American Physical Society March 6, 2007 The MIT TEAL Simulations and Visualizations in Electromagnetism John W. Belcher Kavli Center for Astrophysics and

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


Funding Sources

NSF DUE-0618558

Davis Educational Foundation

d’Arbeloff Fund

iCampus

Helena Foundation

MIT Classes of 51, 55, 60


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


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?


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


One of the two MIT TEAL Classrooms

Modeled after NCSU’s SCALE-UP Classroom



Ideal TEAL Sequence(instructor’s fantasy)

1.Lecture2.Pre-Experiment Predictions3.Experiment4.Visualization of ExperimentI will illustrate this sequence

for Faraday’s Law


Magnetic Flux

Move down

1. Lecture: Faraday’s Law

Bd

dt


Magnetic Flux

Move down

2. Pre-Experiment Predictions

Personal Response System used for pre-experiment questions and responses


3. Experiment

Experiment includes sliding an aluminum sleeve over the magnet and feeling the slowdown due to

eddy currents


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


Loop of wire has inductance L and

resistance R and a decay time of L/R


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


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




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


We had a full page of Wired

Magazine devoted to

one of these in

Sept 2004


Mapping Fields Applet

(http://web.mit.edu/viz/soft/


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?



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



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



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


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


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


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


DLIC: Falling Magnet


DLIC: Oscillating Electric Dipole

4

ˆ)ˆ(

4

)ˆ(ˆ3

4

)ˆ(ˆ3),(

223 rcrcrt

ooo nxnxppnpnpnpn

rE


DLIC: Turning On An Electric Dipole

4

ˆ)ˆ(

4

)ˆ(ˆ3

4

)ˆ(ˆ3),(

223 rcrcrt

ooo nxnxppnpnpnpn

rE


DLIC: Light charges around heavy charge

The Seen Versus The Unseen

Link to 10 Meg AviLink to 1 Meg Avi


Two Other Visualizations

Electrostatic Video Game Interactive


Two Other Visualizations

Generating Plane Waves Interactive


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



Applications and software are open source

http://web.mit.edu/viz/soft/

Documents

American Physical Society March 6, 2007 The MIT TEAL Simulations and Visualizations in Electromagnetism John W. Belcher Kavli Center for Astrophysics and