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Workshop: Using Visualization in Teaching Introductory E&M

AAPT National Summer Meeting, Edmonton, Alberta, Canada.

Organizers: John Belcher, Peter Dourmashkin, Carolann Koleci, Sahana Murthy

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MIT Class: Fields and Fluids Flow

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8.02: Electricity and MagnetismAlso new way of thinking…

How do objects interact at a distance? Fields We will learn about Electric & Magnetic

Fields: how they are created & what they effectBig Picture (Mathematical) Summary: Maxwell’s

Equations

0

0 0 00

in

S C S

enc

S C S

Q dd d d

dt

dd d I d

dt

E A E s B A

B A B s E A

q F E v B

Lorentz Force:

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Today: FieldsIn General, then

Gravitational & Electric

Review Vectors Analysis in

MIT 8.02t Study Guide Online

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Scalar Fields

e.g. Temperature: Every location has associated value (number with units)

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Scalar Fields - Contours

• Colors represent surface temperature• Contour lines show constant

temperatures

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Fields are 3D

•T = T(x,y,z)

•Hard to visualize Work in 2D

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Vector FieldsVector (magnitude, direction) at every

point in space

Example: Velocity vector field - jet stream

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Vector Field Examples

Begin with Fluid Flow

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Vector Field Examples

Flows With Sources (link to movie)

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Vector Field Examples

Flows With Sinks (link to movie)

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Vector Field Examples

Circulating Flows (link to movie)

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Visualizing Vector Fields:Three Methods

Vector Field DiagramArrows (different colors or length) in direction

of field on uniform grid.Field Lines

Lines tangent to field at every point along lineGrass Seeds

Textures with streaks parallel to field direction

All methods illustrated inVector Field Diagram Java Applet

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Vector Fields – Field Lines• Direction of field line at any point is

tangent to field at that point

• Field lines never cross each other

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PRS Question:Vector Field

In General: Don’t pick up unit until ready to answer

Then I’ll know when class is ready

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PRS: Vector FieldThe field line at left corresponds to the vector field:

ˆ ˆ( , ) sin( )x y x F i j

ˆ ˆ( , ) sin( )x y x F i j

ˆ ˆ( , ) cos( )x y x F i j

ˆ ˆ( , ) cos( )x y x F i j

1. 1 2. 2

3. 3

4. 4

5. I don’t know

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PRS Answer: Vector Field

The curve above has a slope of 1 at the origin, and only (3) or (4) has this property. Moreover, the tangent to the curve above has a y-component changes sign as x changes and an x-component that is always positive, so the answer must be (4).

Answer:4. ˆ ˆ( , ) cos( )x y x F i j

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Vector Fields – “Grass Seeds”

Source/Sink Circulating

Although we don’t know absolute direction, we can determine relative direction

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PRS Questions:“Grass Seed” Visualizations

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PRS: Grass Seeds

The vector field at left is created by:

0%0%0%0%0%0%0% 1. Two sources (equal strength)

2. Two sources (top stronger)3. Two sources (bottom stronger)4. Source & Sink (equal strength)5. Source & Sink (top stronger)6. Source & Sink (bottom stronger)7. I don’t know

20

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PRS Answer: Grass Seeds

3. Two sources (bottom stronger)

Answer:

Both sources because lines leaving one don’t enter the other.

Bottom is stronger because it “pushes” further

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PRS: Grass SeedsHere there is an initial downward flow.

0%

0%

0% 1. The point is a source2. The point is a sink3. I don’t know

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PRS Answer: Grass Seeds

1. The point is a sourceAnswer:

It’s a source, because otherwise the downward flow would flow right into it.NOTE: If the background were upward, then it would be just flowing right into it, so it would be a sink.

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PRS: CirculationThese two circulations are in:

0%

0%

0% 1. The same direction (e.g. both clockwise)2. Opposite directions (e.g. one cw, one ccw)3. I don’t know

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PRS Answer: Circulation

2. Opposite directions(link to movie)

These two circulations are in:

You can tell by looking in between. Both circulations push the flow in the same direction, so they must be circulating counter to each other.

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PRS Answer cont.: CirculationIf they were in the same direction they’d look like (link to movie)

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0%

0%

0%

0%

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PRS: Vector Field

2 2ˆ ˆ( , )x y x y F i j

The grass seeds field plot at left is a representation of the vector field:

2 2ˆ ˆ( , )x y x y F i j

2 2ˆ ˆ( , )x y y x F i j

ˆ ˆ( , ) sin( ) cos( )x y x y F i j

ˆ ˆ( , ) cos( ) sin( )x y x y F i j

20

1. 1 1

2.

3.

4.

5. I don’t know

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PRS Answer: Vector Field

Answer:2 2ˆ ˆ2. ( , )x y y x F i j

Look along the positive x-axis. Along this axis the grass seed textures are vertical. This means F has only a y component when y is zero and x is non-zero. Only consistent with (2).