I play guitar as a hobby–a little bit of training in jazz, and self-taught from there. It’s fun. I own three instruments, two electric, and both of those are fitted with something that is a very common sight in hard rock and heavy metal: the humbucking pickup. I love this gadget because it’s like a little physics detector, designed for maximum signal and minimum noise. In case you’re not familiar, here’s a handy reference.
In an electric guitar pickup there are two fundamental pieces. There is a permanent bar magnet, much like the one you might use to tack reminders up on your refrigerator, and there is a wire coil wrapped around the magnet. The other critical piece is in the guitar’s strings. These must be weakly magnetic, in the same way your refrigerator will attract a magnet, but not your silverware (even if it’s made of iron). When you bring a magnet nearby something like iron, the iron acts as if it were a magnetic mirror and becomes magnetic itself as long as the external magnetic field is present, with the poles of this “magnetic image” aligned with those of the external field.
Now for this next part I have a bit of a hacked-together diagram, but I think it helps get the point across nicely. As the string vibrates, it will move with relation to the coil directly below it. Since the string is also a small magnetic dipole thanks to the bar magnet inside the coil, this will create a changing magnetic flux through the coil. Magnetic flux is the magnetic field strength in a two-dimensional area, in this case a circular slice of the coil. This changing flux is very important, because of something called Lenz’s law, which says colloquially that “Nature abhors a changing flux.” This means that the changing flux induces in the coil an electromotive force and current which will produce a magnetic field to oppose the changing flux.
A current-carrying loop is one of the simplest entities in magnetostatics. If you use the “right hand rule” and curl your fingers in the direction the current is flowing, your thumb will point in the direction of the magnetic field. From this, we can determine the direction the current will flow when the string moves back and forth across the top of the coil–it will create an alternating current with the same frequency as the vibrations in the string. So all we need to do is use a known resistance to get a changing voltage, which will become the signal that is amplified to produce sound.
But there is a small catch! Electromagnetic fields are everywhere. And unlike the first chapter of an E&M textbook, they aren’t all constant. So even without the string vibrating, the magnetic flux through the coil could constantly be changing. In fact, this causes a humming sound in single-coil pickups which you can hear with enough gain. This hum is eliminated in the so-called humbucking pickup first designed by Seth Lover for Gibson guitars.
The first coil and magnet arrangement is oriented exactly as it would be in a single-coil pickup, but then a second is added. This second is effectively inverted–the magnet’s polarity is reversed and the winding on the coil goes in the opposite direction. If you take your right hand again and check to see the direction in which current is flowing when the string is vibrating, you’ll see that both coils have current in the same direction. Since they are effectively current sources, their signals can be “added” by simply connecting both leads and treating it as a single pickup. Invoking the right-hand rule once more, when the changing flux has the same sign in both coils (as would be the case for ambient fields), you’ll see that the current in each coil opposes the other. These two signals will mostly cancel out, resulting in a less noisy final signal being sent to the amplifier.