Physics 8.02: Faraday’s Law
John Belcher
This presentation is online now
at
http://web.mit.edu/viz/MERLOT/
MERLOT 2007
August 9, 2007
The MIT TEAL Simulations
and Visualizations for
Faraday’s Law
John W. Belcher
Kavli Center for Astrophysics and
Space Research
MIT Department of Physics
MERLOT 2007
August 9, 2007
Funding Sources
NSF CCLI DUE-0618558
Davis Educational Foundation
d’Arbeloff Fund for Excellence in MIT
Education
iCampus, the MIT/Microsoft Alliance
Helena Foundation
MIT Classes of 51, 55, 60
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Credits for TEAL Visualizations:
Project Manager: Andrew McKinney
Java Simulations: Andrew McKinney, Philip Bailey,
Pierre Poignant, Ying Cao, Ralph Rabat, Michael
Danziger
3D Illustration/Animation: Mark Bessette, Michael
Danziger
ShockWave Visualizations: Michael Danziger
Visualization Techniques R&D: Andreas Sundquist
(DLIC), Mesrob Ohannessian (IDRAW)
These visualizations were developed in the context of
TEAL, a much larger freshman physics reform
project at MIT for interactive studio physics
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My Career Before Visualization
PI on the Voyager Plasma
Science Instrument on the
Voyager Spacecraft
I have spent a lot of time
trying to explain the unseen
to reporters at Voyager
press conferences since
1979
I have taught E&M at all
levels at MIT for 35 years
Neptune’s Magnetosphere 1989
Going to Jupiter
Saturn Uranus and
Neptune is easy
Reforming
introductory
physics is hard
I spent 6 years helping
change freshman E&M to
an interactive format
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TEAL: Technology Enabled Active
Learning
Large freshman physics courses have inherent
problems
Lecture/recitations are passive
No labs (at MIT) leads to lack of physical intuition
Math is abstract, hard to visualize (esp. E&M)
TEAL/Studio addresses these by
Replacing large lectures with interactive,
collaborative pedagogy
Incorporating desk top experiments
Incorporating visualization/simulations to make
the unseen seen
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Outline of Talk
What do we mean by the concept of fields?
Why is the field concept hard to understand?
Examples of Faraday’s Law experiments
How do visualizations help in understanding these
experiments?
Examples of Visualizations
How Does This Contribute to E&M Understanding?
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What do we mean by the concept
of fields?
Electromagnetic fields are invisible stresses that
exist at every point in space
They are generated by the electric charge carried
by material objects
All everyday interactions between material objects
are mediated by the electromagnetic fields they
produce
Material objects never touch—instead, their fields
interact, giving the illusion of “touching”
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The illusion of touch
You are convinced that your hand reaches out and
touches the hand of a loved one, because that is the
way you have learned to internalize reality…
…in reality the matter in your hand generates
electromagnetic fields that surround your hand …
…and when you put your hand near the hand of a
loved one the fields in their hand set up a repulsion…
…that keeps the matter in your hand from
interpenetrating the matter in their hand…
…and you interpret that repulsion as your hand
having touched the hand of your loved one …
…even though the matter in your hand never touches
your loved one’s hand…
…or anything else for that matter…
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The illusion of touch
Of course I don’t really believe this, even though I
know it is true
Why don’t I believe this?
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Why is the field concept hard to
understand?
Fields are invisible
Our experience with them is indirect—other than
playing with magnets and experiencing the
effects of static electricity, we have no intuition
about them
The theory that describes them is very
mathematical
How do we make the idea of fields more accessible?
Make visible representations of them!
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Examples of Faraday’s Law
experiments: I
Magnet and a coil. Moving magnet induces a
current in a stationary coil. The coil has no source
of power, but a current flows in the coil when I move
a magnet near it.
Where does the energy
come from to make the
current in the coil flow?
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Examples of Faraday’s Law
experiments: I
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Examples of Faraday’s Law
experiments: I
This looks magical!
Why? Because we don’t see the
intervening agent that links the magnet
and the coil—the field!
So lets show the field:
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Examples of Faraday’s Law
experiments: I
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Examples of Faraday’s Law
experiments: I
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Examples of Faraday’s Law
experiments: II
Magnet falling through a non-magnetic conducting
ring—e.g. one made of copper.
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Falling Magnet
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Falling Magnet
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How do visualizations help in
understanding fields?
In visualizations we can make the fields visible
The dynamical effects of fields can be understood
by analogy with rubber bands and strings
This insight is due to Faraday, the father of the
concept of fields
Making the fields visible and animated and using
the analogy of rubber bands and strings gives
insight into the reasons that fields have the effects
they do
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Examples of Interactive
Visualizations
Moving a wire coil past a stationary magnet
We do this experiment in class and then we look at
a virtual interactive representation of it.
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Loop of wire has
inductance L and
resistance R and a
decay time of L/R
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Guiding Principles
• Do or show a real experiment
• Build a virtual model of the real
experiment
• Add field representation
• Show the field three ways:
• Vector Field Grid
• Field Lines
• Line Integral Convolution
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Moving Field Lines
Helps with higher order concepts, most obviously
the flow of electromagnetic energy, but also the
flow of electromagnetic momentum and the
stresses transmitted by fields, that is, the Maxwell
Stress Tensor

d
Pmech  Pem  dV   T  dA  0

dt
S

1 2  1 
1 2 

T   o E E  E I  
B B  B I

2
2

 o 

Fields transmit a pressure perpendicular to
themselves and a tension parallel to
themselves—that is you can intuit their dynamical
effects by looking at their shape!
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How Much Does This Contribute to E&M
Understanding?
1.No clear evidence they are useful in the
way we have been using them in TEAL
2.Need to embed these visualizations into a
“Guided Inquiry” framework
3.Need more than just accessibility and
exploration and “gee whiz”
4.I currently have an NSF Grant to do just
this
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All of these visualizations
and many more are located
at
http://web.mit.edu/8.02t/www/
802TEAL3D/
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Applications and software are
open source, but not well
documented
We are working on the
documentation
http://web.mit.edu/viz/soft/
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Oscillating Electric Dipole
xnˆ )xnˆ

3nˆ (pnˆ )  p 3nˆ (p nˆ )  p  (p
E(r, t ) 


4  o r
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3
4  o cr
2
4  o rc
2
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DLIC: Turning On An
Electric Dipole
xnˆ )xnˆ

3nˆ (pnˆ )  p 3nˆ (p nˆ )  p  (p
E(r, t ) 


4  o r 3
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4  o cr 2
4  o rc 2
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DLIC: Light charges around
heavy charge
Link to 1 Meg Avi
Link to 10 Meg Avi
The Seen Versus The Unseen
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Two Other Visualizations
Electrostatic Video Game Interactive
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August 9, 2007
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