Faraday’s Law
Equipment
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Vernier LabPro
Vernier voltage sensor
Banana cables
Coil
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Bar magnet
Compass
Ruler
Meter stick
Goals of the Experiment
Faraday’s law relates time-varying magnetic field to a “curly” electric field, whose path integral around a closed path is not zero but
provides an emf that can drive current. In this lab you will:
• Explore the meaning of Faraday’s law qualitatively.
• Predict the emf you can produce in a coil due to a time-varying
magnetic field.
• Measure the emf in the coil and compare with your prediction.
A list of useful equations and constants is given at the end of this
document.
Experimental Procedure
Faraday’s law: Qualitative aspects
1. Use the compass to determine which end is the North pole and
mark it with an "N".
2. Set up the Vernier LoggerPro interface to measure the emf generated in a coil.
(a) Log on to the lab computer and open the LoggerPro program.
(b) Make sure that the Vernier voltage sensor is connected to the
LabPro and to the coil terminals. Put the red lead in the side of
the coil that shows the winding direction.
3. Click Start to start recording.
• You can stop recording by clicking Stop.
4. Move the magnet back and forth toward and away from the coil to
see what happens. What quantity is being graphed on the display?
Why is this quantity sometimes positive and sometimes negative?
magnet
coil
5. On your graph, identify an instant when the magnet was stationary.
How can you tell?
6. On your graph, identify the instant when the magnet was moving
fastest. How can you tell?
7. What do you see if the North pole approaches the coil? Moves
away?
8. What if the South pole approaches the coil? Moves away?
9. How does the speed of the magnet affect the emf of the coil? Why?
~
10. Check that − ddtB does correctly predict the direction of the curly
electric field.
Remember that if your right-hand thumb points in the direction of
~
− d B (which is the direction of minus the change in ~B), your fingers
dt
curl around in the direction of the curly electric field.
11. On the side of the coil is marked the direction of the winding of
the coil. The scope displays a positive emf if the curly electric field
in the wire would drive current into the red lead of the voltage
probe (almost no current actually runs, because the scope has very
high resistance, like a voltmeter). If you move the North pole of the
magnet toward the coil, should the emf on the scope be + or −?
12. Move the North pole of the magnet toward the coil. Is your prediction from part 11 correct?
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Faraday’s Law: Quantitative prediction of emf
To predict the magnitude of the emf in the coil, you need to calculate the (approximate) rate of change of magnetic flux through all
turns of the coil due to rapid motion of the magnet.
Determine the magnetic dipole moment of the bar magnet.
Make sure all members of your group understand why you need
this quantity. Remember that you can do this with a compass and a
ruler. Find the center-to-center distance at which the magnet deflects
the compass 70 degrees from North and treat the magnet as a magnetic dipole to determine its magnetic dipole moment. Equations and
constants are given at the end of this handout.
Magnetic flux: Initial position
1. Hold the bar magnet so the closer end of the magnet is just outside
the coil, as shown at right. You need to calculate the approximate
magnetic flux Φ due to the bar magnet through one turn of the coil
at the center of the coil. The negative rate of change of that flux,
− dΦ
dt , is equal to the emf around that central turn of wire.
magnet
coil
2. Examine the coil, which has many turns of wire in many layers.
The number of turns is marked on the coil. Note that the inside and
outside dimensions of the coil are rather different.
3. What value will you use for the area of one turn of the coil? How
did you determine this value?
4. What value will you use for the magnetic field of the bar magnet at
the center of a central turn of the coil?
5. What is the approximate initial magnetic flux through a central turn
of the coil? Why is this flux calculation only approximate?
6. The negative time rate of change of the magnetic flux on one turn of
the coil, − dΦ
dt , is the emf around one turn. If you knew the value of
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dΦ − dt on one turn was 1 × 10−6 volts, what would be the approximate |emf| from one end of the coil to the other? Why would this
|emf| from one end of the coil to the other be only approximate?
Magnetic flux: Final position
1. Move the bar magnet 4 times as far from the center of the coil as
it was initially. By about how much does the magnetic field at the
center of the coil decrease?
2. Therefore, what is the approximate final magnetic flux through a
central turn of the coil?
Time interval ∆t
You need to know the time ∆t required to move the magnet, since
the emf around the central turn of the coil is − dΦ
dt , which is approximately − ∆Φ
,
where
∆Φ
is
the
final
flux
minus
the
initial flux, Φ f − Φi .
∆t
1. Determine the time ∆t during which the flux changes from Φi to
Φf .
(a) You should be able to determine the time required from your
graph of voltage vs. time. Make sure you can identify on your
graph the moments at which motion began and ended, for one
trial. Move the magnet fast. (Why?)
Predict the |emf| generated in the coil
Now predict approximately the |emf| you should observe from one
end of the coil to the other.
Measure the |emf| generated in the coil
1. What is the approximate |emf| you observe on the scope?
2. How does your experimental value compare to your predicted value?
3. Which approximations in your prediction are likely to be most responsible for the difference between your predicted value and your
experimental value?
4. Save a copy of your scope display that shows your observed emf
readings. A reminder on how to save a graph:
• Press the "PrtScn" button at which time a window should pop up
with a picture of your screen.
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• In the "Capture mode" drop-down menu choose "Rectangular Region" and then click "Take a New Snapshot".
• Adjust the non-shaded region with your mouse until it covers the
entirety of your graph and double-click within the non-shaded
region. This will take you back to the previous window.
• Click on the "Save As..." button. Create a proper name, choose to
save to the Desktop and remember to save your file as a .jpg file.
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