NAME:
DATE:
AP-LAB22: Electromagnetic Induction and Faraday's Law
BACKGROUND
We have seen that a potential difference applied to a wire will cause an electric current to
flow through that wire. We have also seen that a current flowing through a wire creates a
magnetic field. At the heart of the phenomenon known as electromagnetic induction is the
idea that we can use a changing magnetic field (or, more accurately, a changing magnetic
flux) to induce an electric current in a nearby wire. We define magnetic flux in the
following way: imagine a loop which encloses an area A in magnetic field B. The magnetic
flux is then equal to
G G
Φ B = B ⋅ A = BA cos φ
(Eq. 1)
The S.I. unit for magnetic flux (ΦB) is the weber (Wb), where 1 weber = 1 tesla-square meter (1 Wb = 1 T·m2).
Having defined magnetic flux, we can now go on to state Faraday’s Law, which relates the time-rate of change of the
magnetic flux to the electromotive force (emf or ε) induced by that change:
ε =−
ΔΦ B
Δt
(Eq. 2)
While we typically discuss Faraday’s law in the context of the current induced in a conducting wire or material, it should
be noted that Eq. 2 holds even in the absence of any conductor. That is to say, that an electric field is induced in the vicinity
of any changing magnetic field. If a conductor is present, the electric field induced by the changing magnetic flux will
induce a current to flow through the conductor. We refer to this current as the induced current, and the electric potential
difference that must be present as the induced emf (ε).
The minus sign in equation 2 indicates that the electric field or the emf tend to oppose the change in magnetic flux that
created them. We can restate this in the form now commonly known as Lenz’s law:
An induced current has a direction such that the magnetic field created by the induced current opposes the
change in magnetic flux that induced the current in the first place.
PURPOSE
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To explore the electric current/potential induced (emf) by a changing magnetic flux.
To explore how the induced current/potential (emf) depends upon the rate of change of magnetic flux.
To explore how the number of coils in a Faraday coil affects the induced current/potential (emf).
To explore and understand how a magnet moving near a coil induces an emf.
MATERIALS
Windows PC
LabPro
LoggerPro
Vernier Voltage Probe
Wires and clips
APLab 22: Electromagnetic Induction and Faraday's Law Mr. Maloney Physics … 200, 400, 800 loop Faraday coils
Neodymium Magnet(s) with bolt
Slotted PVC Tube with toothpick
Physics Stand with clamp
Magnetic Compass
1/4 NAME:
DATE:
PRELIMINARY QUESTIONS
P1. What are some ways that you can change the magnetic flux through a coil?
P2. Sketch a graph of the induced emf measured as you drop a magnet through a coil.
P3. How do you think changing the number of coils in a Faraday coil will affect the induced emf?
P4. How do you think stacking two magnets on top of each other and dropping them through a Faraday coil
will change the induced emf with respect to just dropping one magnet through?
P5. How do you think changing the velocity that a magnet enters a Faraday coil at will affect the induced
emf in the coil?
P6. You will be changing the velocity through the coil by dropping the magnet from different heights.
From your knowledge of freefall, determine the relation between drop height and velocity.
P7. The pipe you have is approximately 0.56 m long. Determine three drop heights that will give you
velocities of the ratios: v, 2v, 3v. Remember the highest height cannot be more than 0.560 m, so you
might want to start there.
PROCEDURE
The specifics of the procedure will again be up to you. You will be given some guidance since some of the
equipment and mathematical techniques are new to you, but in terms of number of trials, order, measuring, etc it
will be up to you to choose a process that will give you good data. This lab is also a little different as you will
be answering some questions as you go along in your lab notebook and clean them up at the end for your report.
You will be determining four main ideas
A) What does a plot of Induced emf vs. time in a coil look like and why does it look that way?
B) How does changing the flux (in different ways) affect the induced emf?
C) How doe those different ways change the flux and in turn the emf produced?
D) What is the peak magnetic field strength of your magnet?
Part A: A plot of Induced EMF through a Faraday Coil. In this part you will get use to the collection apparatus and also discover
what a plot of induced emf looks like for a magnet dropping through a coil.
Setup the apparatus shown to the right if it is not set up already.
One side of your magnet is colored blue. Use a compass to determine if
the blue side is the north or south pole of the magnet.
Open the file [APLab22-Induction.cmbl] in LoggerPro. Make sure
the LabPro is plugged in with the Voltage Probe attached to Channel 1.
Connect the Voltage probe to the leads coming from the coil. Make sure
you
the probe before taking data.
