HomeworkdueWednesdaynight11:59PMExam2:SundayApril9,6:10-7:10PM,onBuschpracHceproblemspostedonwebsitestartmakingyourformulasheetnow!BEFORECLASS:PlaywithmagnetsandmovingchargedparHclesLectureslidespostedonmainclasswebsite

CONGRATSON3/3toAlnadi,Balance,AlisonBansil,Buznitsky,Dias,Dormer,Z.Feng,Huang,Johnson,Kanagala,Kershaw,McKeown,Motyala,Ning,Parikh,Ravichandran,Rivera,Rondel,Scot,Smith,Suresh,Thuel,Tournoux,Yao

Chapter 28 Magnetic Field and Forces, part 2

2 Phys 272

LodestoneandbarmagnetsexertforceonmovingchargedparHclesbycreaHngamagne&cfieldBarmagnetfield:(nearends)ForcedependsonqandandonthemagneHcfield

B(r)

NS

!v B(r)

ThemagneHcforceonachargedparHcleatCrossproductoftwovectorsDirec&on:PerpendiculartodirecHonofPerpendiculartodirecHonof->normaltotheplanedefinedbyandTwochoices–useright-handruletochooseThumbalongv;fingersalongB:outofpalm

!F = q"v ×

!B

q

!r

!v!v

!v

!B !

B

!B

ThemagneHcforceonachargedparHcleatCrossproductoftwovectorsIfthevelocityandmagneHcfieldvectorsaregivenincomponentform,computebyexpandingthetermsExample:

!F = q"v ×

!B

!r

!v = vxi!B = Bxi + By j!v ×!B = vxi × (Bxi + By j) = vxBx (i × i )+ vxBy (i × j)

= vxByk

i-clicker:AparHcleofcharge+1.0Cwithvelocity(inm/s)movesthroughtheuniformmagneHcfield(inT)WhatisthemagnitudeofthemagneHcforceontheparHcle?a)  12Nb)  6.0Nc)  4.5Nd)  1.5Ne) Noneoftheabove

6Phys272

!v = 2i +3 j!B = 3i −1.5 j

i-clicker:AparHcleofcharge+1.0Cwithvelocity(inm/s)movesthroughtheuniformmagneHcfield(inT)WhatisthemagnitudeofthemagneHcforceontheparHcle?a)  12Nb)  6.0Nc)  4.5Nd)  1.5Ne) Noneoftheabove

7Phys272

!v = 2i +3 j!B = 3i −1.5 j

MoHonofachargedparHcleqinauniformfieldBv0perpendiculartothefieldIniHallyF=qv0Bdownward

Boutofthescreen

MoHonofachargedparHcleqinauniformfieldBv0perpendiculartothefieldIniHallyF=qv0BdownwardVelocitystaysconstant:magneHcforcedoesnoworkFstaysqv0Bperpendiculartovelocity

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MoHonofachargedparHcleqinauniformfieldBv0perpendiculartothefieldIniHallyF=qv0BdownwardVelocitystaysconstant:magneHcforcedoesnoworkFstaysqv0Bperpendiculartovelocity

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MoHonofachargedparHcleqinauniformfieldBv0perpendiculartothefieldUniformcircularmoHonTogettheradiusofthecircle,setthemagneHcforceequaltothecentripetalforceqv0B=mv02/rsor=mv0/qB

Boutofthescreen

Typicalproblem:x=2mv0/(qB)Bintothescreen:posbendslek,negbendsright

MoHonofachargedparHcleqinauniformfieldBv0xperpendiculartothefieldv0zparalleltothefield

Boutofthescreen

helixElectronbeamdemo

ForceonacurrentcarryingwireinauniformmagneHcfieldBpointsoutofthescreenMagneHcforceistotherightForceonthechargesistransmiledtothewire

Electronsarethefreechargeshere

isinthedirecHonofthecurrent!L

TorquealongtherotaHonaxis=Ftr(posiHve)

Phys272 16

i-clicker:WhatisthesignofthetorqueontherectangularlooprotaHngonthefixedaxiswithauniformBfieldpoinHngtotheright?a)  PosiHve(upalongaxis)b)  NegaHve(downalongaxis)c)  Zerod)  Justguessing

!B

ii

Phys272 17

i-clicker:WhatisthesignofthetorqueontherectangularlooprotaHngonthefixedaxiswithauniformBfieldpoinHngtotheright?a)  PosiHve(upalongaxis)b)  NegaHve(downalongaxis)c)  Zerod)  Justguessing

Torque=2(iBa)(b/2)=iB(ab)=iBarea

!B

ii

Phys272 18

Chapter 29 Currents Produce Magnetic Fields

19 Phys 272

Calculating the Magnetic Field due to a Current: Biot-Savart Law

20Phys272

!B = d

!B∫

Magnetic Field due to a Long Straight Wire

21Phys272

29.2: Magnetic Field due to a Long Straight Wire:

DEMO:needleandwireDEMO:ironfilingsontransparency

Magnetic Field due to a Long Straight Wire

23Phys272

Phys272 24

i-clicker:Whereonthex-axis(excludinginfinity)isBtot=0?a)  Atapointx<0b) Atapointxsuchthat0<x<dc)  Atapointx>dd) Onlyatinfinity

Phys272 25

i-clicker:Whereonthex-axis(excludinginfinity)isBtot=0?a)  Atapointx<0b) Atapointxsuchthat0<x<dc)  Atapointx>dd) Onlyatinfinity

⊗ ⊗a b

i-clicker:

Atpointsonwireb,whatdirecHondoesthemagneHcfieldduetocurrentiain“wirea”point?a)Totherightb)Tothelekc)Upd)Downe)it’szero

⊗ ⊗a b

i-clicker:

Atpointsonwireb,whatdirecHondoesthemagneHcfieldduetocurrentiain“wirea”point?a)Totherightb)Tothelekc)Upd)Downe)it’szero

⊗ ⊗a b

i-clicker:

WhatisthedirecHonofthemagneHcforceonwirebduetothecurrentinwirea?a)Totherightb)Tothelekc)Upd)Downe)it’szeroDEMO

!B

⊗ ⊗a b

i-clicker:

WhatisthedirecHonofthemagneHcforceonwirebduetothecurrentinwirea?a)Totherightb)Tothelekc)Upd)Downe)it’szeroDEMO

!B

Force Between Two Parallel Wires

30Phys272

Magnetic Field due to a Current in a Circular Arc of Wire:

31Phys272

B = dB = µ0iR2∫ ds =∫ µ0i

R2Rφ

Phys272 32

Ex: