LPC Physics 2
Electromagnetic Induction
©
2003 Las Positas College, Physics Department Staff
Electromagnetic Induction
Purpose:
To understand the relationship between current, magnetic field and voltage induced by
changing magnetic flux.
Equipment:
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Large Pole Magnet
Smaller Pole Magnet
Large Loop of Blue Wire
Galvanometer
CRT Oscilloscope (not digital)
Function Generator (AC Power Supply)
DIGI 35A DC Power Supply
2 DMMs
200-Turn Field Coil
2000-Turn Detector Coil
BNC “T” Adapter
1 BNC-BNC Cable
2 BNC-Alligator Cables
Patch Cords
Theory:
In the previous lab we learned how moving charges, or currents, are the sources of all
magnetic fields. Two previously unrelated fields of study, Electricity and Magnetism,
suddenly combined into two sides of the same coin.
The next step in advancing this new field of Electromagnetism was to step back
and ask:
So... we know that we can create a magnetic field with an electrical
current. Does it then follow that we can create an electric current with an
existing magnetic field?
Because it is demanded that any sweeping physical theory be beautiful, and one of the
components of beauty is symmetry, it was decided that magnetic fields must be able to
create electric currents, and the scientific community set out to prove it.
Michael Faraday in England, and Joseph Henry in the United States each
discovered, without knowledge of the other, that an electric current can be produced by
the relative motion of a magnet and a wire. This means that it doesn’t matter if the wire
is held stationary and the magnet is moved around it, or if the magnet is held stationary
and the wire is moved through the field, either case induces a voltage in the wire, and
causes the electrons to move, producing a current.
If you wanted to double the initial voltage produced in the wire, you would
simply coil the wire so that two loops moved through the magnetic field. To triple the
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LPC Physics 2
Electromagnetic Induction
©
2003 Las Positas College, Physics Department Staff
output, simply loop the wire around once more. More voltage induced in the wire results
in a higher current. Remember, though, the definition of the unit of Voltage:
1 Joule
,
1 Volt =
1 Coulomb
so when we increase the voltage, we’re essentially increasing the energy in the circuit.
All by looping wire into a coil! Doesn’t it seem like we’re getting something for nothing,
violating one of the most Sacred Laws in Physics? It does seem that way, but in reality
you would find that as you increased the number of loops in the coil it would become
increasingly more difficult to move the magnet through the loops (or to pull the coil
through a magnetic field). Thus it takes more Work (one type of energy) on your part to
produce more Voltage (a measure of another type of energy) in the circuit. If you were to
continue experimenting with the magnet and coils, you would find that the more quickly
you pushed the magnet through the coils, the larger the voltage produced. This process
of creating a voltage by changing the magnetic field in a coil of wire is called
electromagnetic induction, and is governed by Faraday’s Law:
The induced voltage in a coil is proportional to the
product of the number of loops and the rate at which
the magnetic field changes within those loops.
ε = − N ∆Φ B
∆t
Eq. 1
The amount of current produced in the wire depends not only on the voltage, but also on
the resistance of the coil and the circuit to which it is connected (remember Ohm’s
Law?). The negative sign in Eq. 1 tells us the polarity of the induced voltage (i.e. which
way will the current flow?), which can be determined easily by use of Lenz’s Law:
The polarity of the induced emf is such that it produces
a current whose magnetic field opposes the change in
magnetic flux through the loop. That is, the induced
current tends to maintain the original flux through the
circuit.
One of the consequences of these discoveries is the creation of electric motors and
generators, allowing inexpensive electricity to be distributed to the populace. Although
important and interesting, we will not discuss motors and generators here, though I
encourage you to read about them on your own. Your book is a good place to start, also
Conceptual Physics by Paul Hewitt, which can be borrowed from your instructor or the
lab tech. Here are a couple of websites you can check out:
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/elemot.html#c1
http://www.howstuffworks.com/motor.htm
http://www.simplemotor.com/
http://www.state.hi.us/dbedt/ert/electgen.html
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LPC Physics 2
Electromagnetic Induction
©
2003 Las Positas College, Physics Department Staff
Another consequence, which we will be exploring today, is the creation of electric
transformers, devices that allow the transformation (hence the name) of a certain input
voltage into a higher or lower output voltage. Transformers that output a higher voltage
are called “step-up”, and transformers that output a lower voltage are referred to as “stepdown”.