Fig. 1: Experimental
This file is set to take triggered data. When the measured Voltage increases by 0.01 V the computer starts
recording data. To take a measurement hit
then drop the magnet down the tube with the north pole
facing down. To make the magnet fall straight, attach the screw to the top side of it before dropping.
You should see a graph with 2 peaks that measures the induced emf as a function of time.
APLab 22: Electromagnetic Induction and Faraday's Law Mr. Maloney Physics 2/4 NAME:
DATE:
QUESTION 1: keeping in mind that the induced voltage is proportional to the rate of change of magnetic
flux, explain why the graph looks they way it does.
Use LoggerPro to measure the following values and record them in your lab notebook.
 The peak voltage of the first peak (maximum emf)
 The peak voltage of the second peak (maximum emf)
 The integral (area under curve) of the first peak
 The integral (area under curve) of the second peak
QUESTION 2: How do the peak voltages of the two peaks compare? Is one always larger than the other?
If so, what might explain this?
QUESTION 3: How do the areas under each peak compare? Should these areas be the same or should
one be larger than the other? Explain.
Repeat the experiment but this time reverse the direction of the magnet. Drop it through from the same height
and collect data with the north pole facing up instead of down.
QUESTION 4: Explain the difference between the curve you get with the north pole up and what you got
before with the north pole down. There are at least two other ways to get the same type of change by
modifying the experimental setup. Find at least one way to do this.
Part B: Investigating the dependence on the number of magnets (strength of B‐field) You can take your magnets apart. Complete trials for 1, 2, and 3 magnets and use them with your data from
Part A for 4 magnets to determine the relationship between the number of magnets and the induced emf.
QUESTION 5: How does the number of magnets affect the value of the maximum induced emf? Can you
write an equation that summarizes this? Try plotting the data and fitting it to a curve.
Part C: Investigating the dependence on N, the number of loops in the coil. You have three coils available, a 200 turn, 400 turn and 800 turn. Using the three coils, create and conduct a
procedure that will allow you to determine the dependence of the induced emf on the number of coils.
QUESTION 6: How does the number of coils affect the value of the maximum induced emf? Can you
write an equation that summarizes this? Try plotting the data and fitting it to a curve.
Part D: Investigating the dependence on v, the speed of the magnet through the coil. If you remember freefall, the velocity of the magnet as it goes through the coil is going to be derermined by the
height you drop the magnet from. Choose 3 heights that will give you velocities in ratios of v, 2v, 3v. Your
highest height will give you the highest velocity (3v) so it will probably be easier to start there and determine
what height will give you 2/3 that velocity, and 1/3 that velocity.
QUESTION 7: How does the velocity affect the value of the maximum induced emf? Can you write an
equation that summarizes this? Try plotting the data and fitting it to a curve.
APLab 22: Electromagnetic Induction and Faraday's Law Mr. Maloney Physics 3/4 NAME:
DATE:
Part E: Estimating the strength of the magnetic field (B) of the magnet. QUESTION 8: At what point during the fall do you think the flux is the largest?
Now it is time for a little calculus. Starting with Equation 2 we can solve for the change in flux (ΔΦ). This
gives us εΔt = ΔΦ. If Δ is small (Δ Æ d) and you use calculus you can get:
ε = −N
dΦ
Æ ε dt = − N dΦ , if you integrate you get,
dt
t
Φ max
0
0
∫ ε dt = ∫
− NdΦ , where
t
∫ ε dt is the area under the
0
curve of your emf vs. time plot from the beginning up to the point of maximum flux. If we assume the initial
flux is zero (i.e. it comes from far away), we have Aplot = - N·Φmax. Combining this with Equation 1 should
allow you to find the value of the maximum magnetic field, B, of your magnet.
Aplot = - N·ΔB·Across = - N·Bmax·Across
(Eq. 3)
QUESTION 9: What area did you use for Across? Why?
QUESTION 10: What is the approximate magnetic field at the maximum point of your magnet?
QUESTION 11: The strength of the magnetic field of the Earth in Boston is approximately
5.5 x 10-5 T. Do you think this affected your results in any way? Why or why not.
Additional Questions QUESTION 12: Is the incoming flux equal to the outgoing flux? Should it be? How can you tell from
your graphs.
QUESTION 13: How is the area under the curve for each peak depend on the speed of your magnet?
How can you tell from your graphs? Is this what you expected? Does it make sense?
QUESTION 14: Is the incoming maximum emf equal to the maximum outgoing emf? Should it be? How
can you tell from your graphs.
QUESTION 15: Do your results fit with Faradays Law (Equation 2)? Explain how each of the different
experiments proves (or disproves) some part of Faraday’s Law of Induction.
APLab 22: Electromagnetic Induction and Faraday's Law Mr. Maloney Physics 4/4