P Workshop: Using Visualization in Teaching Introductory E&M AAPT National Summer Meeting, Edmonton, Alberta, Canada. Organizers: John Belcher, Peter Dourmashkin, Carolann Koleci, Sahana Murthy

P MIT Class: Feeling Magnetic Fields Magnetic Forces on Charges Magnetic Dipoles Experiment: Dipoles in B Fields

P The Biot-Savart Law Current element of length ds carrying current I produces a magnetic field: Moving charges are currents too…

P = 2 Current Sheets Ampere’s Law:. I B B X X X X X X X X X X X X X X X X X X X X X X X X X X X X B Long Circular Symmetry (Infinite) Current Sheet Solenoid Torus

P Review: Right Hand Rules 1.Torque: Thumb = torque, fingers show rotation 2.Create: Thumb = I, Fingers (curl) = B 3.Feel: Thumb = I, Fingers = B, Palm = F 4.Moment: Fingers (curl) = I, Thumb = Moment

P Demonstration: TV in Field

P How a CRT Works: It could…

P How a CRT Works: More Typical

P How a CRT Works

P Moving Charges Feel Magnetic Force Magnetic force perpendicular both to: Velocity v of charge and magnetic field B

P Reminder: B Field Units This is called 1 Tesla (T) Since

P Putting it Together: Lorentz Force This is the final word on the force on a charge Charges Feel… Electric Fields Magnetic Fields

P Application: Velocity Selector What happens here?

P Velocity Selector Particle moves in a straight line when

P PRS Question: Hall Effect

P PRS: Hall Effect A 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. I B V > V(Top) On the basis of this experiment, the sign of the charge carriers carrying the current in the slab is: 1.Positive 2.Negative 3.Cannot be determined 4.I don’t know 0

P 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 I B V > V(Top)

P What Kind of Motion in Uniform B Field?

P Cyclotron Motion (1) r : radius of the circle (2) T : period of the motion (3)  : cyclotron frequency

P Collections of Charges: Current Carrying Wires

P Demonstration: Jumping Wire

P Magnetic Force on Current-Carrying Wire Current is moving charges, and we know that moving charges feel a force in a magnetic field

P Magnetic Force on Current-Carrying Wire

P PRS Question: Parallel Current Carrying Wires

P PRS: Parallel Wires Consider two parallel current carrying wires. With the currents running in the same direction, the wires are I1I1 I2I2 1.attracted (likes attract?) 2.repelled (likes repel?) 3.pushed another direction 4.not pushed – no net force 5.I don’t know 0

P PRS Answer: Parallel Wires I 1 creates a field into the page at I 2. That makes a force on I 2 to the left. I 2 creates a field out of the page at I 1. That makes a force on I 1 to the right. Answer: 1. The wires are attracted I1I1 I2I2 X

P Demonstration: Parallel & Anti-Parallel Currents

P Summary Magnetic Force

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

P Field Pressures and Tensions: A Way To Understand the qVxB Magnetic Force

P 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)

P Example of E Pressure/Tension Positive charge in uniform (downward) E field Electric force on the charge is combination of 1.Pressure pushing down from top 2.Tension pulling down towards bottom (Animation)Animation

P 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)Animation

P PRS Question: Field Strength

P PRS: Field Strength A B C Where is the pictured field the strongest? 1.A 2.B 3.C 4.I don’t know 0

P PRS Answer: Field Strength Answer: 3. The field is the strongest at C Line density is proportional to field strength A B C

P Example of B Pressure/Tension Both cases: repelling “pressure” arises from HIGH field strength  HIGH energy density (Animation)Animation

P Loops of Current

P Group Problem: Current Loop Place rectangular current loop in uniform B field 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

P Torque on Rectangular Loop Familiar? No net force but there is a torque x

P Magnetic Dipole Moment Analogous to  tends to align  with B Define Magnetic Dipole Moment: Then:

P Animation: Another Way To Look At Torque External field connects to field of magnet and “pulls” the dipole into alignment

P Demonstration: Galvanometer

P Magnetic Dipole Moment

P PRS Question: Force on Magnetic Dipole

P PRS: Dipole in Field  From rest, the coil above will: 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

P 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)

P 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?

P Something New Dipoles in Non-Uniform Fields: Force

P Force on Magnetic Dipole? We Want to Know: What is the force on this dipole?

P PRS Question: Force on Magnetic Dipole

P PRS: Dipole in Field The current carrying coil above will feel a net force 1.upwards 2.downwards 3.of zero 4.I don’t know 0

P PRS Answer: Dipole in Field Answer: 2. Feels downward force The I ds x B forces shown produce a net downward force

P Can just sum I ds x B forces Is there another way?

P Energy of Magnetic Dipole This equation gives you a general way to think about what dipoles will do in B fields

P Magnetic Dipole Moments Generate: Feel: 1) Torque to align with external field 2) Forces as for bar magnets

P Force on Magnetic Dipole Alternate Thought #1 Where does the dipole want to be?

