Physics 15b PSI Week 6: Electromagnetic Induction
So far, we have investigated the relationship between electric current and
magnetic fields, and how magnetic fields acting on electric currents can generate forces
and therefore motion. This week, we’ll turn it around and take a look at how motion plus
magnetism can generate electricity. This phenomenon is called electromagnetic induction.
Induction is the subject of Chapter 7 of Purcell.
Faraday’s Law of Induction states that if the magnetic flux ! through a loop of
wire is changing, there will be an electromotive force (EMF) induced in the loop, which
acts just like a voltage source. The mathematical statement of Faraday’s Law is that the
EMF E is given by the equation
d"
.
E =!
dt
The minus sign in Faraday’s Law is significant enough that it has its own name:
Lenz’s Law. Lenz’s Law can be stated as such: the direction of the induced EMF is such
that the induced current will produce its own magnetic field to counteract the change in
the magnetic flux.
1. Faraday’s Law
Materials: Pendulum with a permanent magnet mounted in it; 1-inch diameter
wire spool with 100 turns; alligator clips; wire spool holder; oscilloscope; scope
probe
Apparatus Assembly Directions
a. Align the magnet on the pendulum with the wire spool as shown above
i. Make the faces parallel
ii. Align the centers
iii. Make the separation between the magnet and the spool 1 to 2 mm
b. Connect the leads of the spool to the oscilloscope probe and plug into
channel 1 of the scope.
i. Turn on the scope and press the Autoset button (highlighted in blue
below).
ii. Adjust the time scale to 400 ms/box. The scope should go into “roll”
mode where the voltage display slowly rolls across the screen.
iii. Turn the voltage scale to 5 mV/box.
c. Start the pendulum
i. Displace the pendulum so that the center of the magnet is about 20 cm
from the center of the spool
ii. Release the pendulum. You should begin to see a signal like the one on
the right above.
d. Begin data acquisition
i. Once you see a signal, change the time scale to 4 ms/box.
ii. Decrease the voltage sensitivity until voltage peaks are visible on the
screen. An example is shown here:
iii. When you have a signal on the screen, freeze it by pressing the
Run/Stop button, highlighted in green on the picture of the scope
above. (You can press the button again to resume data acquisition.)
e. Send the scope display to the computer
i. Open a browser and click on the bookmark for “Scope View”. You
should see the scope display in the browser window.
ii. Right-click on the image of the scope trace and select “Save image to
Desktop”.
Paste a scope trace from the swinging pendulum into your solution template.
Explain the qualitative features of the EMF vs time by describing the relationship
between the position of the magnet with respect to the coil and the measured EMF.
What is the relationship between the frequency of the EMF signal and the frequency
of the pendulum? Why is the EMF vs time the same regardless of the direction the
pendulum is moving?
If you let the pendulum swing for a long time, does the EMF signal change
gradually? Why?
What is the period of the pendulum? What is the maximum speed of the magnet?
(Don’t try to calculate this theoretically; instead use your scope trace and/or
stopwatch to get an approximate measurement.)
If the B field of the magnet is 0.2 T, what is the approximate magnetic flux when the
magnet is entirely within the coil? What is the approximate flux through the coil
when the magnet is only “halfway in” the coil? If the coil has 100 turns, what is the
magnitude of the EMF you would predict? How well does this match your result?
2. Puzzler
The analysis of this week’s puzzler will be done with pencil & paper on a separate
handout. When you get to this point, save your solution template and upload it.
Then ask one of the instructors for a puzzler handout.