Transformers work on the principle of electromagnetic induction. The simplest
transformer consists of two coils of wire sitting side-by-side but not connected by any
circuitry. The first coil, or primary coil, is connected to a DC voltage source, a battery.
The second coil, or secondary coil, is connected to a galvanometer, a small lamp, or some
other way to detect voltage through the coil. If the primary coil is initially disconnected
from the voltage source, there is no current in the coil, and therefore no magnetic field
produced. When the circuit is closed, current begins to flow through the coil, and a
magnetic field is created. This magnetic field extends through space to include the
secondary coil. In the time when the magnetic field is “ramping up” from zero to its final
value, the secondary coil is experiencing a changing magnetic field. This causes a
voltage in the secondary coil, which can be seen by a swing of the galvanometer needle,
or the lamp lighting. However, once the magnetic field has reached its final value, it is
no longer changing. We say it is in a steady state. Thus, the secondary coil no longer
sees a changing magnetic field so the induced voltage returns to zero: the galvanometer
needle returns to its initial position, the lamp turns off. This is the case until the primary
coil is again disconnected from the battery: then the galvanometer needle will swing the
other direction, and the lamp will flicker once more.
A DC transformer is not particularly useful, and will rarely (if ever) be seen in the
real world. A much more useful device is the AC transformer. AC stands for alternating
current, which means the current produced by an AC voltage source constantly changes
direction, meaning that the magnetic field produced by the AC current constantly
changes. The system never reaches a steady state, so voltage continues to be induced in
the secondary coil.
So where does the transforming come in?
If the primary coil is a single loop of wire, connected to a 1V AC source, and the
secondary coil is also a single loop of wire, then we will find that 1V AC is induced in
the secondary coil.
1V
1V AC
iron core, often used
to strengthen
magnetic fields
Figure 1
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LPC Physics 2
Electromagnetic Induction
©
2003 Las Positas College, Physics Department Staff
If two (separate) secondary coils are looped around the iron core, each will have induced
in it 1 volt.
1V
1V
1V AC
iron core, often used
to strengthen
magnetic fields
Figure 2
Thus, if we wind one single wire in two loops around the iron core, each loop will have
induced in it 1 volt, for a total induced voltage of 2 volts.
2V
1V AC
iron core, often used
to strengthen
magnetic fields
Figure 3
If we wound three loops of wire in the secondary coil, we would induce a total of 3 volts.
In general, however, the primary coil is made up of more than one loop, or turn, of wire.
This allows us to step down the secondary voltage, as well as stepping up by a noninteger factor. The relationship between primary and secondary voltages with respect to
the number of turns of wire is
Primary voltage
secondary voltage
=
.
Number of primary turns number of secondary turns
Eq. 2
Now it may seem again that we are violating that same Sacred Law, but we’re not.
Remember again, that voltage is not quite the same as energy: it is a measure of energy
per coulomb of charge. So, if I have a higher amount of energy per coulomb, but fewer
coulombs, it can all work out.
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LPC Physics 2
Electromagnetic Induction
©
2003 Las Positas College, Physics Department Staff
(Voltage × current )primary = (voltage × current )secondary
⎛ Joules coulomb ⎞
⎛ Joules coulomb ⎞
×
=⎜
×
⎜
⎟
⎟
⎝ coulomb second ⎠ primary ⎝ coulomb second ⎠ secondary
⎛ Joules ⎞
⎛ Joules ⎞
=⎜
⎜
⎟
⎟
⎝ second ⎠ primary ⎝ second ⎠ secondary
Powerprimary = Powersecondary
The current must change along with the voltage such that the power in the primary coil,
or the energy delivered each second, equals the power in the secondary coil. Energy is
conserved, and all is right with the world.
Using this simple transformer formula assumes that the primary and secondary coils have
the same area. If they do not, we must take into account the fact that the magnetic flux
through each of the coils is not the same.
The magnetic field produced by a loop of wire is given by
r
Bz =
(
µ 0 IR 2
2 z2 + R2
)
3
Eq. 3
2
where
I is the current in the wire,
R is the radius of the loop,
z is the perpendicular height from the center of the loop, and
µo is the permeability of free space = 1.26 × 10 −6 T ⋅ m / A
r
θ
z
dl
R
y
I
Figure 4
When z → 0, this becomes
B0 =
µ0 I
,
2πR
B0 =
µ 0 NI
.