P Think Using Energy Where does dipole go to reduce its energy? Aligned dipoles seek high fields!  Force here is down

P Force on Magnetic Dipole Alternate Thought #2 What makes the field pictured?

P Force on Magnetic Dipole Bar magnet below dipole, with N pole on top It is aligned with the dipole pictured, they attract! N S N S 

P PRS Questions: Force on Dipole

P PRS: Dipole in Field The current carrying coil above will feel a net force 1.upwards 2.downwards 3.of zero 4.I don’t know 0

P PRS Answer: Dipole in Field Answer: 2. The coil feels a force down Many ways to know this:  I ds x B forces  Energy (aligned seeks high B)  Equivalent bar magnets S N S N 

P PRS: Free Dipoles If a number of dipoles are randomly scattered through space, after a while they 1.Attract (move together) 2.Repel (move apart) 3.Basically stay put 4.I don’t know 0

P 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

P Some Fun: Magnetic Levitation

P Put a Frog in a 16 T Magnet… For details:

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

P Para/Ferromagnetism Applied external field B 0 tends to align the atomic magnetic moments (unpaired electrons)

P Diamagnetism Everything is slightly diamagnetic. Why? More later. If no unpaired electrons then this effect typically dominates.

P Back to Levitation

P 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 SNSN NSNS Most importantly, in a certain region it is stable: Restoring force always towards the center SNSN

P Using  B to Levitate For details:

P Using  B to Levitate For details:

P Using  B to Levitate For details:

P Using  B to Levitate For details:

P Demonstration: Levitating Magnet over Superconductor

P Perfect Diamagnetism: “Magnetic Mirrors” N S N S

P Perfect Diamagnetism: “Magnetic Mirrors” N S N S No matter what the angle, it floats -- STABILITY

P Using  B to Levitate For details: kun.nl/levitate.html

P Levitate Magnet with your Fingers?

P Well… and a lifting magnet NSNS 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

P Experiment 4: Magnetic Forces on Dipoles This is a little tricky. We will lead you through with lots of PRS questions

P 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

P Field Profiles Single CoilHelmholtz VERY UNIFORM! Anti-Helmholtz ZERO FIELD!

P PRS Prediction: Dipole in Helmholtz

P PRS: Dipole in Helmholtz A randomly aligned dipole at the center of a Helmholtz coil will feel: 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

P PRS Answer: Dipole in Helmholtz The Helmholtz coil makes a UNIFORM FIELD Dipole feels only torque (need gradient for F) Answer: 2. a torque but not a force

P 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?

P PRS Prediction: Reverse Helmholtz

P PRS: Reverse Helmholtz Using aligned dipole, flip the field. Ideally the dipole will feel: 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

P 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

P Next: Reverse Helmholtz (Q3) Starting from end of previous (aligned dipole at center) Turn off current VERY CAREFULLY (don’t bump!) Reverse leads at power supply Turn on current What happens?

P PRS Predictions: Moving in Helmholtz

P PRS: Moving in Helmholtz When moving through the above field profile, a dipole will: 1.Never rotate 2.Rotate once 3.Rotate twice 0

P 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

P PRS: Moving in Helmholtz When pulling the dipole through the above field profile, the spring stretch direction will: 1.Always be the same 2.Change once 3.Change twice 4.Change three times 0

P 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

P 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?)

P PRS Prediction: Dipole in Anti-Helmholtz

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

P PRS Answer: Anti-Helmholtz No field  no torque Field gradient  force Answer: 1. A force but not a torque

P Next: Dipole in Anti-Helmholtz (Q6-7) Set in Anti-Helmholtz Mode (~2 A) Turn off current Put dipole in center (0 on scale) Randomly align using bar magnet Turn on current What happens?

P PRS Predictions: Moving in Anti-Helmholtz

P PRS: Moving in Anti-Helmholtz When moving through the above field profile, a dipole will: 1.Never rotate 2.Rotate once (at sign change) 3.Rotate twice (at slope changes) 0

P 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

P PRS: Moving in Helmholtz When pulling the dipole through the above field profile, the spring stretch direction will: 1.Always be the same 2.Change once 3.Change twice 4.Change three times :00

P 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

P 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?)

P 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

P PRS Questions: Force from Single Coil Fields from Coils

P PRS: Single Coil A field-aligned dipole located as pictured feels forces: A B C 1.F A > F B > F C 2.F A > F B ~ F C 3.F B > F A ~ F C 4.F A ~ F B ~ F C 5.No force, only a torque 0

P 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. F B > F A ~ F C A B C

P PRS: Current Carrying Coils The above coils have 1.parallel currents that attract 2.parallel currents that repel 3.opposite currents that attract 4.opposite currents that repel :00

P 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

P Force on Dipole from Dipole: Anti-Parallel Alignment

P Force on Dipole from Dipole: Parallel Alignment

P Applications

P Speakers

P Speakers

P DC Motor