P17 - 1 Workshop: Using Visualization in Teaching Introductory E&M AAPT National Summer Meeting,...

1P17-

Workshop: Using Visualization in Teaching Introductory E&M

AAPT National Summer Meeting, Edmonton, Alberta, Canada.

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

P17- 2

MIT Class: Feeling Magnetic Fields

Magnetic Forces on ChargesMagnetic Dipoles

Experiment: Dipoles in B Fields

P17- 3

The Biot-Savart LawCurrent element of length ds carrying current I produces a magnetic field:

20 ˆ

4 r

dI rsBd

2

ˆx

4o q

r

v r

B

Moving charges are currents too…

P17- 4

=

2 Current Sheets

Ampere’s Law: . encId 0sB

IB

B

X XX

X

X

XX

X

XXX

X

X

XX

X

XXXXXXXXXXXX

B

Long

Circular

Symmetry(Infinite) Current Sheet

Solenoid

Torus

P17- 5

Review:Right Hand Rules

1. Torque: Thumb = torque, fingers show rotation2. Create: Thumb = I, Fingers (curl) = B3. Feel: Thumb = I, Fingers = B, Palm = F4. Moment: Fingers (curl) = I, Thumb = Moment

P17- 6

Demonstration:TV in Field

P17- 7

How a CRT Works: It could…

P17- 8

How a CRT Works: More Typical

P17- 9

How a CRT Works

P17-10

Moving Charges Feel Magnetic Force

B q F v B

Magnetic force perpendicular both to:Velocity v of charge and magnetic field B

P17-11

Reminder: B Field Units

This is called 1 Tesla (T)

41 T = 10 Gauss (G)

Since B q F v B

mA

N1

smC

N1

ndmeter/secocoulomb

newton UnitsB

P17-12

Putting it Together: Lorentz Force

q F E v B

This is the final word on the force on a charge

B q F v B

E qF ECharges Feel…

Electric Fields Magnetic Fields

P17-13

Application: Velocity Selector

What happens here?

P17-14

Velocity Selector

Particle moves in a straight line when

( ) 0net q F E v B

E

vB

P17-15

PRS Question:Hall Effect

P17-16

PRS: Hall EffectA conducting slab has current to the right. A B field is applied out of the page. Due to magnetic forces on the charge carriers, the bottom of the slab is at a higher electric potential than the top of the slab.

IB

V > V(Top)

On the basis of this experiment, the sign of the charge carriers carrying the current in the slab is:

0%

0%

0%

0% 1. Positive2. Negative3. Cannot be determined4. I don’t know

0

P17-17

PRS Answer: Hall Effect

Look at the force on the carriers. If positive, they are flowing to the right, and F will be down. If negative they are flowing to the left and F will be down (don’t forget the sign of q!) So either way the force is down. But we know that the result is a higher potential at the bottom – positive charges are moving down. So the carriers are positive

Answer: 1. Here the charge carriers are positive

IB

V > V(Top)

P17-18

What Kind of Motion in Uniform B Field?

P17-19

Cyclotron Motion

2mvqvB

r

2 2r mT

v qB

2v qB

fr m

(1) r : radius of the circle

(2) T : period of the motion

(3) : cyclotron frequency

mvr

qB

P17-20

Collections of Charges:Current Carrying Wires

P17-21

Demonstration:Jumping Wire

P17-22

Magnetic Force on Current-Carrying Wire

Current is moving charges, and we know that moving charges feel a force in a magnetic field

P17-23

B q F v B

Magnetic Force on Current-Carrying Wire

mcharge

s B

B I F L B

chargem

s B

P17-24

PRS Question:Parallel Current Carrying Wires

P17-25

PRS: Parallel Wires

Consider two parallel current carrying wires. With the currents running in the same direction, the wires are

I1 I2

0%

0%

0%

0%

0% 1. attracted (likes attract?)

2. repelled (likes repel?)

3. pushed another direction

4. not pushed – no net force

5. I don’t know

0

P17-26

PRS Answer: Parallel Wires

I1 creates a field into the page at I2.

That makes a force on I2 to the left.

I2 creates a field out of the page at

I1. That makes a force on I1 to the

right.

Answer: 1. The wires are attracted

I1 I2

X

P17-27

Demonstration:Parallel & Anti-Parallel Currents

P17-28

B

B

B

q

d Id

I

F v B

F s B

F L B

Summary Magnetic Force

P17-29

Can we understand why?Whether they attract or repel can be seen in the shape of the created B field

(Animation) (Animation)

P17-30

Field Pressures and Tensions:A Way To Understand the

qVxB Magnetic Force

P17-31

Tension and Pressures Transmitted by E and B

E & B Fields:• Transmit tension along field direction

(Field lines want to pull straight)• Exert pressure perpendicular to field

(Field lines repel)

P17-32

Example of E Pressure/Tension

Positive charge in uniform (downward) E fieldElectric force on the charge is combination of 1. Pressure pushing down from top 2. Tension pulling down towards bottom

(Animation)

P17-33

Example of B Pressure/Tension

Positive charge moving out of page in uniform (downwards) B field. Magnetic force combines:

1. Pressure pushing from left 2. Tension pulling to right

(Animation)

P17-34

PRS Question:Field Strength

P17-35

PRS: Field StrengthA

B

C

Where is the pictured field the strongest?

0%

0%

0%

0% 1. A

2. B

3. C

4. I don’t know 0

P17-36

PRS Answer: Field Strength

Answer: 3. The field is the strongest at C

Line density is proportional to field strength

A

B

C

P17-37

Example of B Pressure/Tension

Both cases: repelling “pressure” arises from HIGH field strength HIGH energy density

(Animation)

P17-38

Loops of Current

P17-39

Group Problem: Current LoopPlace rectangular current loop in uniform B field

i

j

k

1) What is the net force on this loop?

2) What is the net torque on this loop?

3) Describe the motion the loop makes

P17-40

Torque on Rectangular Loop

ˆ ˆ: area vectorA ab A n n

I τ A B

ˆˆˆ , =Bn k B i

jτ ˆIAB

Familiar? No net force but there is a torque

ijk

x

P17-41

Magnetic Dipole Moment

τ μ B

Analogous to τ p E

tends to align with B

AnμIIA ˆ

Define Magnetic Dipole Moment:

Then:

P17-42

Animation:Another Way To Look At Torque

External field connects to field of magnet and “pulls” the dipole into alignment

P17-43

Demonstration:Galvanometer

P17-44

Magnetic Dipole Moment

AnμIIA ˆ

P17-45

PRS Question:Force on Magnetic Dipole

P17-46

PRS: Dipole in Field

From rest, the coil above will:

0%

0%

0%

0%

0%

0%

0%

0% 1. rotate clockwise, not move

2. rotate counterclockwise, not move

3. move to the right, not rotate

4. move to the left, not rotate

5. move in another direction, without rotating

6. both move and rotate

7. neither rotate nor move

8. I don’t know :00

P17-47

PRS Answer: Dipole in Field

Answer: 1. Coil will rotate clockwise (not move)

No net force so no center of mass motion. BUT Magnetic dipoles rotate to align with external field (think compass)

P17-48

Dipoles don’t move???

This dipole rotates but doesn’t feel a net force

But dipoles CAN feel force due to B. What’s up?

P17-49

Something NewDipoles in Non-Uniform Fields:

Force

P17-50

Force on Magnetic Dipole?

We Want to Know:

What is the force on this dipole?

P17-51

PRS Question:Force on Magnetic Dipole

P17-52


The current carrying coil above will feel a net force

0%

0%

0%

0% 1. upwards

2. downwards

3. of zero

4. I don’t know0

P17-53


Answer: 2. Feels downward force

The I ds x B forces shown produce a net downward force

P17-54

Can just sum I ds x B forces

Is there another way?

P17-55

Energy of Magnetic Dipole

-DipoleU μ B

This equation gives you a general way to think about what dipoles will do in B fields

P17- 56

Magnetic Dipole Moments

AnμIIA ˆ

Generate:

Feel:

1) Torque to align with external field

2) Forces as for bar magnets

-DipoleU μ B

P17-57

Force on Magnetic Dipole

Alternate Thought #1

Where does the dipole want to be?

P17-58

Think Using Energy

-DipoleU μ B

Where does dipole go to reduce its energy?

Aligned dipoles seek high fields!

Force here is down

P17-59


Alternate Thought #2

What makes the field pictured?

P17-60


Bar magnet below dipole, with N pole on top It is aligned with the dipole pictured, they attract!

N

S

N

S

P17-61

PRS Questions:Force on Dipole

P17-62


The current carrying coil above will feel a net force

0%

0%

0%

0% 1. upwards

2. downwards

3. of zero

4. I don’t know

0

P17-63


Answer: 2. The coil feels a force downMany ways to know this:

I ds x B forces Energy (aligned seeks high B) Equivalent bar magnets

S

N

S

N

P17-64

PRS: Free Dipoles

If a number of dipoles are randomly scattered through space, after a while they

0%

0%

0%

0% 1. Attract (move together)2. Repel (move apart)3. Basically stay put4. I don’t know

00

P17-65

PRS Answer: Free Dipoles

Answer: 1. Free Dipoles Attract

• Torque on dipole aligns it with the local field

• Dipole then moves toward stronger field — closer to another dipole

Shockwave

P17-66

Some Fun:Magnetic Levitation

P17-67

Put a Frog in a 16 T Magnet…

For details: http://www.hfml.sci.kun.nl/levitate.html

P17-68

How does that work?First a BRIEF intro to magnetic materials

P17-69

Para/Ferromagnetism

Applied external field B0 tends to align the atomic magnetic moments (unpaired electrons)

P17-70

Diamagnetism

Everything is slightly diamagnetic. Why? More later.

If no unpaired electrons then this effect typically dominates.

P17-71

Back to Levitation

P17-72

Levitating a Diamagnet

1) Create a strong field (with a field gradient!)

2) Looks sort of like dipole field

3) Toss in a frog (diamagnet)

4) Looks like a bar magnet pointing opposite the field

5) Seeks lower field (force up) which balances gravity

S

NN

S

Most importantly, in a certain region it is stable:

Restoring force always towards the center

SN

P17-73

Using B to Levitate


P17-74

Using B to Levitate


P17-75

Using B to Levitate


P17-76

Using B to Levitate


P17-77

Demonstration:Levitating Magnet over

Superconductor

P17-78

Perfect Diamagnetism:“Magnetic Mirrors”

N

S

N

S

P17-79

Perfect Diamagnetism:“Magnetic Mirrors”

N

S

N

S

No matter what the angle, it floats -- STABILITY

P17-80

Using B to Levitate


P17-81

Levitate Magnet with your Fingers?

P17-82

Well… and a lifting magnet

N

S

Why need diamagnetic stabilization?

1) Magnet seeks STRONG field, wants to snap up to lifter

2) Downward oscillation will move it to region where field gradient is too weak to lift it

Diamagnetic sheets above, below prevent these effects, since they repel the floating magnet

P17-83

Experiment 4:Magnetic Forces on Dipoles

This is a little tricky. We will lead you through with lots

of PRS questions

P17-84

First: Set up current supply

• Open circuit (disconnect a lead)

• Turn current knob full CCW (off)

• Increase voltage to ~12 V§This will act as a protection: V<12 V

• Reconnect leads in Helmholtz mode

• Increase current to ~1 A

P17-85

Field Profiles

Single Coil Helmholtz

VERY

UNIFORM!

Anti-Helmholtz

ZERO

FIELD!

P17-86

PRS Prediction:Dipole in Helmholtz

P17-87

PRS: Dipole in Helmholtz

A randomly aligned dipole at the center of a Helmholtz coil will feel:

0%

0%

0%

0% 1. a force but not a torque2. a torque but not a force3. both a torque and a force4. neither force nor torque

:00

P17-88

PRS Answer: Dipole in Helmholtz

The Helmholtz coil makes a UNIFORM FIELDDipole feels only torque (need gradient for F)

Answer: 2. a torque but not a force

P17-89

Next: Dipole in Helmholtz (Q1-2)

• Set in Helmholtz Mode (~1 A)

• Turn off current

• Put dipole in center (0 on scale)

• Randomly align using bar magnet

• Turn on current

What happens?

P17-90

PRS Prediction:Reverse Helmholtz

P17-91

PRS: Reverse Helmholtz

Using aligned dipole, flip the field. Ideally the dipole will feel:

0%

0%

0%

0% 1. a force but not a torque

2. a torque but not a force

3. both a torque and a force

4. neither force nor torque

0

P17-92

PRS Answer: Reverse Helmholtz

The dipole is exactly anti-aligned, so the torque is 0. Still uniform field means still no force.

Answer: 4. IDEALLY neither force nor torque

P17-93

Next: Reverse Helmholtz (Q3)

Starting from end of previous (aligned dipole at center)


• VERY CAREFULLY (don’t bump!) Reverse leads at power supply

• Turn on current

What happens?

P17-94

PRS Predictions:Moving in Helmholtz

P17-95

PRS: Moving in Helmholtz

When moving through the above field profile, a dipole will:

0%

0%

0% 1. Never rotate

2. Rotate once

3. Rotate twice

0

P17-96

PRS Answer: Moving in Helmholtz

The dipole is always aligned with the field so it will never rotate

Answer: 1. The dipole will never rotate

P17-97


When pulling the dipole through the above field profile, the spring stretch direction will:

0%

0%

0%

0% 1. Always be the same

2. Change once

3. Change twice

4. Change three times

0

P17-98

PRS Answer: Moving in Helmholtz

The dipole always wants to be at the peak field, so when below it the force is up, when above it the force is down.

Answer: 2. The direction will change once

P17-99

Next: Moving in Helmholtz (Q4-5)

• Keep in Helmholtz Mode (~1 A)

• Lower dipole to bottom

• Randomly align (is it possible?)

• Slowly & smoothly raise to well above

What happens (torque? force?)

P17-100

PRS Prediction:Dipole in Anti-Helmholtz

P17-101

PRS: Anti-Helmholtz

A randomly aligned dipole at the center of an Anti- Helmholtz coil will feel:

0%

0%

0%

0% 1. a force but not a torque

2. a torque but not a force

3. both a torque and a force

4. neither force nor torque

:00

P17-102

PRS Answer: Anti-Helmholtz

No field no torque

Field gradient force

Answer: 1. A force but not a torque

P17-103

Next: Dipole in Anti-Helmholtz (Q6-7)

• Set in Anti-Helmholtz Mode (~2 A)


• Put dipole in center (0 on scale)

• Randomly align using bar magnet

• Turn on current

What happens?

P17-104

PRS Predictions:Moving in Anti-Helmholtz

P17-105

PRS: Moving in Anti-Helmholtz

When moving through the above field profile, a dipole will:

0%

0%

0% 1. Never rotate

2. Rotate once (at sign change)

3. Rotate twice (at slope changes)

0

P17-106

PRS Answer: Moving in Anti-HH

The dipole always wants to align with the field so when it crosses through zero it will rotate

Answer: 2. Dipole rotates once at sign change

P17-107


When pulling the dipole through the above field profile, the spring stretch direction will:

0%

0%

0%

0% 1. Always be the same

2. Change once

3. Change twice

4. Change three times

:00

P17-108

PRS Answer: Moving in Anti-HH

The dipole always wants to seek the strongest field, so the force reverses 3 times

Answer: 4. Force direction changes 3 times

FF

FF

FF

FF

P17-109

Next: Moving in Anti-Helmholtz (Q8-9)

• Keep in Anti-Helmholtz Mode (~2 A)

• Lower dipole to bottom

• Randomly align (is it possible?)

• Slowly & smoothly raise to well above

What happens (torque? force?)

P17-110

Moving in Anti-Helmholtz (Q8-9)

Where does it want to be?

F

F

Force 0, then flips

Field reverses, so does dipole

F

Force 0, then flips

F

NOTE:

Field Up/Down Motion Up/Down

Bottom Top

P17-111

PRS Questions:Force from Single Coil

Fields from Coils

P17-112

PRS: Single Coil

A field-aligned dipole located as pictured feels forces:

A

B

C

0%

0%

0%

0%

0% 1. FA > FB > FC

2. FA > FB ~ FC

3. FB > FA ~ FC

4. FA ~ FB ~ FC

5. No force, only a torque

0

P17-113

PRS Answer: Single Coil

The force goes like the slope of the field. It is ~ 0 at A & C, non-zero at B.

Answer: 3. FB > FA ~ FC

A

B

C

P17-114

PRS: Current Carrying Coils

The above coils have

0%

0%

0%

0% 1. parallel currents that attract2. parallel currents that repel3. opposite currents that attract4. opposite currents that repel

:00

P17-115

PRS Answer: I Carrying Coils

Look at the field lines at the edge between the coils. They are jammed in, want to push out. Also, must be in opposite directions

Answer: 4. Opposite currents that repel

P17-116

Force on Dipole from Dipole:Anti-Parallel Alignment

P17-117

Force on Dipole from Dipole:Parallel Alignment

P17-118

Applications

P17-119

Speakers

P17-120

Speakers

P17-121

DC Motor

P17 - 1 Workshop: Using Visualization in Teaching Introductory E&M AAPT National Summer Meeting,...

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