Barry C. Walker Copyright University of Delaware, 2001. Materials may be distributed forDepartment of Physics and Astronomy educational purposes from www.physics.udel.edu/courses. html and the linksbcwalker@udel.edu 302- 831- 2673 contained therein. Not to be sold or otherwise used commercially in whole or part.

1

Lab 7: Electric Guitar and Faraday’s Law

Introduction:

•Similar to E fields from charged material, B fields come from magnetic matter. One of the most basic characteristics of a

magnetic field is its flux, or quantity of field lines per unit area: . The link between moving charges and

magnetic fields is expanded in this lab with investigations of changing magnetic flux. Changes in the flux through an

electrical circuit will induce an electromagnetic force (emf) on the charges in the circuit. This relationship is given

succinctly by Faraday’s law: Faraday’s law has a variety of applications in the real world. For example, the

electric guitar is a popular instrument whose function relies completely on Faraday’s Law. Throughout this lab we will be

examining the behaviors of induced current from changing magnetic fields. By the end of the lab you should:

•Understand the concept of Faraday’s Law

•Understand the emf that influences the induced current in a coil.

•Measure time dependent voltages with an oscilloscope

Materials:

• multimeter

• magnets (a)

• Field coil (b)

• Magnetic field sensor

• Electric guitar string/pickup apparatus (c)

• Oscilloscope

∫ ⋅=Φ AdBrr

dtd

emf BΦ−=

(a)(a)

(c)

(b)

Barry C. Walker Copyright University of Delaware, 2001. Materials may be distributed forDepartment of Physics and Astronomy educational purposes from www.physics.udel.edu/courses. html and the linksbcwalker@udel.edu 302- 831- 2673 contained therein. Not to be sold or otherwise used commercially in whole or part.

2

Experiment 1: Induced Current

If you move charge, you create magnetic fields. Conversely, when a magnetic

field moves their can be a force acting on charges. This is the physics behind

Faraday’s law, , where emf is the electromotive force causing

the charges in the conductor to move and dΦ/dt is the changing magnetic flux.

Since the current is induced there is a negative sign, i.e. field is being put into

the loop rather than created by the loop.

This phenomenon can be examined in the following experiment. You have a

coil of N turns and a variety of magnets. Connect the coil to a multimeter and

examine the emf voltage across the coil when the magnet is in motion near the

coil. Answer the following questions to explore Faraday’s Law and its

characteristics:

•When does the sign of the emf change? Does it matter if you use the S or N

end of the magnet? Why?

•Under what other conditions does the sign of the emf change and why?

•Explain what happens if you bring the magnet toward the coil and then hold it

still?

•Vary the speed at which you move the magnet. What does this do to the emf?

• What orientation of the magnet gives the maximum emf and why?

---

-+

++

+

--+ +

(a)

(b)

(c)

dtd

emfΦ

−=

Figure: The number of field lines in the coil are show to increase (a-c). This increase in flux induces a force, i.e. emf. This force moves the free charges in the loop.

Figure: Measurement of voltage (emf) across a coil when changing the magnetic field. (Note: magnet is being moved by student.

Barry C. Walker Copyright University of Delaware, 2001. Materials may be distributed forDepartment of Physics and Astronomy educational purposes from www.physics.udel.edu/courses. html and the linksbcwalker@udel.edu 302- 831- 2673 contained therein. Not to be sold or otherwise used commercially in whole or part.

3

Clearly there is a phenomena due to the changing of the magnet and the

emf. The figure on the left shows how changing the position changes the

amount of field flux in the loop from a normal dipole bar magnet. With

all of the qualitative features you have observed, make a sequence of

measurements, plotting the results to verify the dependence of the emf

upon the changing B field. For example, verify with a sequence of

measurements that,

emf α ∆B field

A separate set of experiments should be done to verify,

emf α 1/∆t

for a fixed flux change, i.e. verify the rate dependence. These are

qualitative measurements but they can be done scientifically and you will

be graded on the soundness of the reason and conclusion.

N

S

Figure: You can see the increase in flux lines through the loop the closer as it gets closer to the magnet.

Barry C. Walker Copyright University of Delaware, 2001. Materials may be distributed forDepartment of Physics and Astronomy educational purposes from www.physics.udel.edu/courses. html and the linksbcwalker@udel.edu 302- 831- 2673 contained therein. Not to be sold or otherwise used commercially in whole or part.

4

Experiment 2: The Electric Guitar

The electric guitar utilizes the concept of Faraday’s Law as well

as other concepts related to magnetism. All electric guitars have a

device called a pick up which is placed underneath the magnetic

guitar strings. These pickups are wire coils with an average of

4,000 to 7,000 turns! When the magnetized string is plucked, it

vibrates like a little magnet and changes the magnetic flux going

through the coil, inducing an emf through the coil, and producing

an electric signal in the amplifier. For our purposes we will

separate the coil magnet and wire to discover properties of

magnetic materials and Faraday’s Law in the electric guitar.

