electricity & magnetism lecture 13

Today’sConcept:

Torques

Electricity & MagnetismLecture 13

Electricity&Magne9smLecture13,Slide1

Worms Feel B field

Worms(C.elegans)cansensetheearth’smagne9cfield.

https://news.utexas.edu/2015/06/17/first-magnetic-field-sensor-discovered-in-animal

Whyisthezeroofpoten9alenergyfortheclosedlooptakenfromwhereitisperpendiculartotheelectricfield?

Idonotunderstandifthereisnonetforceontheloophowtherecanbetorqueandhowthetorquedoesn'teventuallystop.

canyouprovehowthecrossproductworks?

WhenarewegeOngourmidtermmarksback:o

Velocity Selector

Source: Wikipedia and youtube

https://youtu.be/MT-I0oUHMZc

Application: Mass spectrometer

Avelocityselectorisusedtoselectionsofgivenvelocity.

ThentheyareprojectedintoaregionofconstantBandzeroE.

Theradiusofcurvaturedependsontheion’smass.

Adetectorshowsthevariousmassesinthebeam.

Torque Review

Comparethetorques?R⊥

Torque(A) > Torque(B) > Torque(C)

~⌧ = ~R ⇥ ~F|~⌧| = R?F

R⊥

R⊥

LastTime:


yz

x

BF

I

ThisTime:qv and IL have same

Dimensions!

Clicker Question

A B C


What is the force on section a-b on the loop?

A. Zero B. Out of page C. Into the Page

A square loop of wire is carrying current in the clockwise direction. There is a horizontal uniform magnetic field pointing to the right.

A B C

Clicker Question


What is the force on section b-c on the loop?



What is the force on section c-d on the loop?


Clicker Question



CheckPoint 2


What is the direction of the net force on the loop?

A. Out of page B. Into the Page C. Zero



CheckPoint 4

Inwhichdirec9onwillthelooprotate?(assumethezaxisisoutofthepage)

A) AroundthexaxisB) AroundtheyaxisC) AroundthezaxisD) Itwillnotrotate

x

y



CheckPoint 6


Whatisthedirec9onofthenettorqueontheloop?

A) up(onpage)B) down(onpage)C) outofpageD) intopageE) nettorqueiszero

into page out of page

Magnetic Dipole Moment

Areavector Magnitude=Area

Direc9onusesR.H.R.

Magne9cDipolemoment


µ Makes Torque Easy!

Thetorquealwayswantstolineµ upwithB!


Bµ

turns µ toward B

x

y

z

B

µ

turnsµ toward Bx

y

z

Practice with µ and τ

Bµ

Inthiscaseµ isoutofthepage(usingrighthandrule)

I


Bµ

xy

z

isup(turnsµ toward B)

Practice with µ and τ

Bµ

Inthiscaseµ isINtothepage(usingrighthandrule)

I


B

µ

xy

z

isdown(turnsµ toward B)

⨂

CheckPoint 8


Magnetic Field does Work on Current-carrying wire

FromPhysics120:

FromPhysics121:

DefineU = 0 atposi9onofmaximumtorque


-1.0000

-0.7500

-0.5000

-0.2500

0.0000

0.2500

0.5000

0.7500

1.0000

0 45 90 135 180

BµU = ��µ · �B

W =Z ⇥/2

�µB sin ��d�� = µB cos � = ⇤µ · ⇤BText

U

angle (°)

CheckPoint 10

U = 0U = −µBcosθθ

U = +µBcosφ

φ


Which orientation has the lowest potential energy?

Wby f ield = ��U = Ui � U f

U = �µ · �B

BYWHOM?

BYYOU

BYFIELD

θc

θaφa

CheckPoint 12


C):

B):

A):

D’Arsonval Ammeter

N S

Permanent Magnet

Pointer

Scale

WireLoop

Spring

Howmuchdoesthepoten9alenergyofthesystemchangeasthecoilmovesfromitsini9alposi9ontoitsfinalposi9on.

ConceptualAnalysisAcurrentloopmayexperienceatorqueinaconstantmagne9cfield

τ = µ X B Wecanassociateapoten9alenergywiththeorienta9onofloop

U = − µ · B

z

x

y

B .30˚

y

z

I

ini9al final

StrategicAnalysisFind µCalculatethechangeinpoten9alenergyfromini9altofinal

a

B

Calculation

Asquareloopofsidea liesinthex−zplanewithcurrentI asshown.Theloopcanrotateaboutx axiswithoutfric9on.AuniformfieldBpointsalongthe+z axis.Assumea, I,andBareknown.


Whatisthedirec9onofthemagne9cmomentofthiscurrentloopinitsini9alposi9on?

A)+x B)−x C)+y D)−y


xinitial final

z

x

y

B .30˚

y

z

I

ini9al final

a

B

Calculation


Whatisthedirec9onofthetorqueonthiscurrentloopintheini9alposi9on?

A)+xB)−xC)+yD)−y

y

z

x

y

B .30˚

y

z

I

ini9al final

a

B

Calculation



µ

U = ��µ · �B

Calculation

Whatisthepoten9alenergyoftheini9alstate?

A)Uinitial < 0B)Uinitial = 0 C)Uinitial > 0

z

x

y

B .30˚

y

z

I

ini9al final

a

BAsquareloopofsidea liesinthex−zplanewithcurrentI asshown.Theloopcanrotateaboutx axiswithoutfric9on.AuniformfieldBpointsalongthe+z axis.Assumea, I,andBareknown.


Whatisthepoten9alenergyofthefinalstate?

A)Ufinal< 0 B)Ufinal = 0 C)Ufinal > 0

y

initial

z

x

y

B .30˚

y

z

I

ini9al final

a

B

Calculation



µµ

U = ��µ · �B

-1.0000-0.7500-0.5000-0.25000.00000.25000.50000.75001.0000

0 45 90 135 180angle (°)

U

A)B)C)

Whatisthepoten9alenergyofthefinalstate?

z

x

y

B .30˚

y

z

I

ini9al final

a

B

Calculation



µµU = ��µ · �B

electricity & magnetism lecture 13

Documents