2πR
and if the loop has N turns of wire,
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Eq. 4
LPC Physics 2
Electromagnetic Induction
©
2003 Las Positas College, Physics Department Staff
If we hold a smaller, secondary coil of wire in the magnetic field created by the first, we
will find that the flux through the secondary coil is equal to
Φ = B0 A2 cos θ
Eq. 5
where
B0 is the magnetic field produced by the primary coil,
A2 is the area of the secondary coil, and
θ is the angle between the axes of the coils.
Φ2
loop 2
+
ε
- 2
loop 1
I1
Figure 5
Thus, assuming the area of the secondary coil does not change, and that the coils are held
such that θ = 0, Eq. 1 becomes:
ε 2 = − N 2 A2
∆B0
.
∆t
Eq. 6
The magnetic field changes because the current through the primary coil changes as
I (t ) = I p sin(ωt )
where
Ip is the maximum, or peak, value of the current, and
ω is the frequency of the alternating current, as given by the function generator.
The function generator actually supplies voltage to the circuit, not current. The
ε (t )
, where r is the resistance in
current is related to the voltage by Ohm’s Law, I (t ) =
r
the circuit, in this case our primary coil. The voltage can be determined on the
oscilloscope; it will look something like this:
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LPC Physics 2
Electromagnetic Induction
©
2003 Las Positas College, Physics Department Staff
Figure 6
which can be described by an equation like
ε (t ) = ε p sin(ωt ) .
Thus,
εp
sin(ωt ) ,
r
and, using Eq. 4, our simplest expression of the magnetic field, when z → 0,
I (t ) =
∆B0 µ 0 N 1 ∆I (t )
=
∆t
2πR1 ∆t
⎡ε
⎤
∆ ⎢ p sin(ωt )⎥
r
µ N
⎦
= 0 1 ⎣
2πR1
∆t
=
Eq. 7♣
µ 0 N 1 ε pω
cos(ωt )
2πR1 r
which makes Eq. 6,
ε 2 (t ) = − N 2 A2
where
ε2(t)
N2
A2
N1
εp
ω
R1
r
µ 0 N1ε pω
cos(ωt )
2πR1 r
Eq. 8
is the time-varying voltage induced in the secondary coil,
is the number of turns in the secondary coil,
is the area of the secondary coil,
is the number of turns in the primary coil,
is the maximum voltage in the primary coil,
is the frequency of the voltage in the primary coil,
is the radius of the primary coil, and
is the resistance of the primary coil,
♣
The change from “sin” to “cos” comes from a derivative, a process in Calculus for which we substitute
the macroscopic changes denoted by “∆”. If you want to know more about it, ask your instructor!
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LPC Physics 2
Electromagnetic Induction
©
2003 Las Positas College, Physics Department Staff
when the secondary coil is held at a position z = 0.
The maximum voltage induced in the secondary coil is given by
ε 2 p = − N 2 A2
µ 0 N 1ε pω
2πR1 r
Eq. 9
1
Experiment:
Part A: Electromagnetic Induction at Its Simplest
Note: Each group will need to do this part on their own. You do not have to do this part
first, you can move on to the second, and come back to this when the magnet is free!
1. Hook the large coil of blue wire to the galvanometer. A galvanometer is like a very
simple, analog DMM...it indicates a current flowing through the circuit, but is not
calibrated to measure amperes or voltage.
2. Move part of the coil between the poles of the magnet. Observe and record what
happens to the galvanometer meter. Try moving the coil more quickly and then more
slowly. Record your observations.
3. Observe which direction the galvanometer needle deflects when you move the coil
down through the magnet poles. Record this direction.
4. Observe which direction the galvanometer needle deflects when you move the coil up
through the magnet poles. Record this direction.
5. From your last two observations, see if you can determine which pole of the magnet
is the North pole, and which is the South pole. Remember that magnetic field lines
point from North to South, and that FB = qvBsinθ .