Part 1: Begin by setting up the pickup and guitar string so as to

imitate a real guitar, and then connect the coil to the oscilloscope

to measure the signal – are these audible frequencies? (If your

computer has a sound card you can even input the signal to the

computer and record your own jam session) Pluck the guitar string

like a normal guitar and see what kind of signal, if any, is

produced on the oscilloscope. Based on that signal do you think

the string is magnetized or not?

Now magnetize the string by placing the bar magnet on the string

where the coil is, and then remove the magnet.

Figure: Who could rock and roll without PHYSICS? Electric guitars rely on the induced EMF from the vibrating string in the guitar pickup to create sound. Guitar pickup with the coil windings cut away. In a working pickup, a magnet is placed beneath each of the wires (the six magnets can be seen above for the six string guitar) to make sure the wire is magnetized.

Click for: American HiFi“Flavor of the Week”

Click for: Alien Antfarm“Smooth Criminal”

Click for: Cranberries“Go your Own Way”

Click for: Kathleen Lague“Play one for me”

Click for: The Muckrakers

“Longitudes”

Barry C. Walker Copyright University of Delaware, 2001. Materials may be distributed forDepartment of Physics and Astronomy educational purposes from www.physics.udel.edu/courses. html and the linksbcwalker@udel.edu 302- 831- 2673 contained therein. Not to be sold or otherwise used commercially in whole or part.

5

Pluck the string again and examine the signal on the oscilloscope. Why is

the signal on the oscilloscope telling you that the string is magnetized?

Roughly what is the frequency at which your string is moving?

Now take the same magnet and demagnetize the string. To do this you

must put the magnet in contact with the string and swipe it across the

string to randomize the magnetic dipole moments. What is the signal

output now?

Describe in detail how Faraday’s law and the induced dipole on the string

relates to the signal that is shown on the oscilloscope.

The Strummer: In order to magnetize the guitar strings, the material of

the string must have certain qualities. There are three main types of

materials that become magnetized when submerged in a magnetic field:

diamagnetic, paramagnetic, and ferromagnetic. Each of these substances

have different magnetic dipole moments, which is the response of the

material subjected to an external field. Working for Fender Music, you

are trying to recapture the innovation and glory that led to the invention

of the electric guitar. Though much work has gone into developing the

coil pickup, not as much technology has gone into improving the strings.

You realize this is just as important. Imagine the possibilities if you could

improve the pickup response of a wire by an order of magnitude, you

would completely revolutionize the pickup and amplification business.

Figure: Guitar pickup beneath guitar string. The coil is connected to a coaxial cable. An external magnet is placed right above thestring (as shown) and then removed to magnetize it. To demagnetize the wire, quickly swipe the magnet along the length of the wire.

Metal Guitar Stringwith magnetic dipole

To amplifiercoil

Figure: Schematic of electric guitar with magnetic dipole and pickup coil.

Barry C. Walker Copyright University of Delaware, 2001. Materials may be distributed forDepartment of Physics and Astronomy educational purposes from www.physics.udel.edu/courses. html and the linksbcwalker@udel.edu 302- 831- 2673 contained therein. Not to be sold or otherwise used commercially in whole or part.

6

You begin by analyzing the effectiveness of current wires.

Guitar strings are often made of iron and therefore ferromagnetic. When a material’s

magnetic dipole moments are 100% aligned the material is at the point of magnetic

saturation. Look at the oscilloscope to determine the highest possible induced voltage that

you produce from plucking the guitar string. Determine the magnetic field actually

produced. Iron has a density of 7,900 kg/m3, and the magnetic dipole moment of an iron

atom is µB=2.1E-23J/T . Measure the diameter of the guitar string,

calculate the volume of the string subjected to the magnetic field (the width of the

magnet), and determine the number of atoms affected by the outside magnetic field.

Determine the magnitude of the magnetic dipole moment that was induced on the string

by the magnet. Did it reach saturation? What percentage of atoms are aligned?

Do a quick calculation on how much industry is based on just faraday’s law and electric

guitars. Perhaps 3% of the US population buys an electric guitar, some may buy three or

four? Suppose Leo Fender did not know his physics. Since the introduction of the electric

guitar in the 1940’s, how much money in the economy are we talking about. How much

money in just the last 10 years?

http://www.fender.com/spa/guitar-strings.html

http://www.si.edu/lemelson/guitars/

http://www.peavey.com/mi/electric_guitars.html

Figure: Leo Fender, inventor of the electric guitar shown with the paperwork from the patent application.