Inductors and inductance rely on two fundamental interactions between moving electric charge and magnetic fields:

1. Whenever electric charge moves, a magnetic field is produced.


2. Whenever a magnetic field's strength fluctuates, an electric voltage is induced in electrical circuits.

An inductor is a circuit component that's engineered to create a specific magnetic field strength, and hence voltage induction, in either itself (self induction) or in a nearby circuit (mutual induction).

Let's look at the magnetic fields created by various electrical currents.

Current In A Wire

The magnetic field of a current-carrying wire is illustrated below.  The yellow disc is the cross section of a wire whose current flows into the page (the "X" represents the tail of an arrow).

Magnetic "field lines" circulate around the current in a direction called north (N) to south (S).

RIGHT HAND RULE :

Point your right thumb in the direction of the electric current.  Your fingers will curl in the direction of the field.

NOTE :  Keep in mind that, by convention, electric current flows from positive to negative, opposite to the flow of electrons.

Current In A Ring

The magnetic field of a current-carrying loop or ring of wire is illustrated below.

The "X" marks where current is flowing into the page and the "•" marks where current is flowing out of the page (the "•" represents the head of an arrow).

Use the Right Hand Rule to reveal an interesting thing :

The field created by the current at the "X" and the field created by the current at the "•" are directionally aligned and squeezed inside the ring, increasing the overall flux density (symbol B).

Current In A Coil

Finally, look at the magnetic field created by a current-carrying coil of wire having many loops or turns:

The flux density is further multiplied, looking much like that of a bar magnet.  Fluctuations in coil current will now induce even higher voltages.

NOTE :  An Induced voltage is sometimes called an electromotive force, or emf (symbolℰ).  But, despite it's name, emf isn't a force.  Rather, it's the potential energy, in volts, of an electrical source when it's not producing current.

Michael Faraday discovered the law of induction in England in 1871.  In 1872, Joseph Henry discovered the law independently in America.

Faraday's Law says that the emf generated by a loop of current is equal to the rate of change of the magnetic flux (symbol Phi Φ) inside the loop :

Take note of the fact that a flux that changes quickly over time will induce a larger emf than a flux that changes slowly or at a low frequency.

The faster the flux changes, the more emf is generated.

For a tightly wound coil composed of N identical loops, each creating the same flux, Faraday's Law says that:

Lenz's Law

The minus sign in Faraday's Law is called Lenz's Law in honor of Heinrich Emil Lenz who formulated the law way back in 1834.

Lenz's Law states that any electric current induced by a change in magnetic flux will always induce a polar opposite magnetic flux acting against the change.

So, when the electric current through a coil accelerates, a "back emf" is induced, acting against the acceleration.

And when the electric current through a coil decelerates, a "forward emf" is induced, acting against the deceleration.

Each action generates an opposing reaction that tends to preserve the status quo.

Coils are rated using a scale of inductance, symbol L for Heinrich Lenz.  The unit of inductance is the henry, abbreviated capital ‘H’ for Joseph Henry.

Inductance is defined to be the ratio of the amount of flux Φ generated by a coil to the amount of current I flowing through the coil :

So, an inductor that generates one weber of flux per ampere of current has an inductance of one henry (1 H). 

Now, substitute Φ = LI into Faraday's Law [1] as follows :

This shows that, if a coil's inductance (L) doesn't change, the coil will induce a voltage equal to its inductance times the rate of change of current :

So, an emf of 1 V is generated by a 1 H coil when the current through the coil changes by 1 A / s.

Inductors for Tone Control

Faraday's Law [1] says that quick changes in magnetic flux induce more opposing voltage than do slow changes.

In other words, inductors block higher frequency tones more than lower ones, an effect opposite to that of capacitors, which block the lower tones more.

Note that an inductor wired in series with a circuit has an opposite tonal effect to the same inductor wired in parallel with the circuit :

Series-Wired Inductor

This guitar will sound bassy because only lower frequencies can go through the coil to the speaker.

Parallel-Wired Inductor

This guitar will sound trebly because lower frequencies can go through the coil instead of the speaker.

Ampeg^® SVT
Inductor Coils

The following coils control tone in Ampeg^®  'Super Vacuum Tube'  bass guitar amps.

Since the coils are used to mold slow, bass-frequency tones, the coils' size and inductance must be fairly large.

So, to make the SVT coils more compact, they're bent into toroidal (donut) shapes.

This coil sculpts the tone of a mid-1990's Ampeg SVT-CL bass guitar amp.

This is the equivalent coil in an original SVT amp from the late 1960's.

Power Supply Chokes

Inductors are often used in amplifier power supplies, following the AC to DC rectification.  These so-called filter chokes smooth out pulsating direct current by storing and releasing magnetic energy.

This 4 henry choke fits the Fender^® Deluxe-Reverb and Vibrolux-Reverb guitar amps.

It also fits Fender^® Hot-Rod and Blues Deluxes and DeVilles.

Guitar Pickups

Guitar pickups use inductance to generate an electric signal from a magnetic signal.

The magnetic signal comes from a magnetically permeable guitar string that vibrates over the pole of a permanent magnet :

Guitar String Pickup

The permanent magnet magnetizes a length of the guitar string and, as the string vibrates, its shifting magnetic flux cuts across a pickup coil conveniently wrapped around the magnet.

In keeping with Faraday's Law [1], an alternating voltage ℰ is induced in the pickup coil, mimicking the string's motion.  This signal voltage is passed to any connected gear :

Guitar Pickup Connected to Voltmeter

Transformers

Transformers use mutual induction to step AC voltages up or down.

Transformers are also used to transfer AC signals between circuits having differing electrical impedances — for example:  from a microphone to a preamplifier, or from a vacuum-tube amplifier to a loudspeaker.

Transformers comprise two or more wire coils wound around a mutual, magnetically permeable core that directs magnetic flux from the primary winding to one or more secondary windings.

A Simple Transformer Core

Alternating current in the transformer's primary winding creates an alternating magnetic flux in the transformer's core, which in turn induces an alternating voltage In the transformer's secondary winding.

According to Faraday's Law for coils [2], the ratio of the secondary voltage (V_s) to the primary voltage (V_p) is :

But since the flux change (ΔΦ/Δt) is common to both coils, it cancels out of equation [6].  The voltage ratio is simply equal to the ratio of the number of turns in the coils :

Therefore, the secondary voltage equals the primary voltage times the turns ratio :

◉  REMINDER:   V_s and V_p are alternating (AC) voltages.  A steady, DC voltage will give rise to a steady current in the transformer's primary winding and a steady magnetic flux in the transformer's core but this steady flux will not induce any voltage in the secondary winding.  Only a fluctuating flux causes induction.

Sample Transformers

This 100W output transformer is from a Marshall^® JMP amp.

Its primary coil (white and black) is center-tapped (red) for the amp's push-pull output stage.
Its 16Ω secondary coil has 8Ω and 4Ω taps.

This power-supply transformer fits the Fender^® Pro Reverb, Super Reverb, and Bandmaster Reverb guitar amps.

Its primary coil (the white and black wires) connect to the AC house current.  Various AC voltages are induced in several secondary coils, powering the amp's pilot lamp, its tube heaters, and its DC rectifiers.