associated with moving charges they are also found in nature around ferro-magnetic substances such as lode stones and common manufactured permanent magnets.  On a larger scale the earth, sun, and many planets and their moons all have associated magnetic fields.  It is thought that the earth’s magnetic field is related to electric currents within the earth’s iron core and is therefore the magnetic field component of this electric current.  One notable feature of magnetic fields is that they are always bipolar having both a north and south pole.  A magnetic monopole, just a north or south pole without a companion opposite pole, has never been observed on any scale.  A static magnetic field has only magnetic components, a fluctuating magnetic field also has electric components.

The magnetic field is sometimes described as having “flux lines.”  This convention is handy for illustrating some aspects of magnetic fields, but in actuality there are no lines.  Rather, what is there are what we call vector potentials.

A vector is a quantity having both magnitude and direction.  Those vectors are potential in that if certain materials (namely ferrous metals) are placed in the magnetic field, conditions in and near the ferrous substance will change.  Each little vector in the vicinity will change in both direction and intensity; the vector potentials are modulated by the presence of the ferrous substance.  In an electromagnetic field there are vector potentials associated with the magnetic or B-field component and vector potentials associated with the electric or E-field component.  The vector directions of the B-field vectors and those of the E-field are always at right angles to each other everywhere in the field.

Electromagnetic Induction—The basis of Coil-Magnet Pickup Operation

Pickups are input transducers that convert mechanical motion (the string’s vibration) into an electrical signal.  Most descriptions of their operation say only that the movement of the magnetic field produced by the string’s vibration “induces or causes a voltage to appear across the output.”  As if the whole process were not mysterious enough, this sounds like pure magic!  Where does that voltage come from?  This question is answered in the next few paragraphs.

Charge carriers and magnetic fields interact in a way such that a charged particle moving through a magnetic field is deflected from its path in a certain direction dependant on the orientation of the magnetic field and the direction of relative motion between the two.  This is just one of the many phenomena related to electromagnetic induction.

If the charged particle is moving at right angles to the magnetic field (“flux lines”/B-field vector potentials) the charged particle is deflected in a direction at right angles to both its original path and the orientation of the B-field vectors.

A negative charge carrier (electron) moving away from us through a fixed magnetic field with its north pole up will be deflected to the right.  In a conductor oriented at a right angle to the same field and likewise moving away from us, the charge carriers in the conductor will flow toward its right end producing a voltage difference between the two ends of the conductor.  The right end will have an excess of electrons and have a negative charge; the left end will have a deficiency of electrons (an excess of protons) and it will have a positive charge relative to the right end.

If the rod moved back and forth an alternating current would flow in it and the polarity of the voltage at each end would change with each reversal in the direction of the rod’s movement.

The same alternating current would flow if the rod did not move, but it was the magnetic field that moved back and forth.  It is only relative motion that matters.  Replace the rod with a coil of wire and have the magnetic field move; this is the basis of coil-magnet pickup operation.

This charge transport within the wire is the source of the voltage across the two ends of the coil.  Contained in the current within the coil and in the output voltage are components that are analogs of the fundamental and all of the many overtones or partials in the string’s vibrating pattern.  The current within the coil and the output voltage are changing at many different frequencies simultaneously.

The chain of energy generation and transfer in the system is: vibrating string > magnetic field of the pickup modulated by the vibrating string > charge carriers in the coil deflected by the changing magnetic field > AC voltage across the ends of the coil.

The typical pickup produces an output voltage of between ten and one hundred milivolts (10-100mv) on average. A milivolt is equal to one one-thousandth (0.001) of a volt.  This very small signal voltage is used to modulate the input stage of an amplifier where the signal voltage is made larger and converted to a relatively powerful current in the output stage of the amplifier which drives the speaker.

Interestingly, the speaker is another magnet-coil transducer—an output transducer—this one converting electrical energy (the amplified signal from the instrument) into the mechanical motion of the speaker’s voice coil and cone assembly which produces sound waves.