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
r r
magnetic field is its flux, or quantity of field lines per unit area: Φ=∫B⋅dA . 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
dΦB
succinctly by Faraday’s law: emf= −
Faraday’s law has a variety of applications in the real world. For example, the
dt
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:
(b)
• multimeter
• magnets (a)
• Field coil (b)
(c)
• Magnetic field sensor
• Electric guitar string/pickup apparatus (c)
(a)
• Oscilloscope
Barry C. Walker
Department of Physics and Astronomy
bcwalker@udel.edu 302- 831- 2673
1
(a)
Copyright University of Delaware, 2001. Materials may be distributed for
educational purposes from www.physics.udel.edu/courses. html and the links
contained therein. Not to be sold or otherwise used commercially in whole or part.
(a)
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,
emf = −
dΦ
dt
--
+ +
(b)
, 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
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.
-
+
- - ++
(c)
+
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?
Figure: Measurement of voltage (emf) across a coil
when changing the magnetic field. (Note: magnet is
being moved by student.
• What orientation of the magnet gives the maximum emf and why?
Barry C. Walker
Department of Physics and Astronomy
bcwalker@udel.edu 302- 831- 2673
2
Copyright University of Delaware, 2001. Materials may be distributed for
educational purposes from www.physics.udel.edu/courses. html and the links
contained therein. Not to be sold or otherwise used commercially in whole or part.
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,
N
emf α ∆B field
S
A separate set of experiments should be done to verify,
emf α 1/∆t
Figure: You can see the increase in flux lines through
the loop the closer as it gets closer to the magnet.
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.
Barry C. Walker
Department of Physics and Astronomy
bcwalker@udel.edu 302- 831- 2673
3
Copyright University of Delaware, 2001. Materials may be distributed for
educational purposes from www.physics.udel.edu/courses. html and the links
contained therein. Not to be sold or otherwise used commercially in whole or part.
Click for: American HiFi
“Flavor of the Week”
Experiment 2: The Electric Guitar
The electric guitar utilizes the concept of Faraday’s Law as well
Click for: Kathleen Lague
“Play one for me”
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
Click for: The
Muckrakers
“Longitudes”
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.
Click for: Cranberries
“Go your Own Way”
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
Click for: Alien Antfarm
“Smooth Criminal”
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.
Barry C. Walker
Department of Physics and Astronomy
bcwalker@udel.edu 302- 831- 2673
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.
4
Copyright University of Delaware, 2001. Materials may be distributed for
educational purposes from www.physics.udel.edu/courses. html and the links
contained therein. Not to be sold or otherwise used commercially in whole or part.
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
Figure: Guitar pickup beneath guitar string. The coil is connected
to a coaxial cable. An external magnet is placed right above the
string (as shown) and then removed to magnetize it. To
demagnetize the wire, quickly swipe the magnet along the length
of the wire.
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:
Metal Guitar String
with magnetic dipole
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
coil pickup, not as much technology has gone into improving the strings.
To amplifier
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.
Barry C. Walker
Department of Physics and Astronomy
bcwalker@udel.edu 302- 831- 2673
5
Figure: Schematic of electric guitar with magnetic dipole and
pickup coil.
Copyright University of Delaware, 2001. Materials may be distributed for
educational purposes from www.physics.udel.edu/courses. html and the links
contained therein. Not to be sold or otherwise used commercially in whole or part.
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?
Figure: Leo Fender,
inventor
of
the
electric guitar shown
with the paperwork
from
the
patent
application.
http://www.fender.com/spa/guitar-strings.html
http://www.si.edu/lemelson/guitars/
http://www.peavey.com/mi/electric_guitars.html
Barry C. Walker
Department of Physics and Astronomy
bcwalker@udel.edu 302- 831- 2673
6
Copyright University of Delaware, 2001. Materials may be distributed for
educational purposes from www.physics.udel.edu/courses. html and the links
contained therein. Not to be sold or otherwise used commercially in whole or part.