The MIT TEAL Simulations
and Visualizations in
Electromagnetism
John W. Belcher
Kavli Center for Astrophysics and
Space Research
Department of Physics
American Physical Society
March 6, 2007
Funding Sources
NSF DUE-0618558
Davis Educational Foundation
d’Arbeloff Fund
iCampus
Helena Foundation
MIT Classes of 51, 55, 60
American Physical Society
March 6, 2007
Who Am I?
PI on the Voyager Plasma
Science Instrument on the
Voyager Spacecraft
Neptune’s Magnetosphere 1989
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 30 years
I have helped reform
freshman level E&M for the
last six years
American Physical Society
March 6, 2007
Outline of Talk
A Brief Explanation of TEAL
How do visualizations fit into TEAL?
How do we represent fields:
Vector Field Grid
Field Lines (“Eppur Si Mouve”)
Line Integral Convolution (LIC)—the best thing since
sliced bread
Moving Field Lines
When does this make sense? (E, B perpendicular)
What does it represent? (test particle motion)
Why it gives access to high level concepts, e.g. Maxwell
stresses
Dynamic Line Integral Convolution and examples
How Does This Contribute to E&M Understanding?
American Physical Society
March 6, 2007
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
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March 6, 2007
One of the two MIT TEAL Classrooms
Modeled after NCSU’s SCALE-UP
Classroom
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March 6, 2007
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Ideal TEAL Sequence
(instructor’s fantasy)
1.Lecture
2.Pre-Experiment Predictions
3.Experiment
4.Visualization of Experiment
I will illustrate this sequence
for Faraday’s Law
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March 6, 2007
1. Lecture: Faraday’s Law

dB

dt
Magnetic Flux
Move
down
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March 6, 2007
2. Pre-Experiment Predictions
Move
down
Magnetic Flux
Personal Response System
used for pre-experiment
questions and responses
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March 6, 2007
3. Experiment
Experiment includes sliding an aluminum sleeve
over the magnet and feeling the slowdown due to
eddy currents
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March 6, 2007
4.Visualization of Experiment
 Show 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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March 6, 2007
Loop of wire has
inductance L and
resistance R and a
decay time of L/R
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March 6, 2007
Line Integral Convolution (LIC)
 Introduced by Cabral and Leedom
(computer scientists) in 1993
 Uses a texture pattern where the
streaks in the texture are parallel to the
local field direction
 Shows the structure of the field close to
the resolution of the display!
 Vastly superior to either vector field or
field lines in showing structure of 2D
fields
American Physical Society
March 6, 2007
Line Integral Convolution: How?
 Take array of NxN pixels of random brightness
 At any point, average the random pattern along
a line in the direction of the local field for n
pixels, n << N
 Move to an adjacent new point and do this
again
 If you move parallel to the field to get to the new
point, the resulting average is almost the same
as for the old point, e.g. highly correlated
 If you move perpendicular to the field to get to
the new point, the resulting average is not
correlated at all with the average at the previous
point
 This produces correlations along the field
direction
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March 6, 2007
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March 6, 2007
What does a LIC of this function
look like?
2 ˆ
ˆ
F( x, y)  sin( y )i  cos( x ) j
2
This function has zero
divergence and non-zero curl,
so you expect no sources and
lots of circulation
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March 6, 2007
We had a
full page
of Wired
Magazine
devoted to
one of
these in
Sept 2004
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March 6, 2007
Mapping Fields
Applet
(http://web.mit.
edu/viz/soft/
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March 6, 2007
Moving Field Lines (nothing to do
with plasma physics)
Will the proton
gyrating about
the B field
move with the
solenoid if you
slowly start
pushing the
cart? Why or
why not?
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March 6, 2007
Moving Field Lines (nothing to do
with plasma physics)
Yes the
gyrating proton
will move with
the cart
because of the
ExB drift
E  V  B
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Vdrift
E  B  V  B   B
 2 
V
2
B
B
March 6, 2007
Moving Field Lines (nothing to do
with plasma physics)
Valid in situations where E and B are everywhere
perpendicular
In magneto-statics, field motion defined to be motion
of test electric monopoles
E B
Vdrift 
B2
In electrostatics, field motion defined be motion of
test magnetic monopoles
E B
Vdrift  c 2
E2
Useful even in e.g. radiation because the motion is
in the direction of the Poynting flux vector
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March 6, 2007
Moving Field Lines (nothing to do
with plasma physics)
In both the electrostatic and magneto-static case,
for symmetric cases you can relatively easily get
the motion of field lines simply by conserving flux
in source free regions
d
d
 magnetic   B  dA 
dt
dt S
 (E  v  B)  dl  0
C
when v  E  B / B 2
d
d
 electric   E  dA  c 2  (B  v  E / c 2 )  dl  0
dt
dt S
C
when v  c 2 E  B / E 2
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March 6, 2007
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!
American Physical Society
March 6, 2007
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!
American Physical Society
March 6, 2007
Dynamic Line Integral
Convolution
Can also impose the same field line motion defined above
on the line integral convolution method by having the
underlying random pattern move with the test particle drift
velocity
This is called Dynamic Line Integral Convolution (DLIC), and
was originated by Andreas Sundquist
Examples:
Falling Magnet
Oscillating Electric Dipole
Electric Dipole turning on
Light charges around heavy charge
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March 6, 2007
DLIC: Falling Magnet
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March 6, 2007
DLIC: 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
March 6, 2007
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
March 6, 2007
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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March 6, 2007
Two Other Visualizations
Electrostatic Video Game Interactive
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March 6, 2007
Two Other Visualizations
Generating Plane Waves Interactive
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March 6, 2007
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 “Guided Inquiry” with these animations and
visualizations, not just accessibility and exploration
3. Build the guided inquiry into e.g. Mastering Physics?
4. Carolann Koleci and I have been doing just that in a
junior/senior Griffiths based course at WPI and plan to
do a similar study in the corresponding course at MIT
5. Students have to use the visualizations to answer the
Mastering Physics questions
6. We are just beginning to explore how to do this
effectively and how to evaluate it
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March 6, 2007
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Applications and software are
open source
http://web.mit.edu/viz/soft/
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March 6, 2007