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The MIT TEAL Simulations and Visualizations in Electromagnetism. John W. Belcher Kavli Center for Astrophysics and Space Research Department of Physics. Funding Sources NSF DUE-0618558 Davis Educational Foundation d’Arbeloff Fund iCampus Helena Foundation MIT Classes of 51, 55, 60. - PowerPoint PPT Presentation
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American Physical Society March 6, 2007
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
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
Neptune’s Magnetosphere 1989
American Physical Society March 6, 2007
Outline of TalkA 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 LinesWhen 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
American Physical Society March 6, 2007
One of the two MIT TEAL Classrooms
Modeled after NCSU’s SCALE-UP Classroom
American Physical Society March 6, 2007
American Physical Society March 6, 2007
Ideal TEAL Sequence(instructor’s fantasy)
1.Lecture2.Pre-Experiment Predictions3.Experiment4.Visualization of ExperimentI will illustrate this sequence
for Faraday’s Law
American Physical Society March 6, 2007
Magnetic Flux
Move down
1. Lecture: Faraday’s Law
Bd
dt
American Physical Society March 6, 2007
Magnetic Flux
Move down
2. Pre-Experiment Predictions
Personal Response System used for pre-experiment questions and responses
American Physical Society March 6, 2007
3. Experiment
Experiment includes sliding an aluminum sleeve over the magnet and feeling the slowdown due to
eddy currents
American Physical Society March 6, 2007
4.Visualization of Experiment
Show a virtual model of the real experiment
Add field representationShow the field three ways:
Vector Field GridField Lines Line Integral Convolution
American Physical Society March 6, 2007
Loop of wire has inductance L and
resistance R and a decay time of L/R
American Physical Society 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
American Physical Society March 6, 2007
American Physical Society March 6, 2007
American Physical Society March 6, 2007
What does a LIC of this functionlook like?
This function has zero divergence and non-zero curl, so you expect no sources and
lots of circulation
2 2ˆ ˆ( , ) sin( ) cos( )x y y x F i j
American Physical Society March 6, 2007
We had a full page of Wired
Magazine devoted to
one of these in
Sept 2004
American Physical Society March 6, 2007
Mapping Fields Applet
(http://web.mit.edu/viz/soft/
American Physical Society 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?
American Physical Society 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
2 2 drift B B
V B BE B
E V B V V
American Physical Society 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
In electrostatics, field motion defined be motion of test magnetic monopoles
Useful even in e.g. radiation because the motion is in the direction of the Poynting flux vector
2drift B
E B
V
22drift cE
E BV
American Physical Society 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
2 2
2 2
( / ) 0
when /
electric
S C
d dc c
dt dt
c E
E dA B v E dl
v E B
2
( ) 0
when /
magnetic
S C
d d
dt dt
B
B dA E v B dl
v E B
American Physical Society March 6, 2007
Moving Field LinesHelps 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
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!
0 S
emmech dVdt
ddATPP
�
IBBIEET
���22
2
11
2
1BE
oo
American Physical Society March 6, 2007
Moving Field LinesHelps 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
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!
0 S
emmech dVdt
ddATPP
�
IBBIEET
���22
2
11
2
1BE
oo
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 MagnetOscillating Electric DipoleElectric Dipole turning onLight charges around heavy charge
American Physical Society March 6, 2007
DLIC: Falling Magnet
American Physical Society March 6, 2007
DLIC: Oscillating Electric Dipole
4
ˆ)ˆ(
4
)ˆ(ˆ3
4
)ˆ(ˆ3),(
223 rcrcrt
ooo nxnxppnpnpnpn
rE
American Physical Society March 6, 2007
DLIC: Turning On An Electric Dipole
4
ˆ)ˆ(
4
)ˆ(ˆ3
4
)ˆ(ˆ3),(
223 rcrcrt
ooo nxnxppnpnpnpn
rE
American Physical Society March 6, 2007
DLIC: Light charges around heavy charge
The Seen Versus The Unseen
Link to 10 Meg AviLink to 1 Meg Avi
American Physical Society March 6, 2007
Two Other Visualizations
Electrostatic Video Game Interactive
American Physical Society March 6, 2007
Two Other Visualizations
Generating Plane Waves Interactive
American Physical Society 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
American Physical Society March 6, 2007
American Physical Society March 6, 2007
Applications and software are open source
http://web.mit.edu/viz/soft/
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