1
The theory for this lab was written by Jennifer LK Whalen
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LPC Physics 2
Electromagnetic Induction
©
2003 Las Positas College, Physics Department Staff
Part B: DC Induction
1. Hook up the circuit as shown in Figure 7 below. Don’t turn the Power Supply on yet!
The DMM should be set up to measure 10A of current.
oscilloscope
DC power supply
DIGI 35A
V
C
-
G +
DMM
secondary coil
primary coil
Figure 7
2. You should turn on both channels of the oscilloscope so that you can see the voltage
going into the primary coil, and the voltage induced in the secondary coil. Use the
vertical position knobs to move one signal to the top half of the screen and the other
to the bottom half of the screen.
3. Turn the voltage knob on the power supply all the way to the left. Turn on the power
supply and the DMM, and slowly increase the voltage. Watch the DMM display to
be sure you do not exceed 2A of current. Record the voltage, Vin as measured on the
oscilloscope (it is more accurate than the display on the power supply). Record the
current, Iin.
4. Hold the secondary (or detector) coil just above the center of the primary coil.
Record the voltage induced in the secondary coil, V2, as measured on the
oscilloscope. Does this value surprise you? Explain.
5. Wave the secondary coil just above the primary coil. Record the changes in the
induced voltage as best you can. Explain why your results in this step differ from
those in Step 4.
Part C: AC Induction – Exploring the Magnetic Field of A Ring
1. Remove the DC power supply from the circuit and replace with a function generator,
or AC power supply. Be sure to turn everything off before disconnecting! Your new
circuit should look like Figure 8.
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LPC Physics 2
Electromagnetic Induction
©
2003 Las Positas College, Physics Department Staff
oscilloscope
function generator
DMM
detector coil
field coil
Figure 8
2. Turn on the function generator. Set the output voltage to a frequency of
approximately 1 kHz. Set the amplitude of the voltage output to 5 V (10 Vpp). Note:
If you can’t get a full 5 V deflection, a smaller value will work fine. Be sure to record
your actual frequency, ω and voltage amplitude, ε1.
3. Place the secondary coil at the center of the primary coil. Place the wand against the
outer ring to try and keep the coils in the same plane. Sketch and describe the voltage
induced in the secondary coil, ε2 with as much information as you can, i.e. amplitude,
frequency, polarity. Explain how and why the induced voltage in this step differs
from that in the previous section.
4. We are now going to use the secondary coil to qualitatively explore the magnetic field
produced by the primary coil. Place a meter stick across the primary coil, slightly to
one side of the diameter, such that when the secondary coil is placed alongside the
meter stick its center falls along the diameter of the primary coil. See Figure 9.
5. Measure the maximum voltage induced in the secondary coil at a minimum of ten
points along the inside of the primary coil. Record the center of the coil as y = 0, and
the outermost points as y = + 5. Make sure to always measure the position of the
center of the secondary coil.
6. Measure the voltage induced in the secondary coil at a few points outside the primary
coil. Be sure to pay attention to the polarity of the voltage!
7. Plot your data points in Excel or Graphical Analysis. Include this plot with your lab
report.
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LPC Physics 2
Electromagnetic Induction
©
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meter stick
detector
coil
field coil
diameter
Figure 9
Part D: Transformers
1. For this section you may need to borrow field coils from one or more other groups.
Be sure to read the directions before proceeding, so as to not waste any more time
than necessary.
2. Remove the detector coil from the circuit. Replace it with a second field coil. Add a
second DMM in series with this field coil so that you can measure the current.
3. Place the secondary field coil on top of the primary coil. Record the maximum
voltage, ε2exp, induced in the secondary coil. Note its polarity. Record the current,
Iexp, in the secondary coil as shown on the DMM.
4. Use the transformer equation to calculate the expected induced voltage, ε2th.
Calculate the percent difference between ε2th and ε2exp. Use your current and voltage
measurements to determine if the power in both coils is equal, within experimental
errors. If it is not, try and explain why.
5. Hook a third field coil in series with the secondary coil. Place both secondary coils
on top of the primary coil. Record the maximum voltage and current induced in the
secondary coils. Note the polarity of the voltage.
6. Use the transformer equation to calculate the expected induced voltage, Vth.
Calculate the percent difference between Vth and Vexp. Use your current and voltage
measurements to determine if the power in both coils is equal, within experimental
errors. If it is not, try and explain why.
Part E: Quantitative Inductance
1. Return all excess field coils to their owners. Replace the detector coil in the circuit as
the secondary coil.
