Introduction to Active
Learning:
Faraday’s Law
Today’s Objectives
Introduce key concepts from electricity and
magnetism through discovery activities,
experiments, concept questions, discussion,
and visualizations.
Later in the course, we will return to the same
concepts.
Today we are just going to have some fun and
get to know each other.
Introductions
What we are trying to get a feel for:
You Tube Link: http://youtu.be/YywaJkGKOaY
Concept Question: Loop in Uniform
Field
While a rectangular wire loop is
pulled upward though a uniform
magnetic field B field penetrating
its bottom half, as shown, there is
1.  a current in the loop.
2.  no current in the loop.
3.  I do not understand the concepts of current and
magnetic field.
4.  I understand the concepts of current and magnetic field
but am not sure of the answer.
5
Demo: aluminum sleeve moving
past fixed magnet, students do
this at their tables
Demo: we show the demo of
magnet falling through plastic
tube and aluminum tube
6
Seeing the Unseen:
Faraday’s Law Applet
Applet -- Faraday’s law applet (with a magnet and a
coil):
http://public.mitx.mit.edu/gwt-teal/FaradaysLaw2.html
Play with the application until you are familiar with all
the features. In the Actions Menu: try checking Motion
on and unchecking Motion on(manual mode). You can
use the buttons at the bottom to start, pause and reset
the simulation. You can move the magnet and the ring
back and forth using the mouse. Let each person in
the group have a turn.
Seeing the Unseen: First
Concept Flow
Group Discussion Question
What are some examples of flow of “something”
through an area?
Examples of Flow
Electric Current: Flow Of Charge
Electric Current I: Charge ΔQ flowing across area A
in time Δt
ΔQ
I=
Δt
9
Current and Magnetic Field
Current produces a magnetic field as
shown in figure
10
Magnetic Field of Bar Magnet
(1) A magnet has two poles, North (N) and South (S)
(2) Magnetic field lines leave from N, end at S
11
Seeing the Unseen:
Magnetic Field
Run the Applet on motion on and stop the magnet
when it is near the ring
Scroll down on the panel on the right and click on
Magnetic Field: Iron Filings
Seeing the Magnetic Field: Iron
Filings
The iron filings represent the
magnetic field present at the
instant you stopped the
magnet . The direction of the
magnetic field is along the
direction of the iron filings.
Does the magnetic field
intercept the area of the
circular wire?
Magnetic Flux Thru Wire Loop
Flux is the
Generalization of
Flow
Product of
perpendicular
component of
magnetic field and
area
Φ B = B⊥ A
14
Discussion Question: Magnetic
Flux in Ring
The first graph on the right in the Applet shows a plots of the
external magnetic flux and total magnetic flux in the ring versus
time. Briefly describe where the “external flux” (red plot) is
coming from: that is, what kind of flux is this, what creates it,
over what area is the flux being measured.
More Discussion Questions
About Magnetic Flux
1.  Describe different ways that you can change the external flux
2.  Explain how the total magnetic flux (blue plot)
is related to the external magnetic flux (red plot).
Current in Ring
The second graph on the right in the Applet shows a
plot of the current in the ring versus time.
Proposing a
Hypothesis
Propose a qualitative
relationship between
magnetic flux (seen
in top graph) and
current that flows in
the ring (seen in
bottom graph).
Testing Hypotheses
Groups utilizing the application came up with the following
hypotheses.
1.  Group A conjectured that the current through the ring is
proportional to the total magnetic flux.
2.  Group B proposed that the current through the ring is
proportional to the change in the total magnetic flux.
Use the application to test these two hypotheses. Design and
run a virtual experiment that could rule out any of the
hypotheses. Which did you rule out and why?
Faraday’s Law of Induction
Changing magnetic flux induces a
current
dΦ B d( BA) dB
I∝
=
=
A
dt
dt
dt
20
Electromotive Force, Current and
Resistance
Vary the resistance in the applet and
observe the current.
Electromotive force ε looks like a
voltage difference. It’s a “driving force”
for induced current
ε = IR
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Faraday’s Law of Induction
Changing magnetic flux is proportional
to electromotive force
ε
dΦ B d( BA) dB
∝
=
=
A
dt
dt
dt
22
Demo: Electromagnetic Induction
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Demo: Electromagnetic Induction
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Concept Question: Loop in Uniform
Field
While a rectangular wire loop is
pulled upward though a uniform
magnetic field B field penetrating
its bottom half, as shown, there is
1.  a current in the loop.
2.  no current in the loop.
3.  I do not understand the concepts of current and
magnetic field.
4.  I understand the concepts of current and magnetic field
but am not sure of the answer.
25
Concept Question: Loop in Uniform
Field
While a rectangular wire loop is
pulled sideways though a uniform
magnetic field B field penetrating
its bottom half, as shown, there is
1.  a current in the loop.
2.  no current in the loop.
3.  I do not understand the concepts of current and
magnetic field.
4.  I understand the concepts of current and magnetic field
but am not sure of the answer.
26
Lenz’s Law
Direction of Induced Current
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Discussion Question:
Induced Current
Run the Applet and observe the relation between the
sign of current and the slope of the plot of magnetic
flux. What do you observe? Try flipping the coil and
see what result you get for the current.
Direction of Induced
Current
The slope of the total
magnetic flux (blue) is
proportional to the
negative of the
induced current
Minus Sign? Lenz’s Law
ε
dΦ B
=−
dt
Induced EMF is in direction that opposes
the change in flux that caused it
30
Current Loop Acts Like a Magnet
Force between magnet and current loop is like force
between magnets
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Falling Conducting Wire
http://web.mit.edu/viz/EM/visualizations/faraday/fallingCoil/FallingRingResistive/FallingRingResistive.htm
Concept Question: Faraday’s Law:
Loop
A coil is falling
downward directly
beneath a magnet with
its north pole pointing
upward. The current in
the coil and the force
on the coil are:
1.
2.
3.
4.
Current clockwise; force up
Current counterclockwise; force up
Current clockwise; force down
Current counterclockwise; force down
33
Demonstration:
Induction
At this point, students again
move the aluminum tube in
their desktop apparatus to feel
the forcce
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Jumping Ring
An aluminum ring jumps into the air when the
solenoid beneath it is energized
35
What is Going On?
This is a dramatic example of Faraday’s Law.
When the solenoid is energized it produces a
magnetic field. A current is induced in the
aluminum ring. The moving charges in the ring
then feel a force due tot eh magnetic field of the
solenoid.
36
Conclusion: Faraday’s Law of
Induction
Changing magnetic flux generates
electromotive force that opposes that
change in flux
ε
dΦ B
=−
dt
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