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LPC Physics 2
Electromagnetic Induction
©
2003 Las Positas College, Physics Department Staff
2. Place the secondary coil in the center of the primary coil, at a vertical position of
z = 0. Record the maximum induced voltage, ε2p(exp), and its uncertainty.
3. Measure and record all the variables in Eq. 9, with their corresponding uncertainties.
4. Calculate the theoretical maximum induced voltage, ε2p(th), as given by Eq. 9, with
its uncertainty.
5. Are the values in Step 2 and Step 4 equal, within uncertainties?
Part F (Optional): Helmholtz Coils
1. Connect two field coils in series to the ammeter and function generator (you may
have to collaborate with another group to complete this section). Place the large coils
with their axes collinear, and separated by a distance of one radius, R.
2. Now measure the field between the coils (if you get zero, you have the coils hooked
up in opposition – reverse them, so their fields add). Observe as well as you can the
“inhomogeneity” of the field, that is,
B − Bcenter
.
Bcenter
3. Show, by derivation or deduction, that the field should be homogeneous.
Results:
Write at least one paragraph describing the following:
• what you expected to learn about the lab (i.e. what was the reason for conducting
the experiment?)
• your results, and what you learned from them
• Think of at least one other experiment might you perform to verify these results
• Think of at least one new question or problem that could be answered with the
physics you have learned in this laboratory, or be extrapolated from the ideas in
this laboratory.
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LPC Physics 2
Electromagnetic Induction
©
2003 Las Positas College, Physics Department Staff
Clean-Up:
Before you can leave the classroom, you must clean up your equipment, and have your
instructor sign below. If you do not turn in this page with your instructor’s signature with
your lab report, you will receive a 5% point reduction on your lab grade. How you divide
clean-up duties between lab members is up to you.
Clean-up involves:
• Completely dismantling the experimental setup
• Removing tape from anything you put tape on
• Drying-off any wet equipment
• Putting away equipment in proper boxes (if applicable)
• Returning equipment to proper cabinets, or to the cart at the front of the room
• Throwing away pieces of string, paper, and other detritus (i.e. your water bottles)
• Shutting down the computer
• Anything else that needs to be done to return the room to its pristine, pre lab form.
I certify that the equipment used by ________________________ has been cleaned up.
(student’s name)
______________________________ , _______________.
(instructor’s name)
(date)
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LPC Physics 2
Electromagnetic Induction
©
2003 Las Positas College, Physics Department Staff
DATA TABLES
Part A
Observations:
coil goes down, needle goes: ____________
coil goes up, needle goes: ____________
Calculations to determine Poles of magnet:
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LPC Physics 2
Electromagnetic Induction
©
2003 Las Positas College, Physics Department Staff
Part B: DC Induction
Voltage in Primary Coil, Vin: ____________ Current in Primary Coil, Iin: ____________
Voltage Induced in Secondary Coil, V2: ____________
Explain:
Voltage Induced in Secondary Coil:
Explain:
Part C: AC Induction – Exploring the Magnetic Field of a Ring
frequency, ω: ____________
voltage in primary coil, ε1: ____________
ε2:
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LPC Physics 2
Electromagnetic Induction
©
2003 Las Positas College, Physics Department Staff
ε2
y
Part D: Transformers
frequency, ω: ____________
voltage in primary coil, ε1: ____________
1 secondary coil:
maximum voltage induced in secondary coil, εexp: ____________
maximum current induced in secondary coil, Iexp: ____________
calculation of εth:
εth: ____________
percent difference between εexp and εth: ____________
equal? Explain:
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LPC Physics 2
Electromagnetic Induction
©
2003 Las Positas College, Physics Department Staff
2 secondary coils:
maximum voltage induced in secondary coil, εexp: ____________
maximum current induced in secondary coil, Iexp: ____________
calculation of εth:
εth: ____________
percent difference between εexp and εth: ____________
equal? Explain:
Part E: Quantitative Inductance
maximum voltage induced in secondary coil, ε2p(exp): ____________ + ____________
N2: ____________ + ____________
A2: ____________ + ____________
N1: ____________ + ____________
εp: ____________ + ____________
ω: ____________ + ____________
R1: ____________ + ____________
r: ____________ + ____________
theoretical voltage induced in secondary coil, ε2p(th): ____________ + ____________
calculation:
agreement within uncertainties?: ____________
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