# Phys 102 – Lecture 11 Magnetic dipoles & current loops 1

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Phys 102 Lecture 2

Phys 102 Lecture 11Magnetic dipoles & current loops 1

Today we will... Learn how magnetic fields act onMagnetic dipolesCurrent loops Apply these concepts!Magnetotactic bacteriaPrinciples behind NMR/MRI, EPR/ESRMagnetic materials (paramagnets and ferromagnets)Phys. 102, Lecture 11, Slide 2Magnetic dipole & dipole momentA magnetic N and S pole make up a magnetic dipoleMagnetic dipole moment is analogous to electric dipole moment=

DirectionVector from S to N pole (by convention)NSPhys. 102, Lecture 11, Slide 3Recall: electric dipoleMagnetic dipole

+qq=

3Dipole in uniform field

+qq

+qq

+qq

+qq

+qq

Electric & magnetic dipole moments align parallel to fieldDEMO

NSNSNSNSNSTorque:Energy:Lect. 3Lect. 4Phys. 102, Lecture 11, Slide 44NSNSNSACT: CheckPoint 1.1Phys. 102, Lecture 11, Slide 5Which of the three configurations of magnetic dipoles shown below has the highest potential energy?NS

NSNSA.B.C.Calculation: magnetic bacteria

Dipoles are randomized

Dipoles tend to be aligned

Find minimum value of such that cells align to the Earths fieldMagnetospirillum magnetotacticumMagnetotactic bacteria grow a chain of magnets to align to the Earths B fieldPhys. 102, Lecture 11, Slide 6Room temperature kinetic energy tends to randomizes orientation

Spin & magnetic fieldsElectron paramagnetic resonance (EPR) / electron spin resonance (ESR) applies same principle with electron spin

Phys. 102, Lecture 11, Slide 7Electrons, protons, & neutrons (and many others) have an intrinsic property called spin which gives them a magnetic dipole moment

+

+

Nuclear magnetic resonance (NMR) / magnetic resonance imaging (MRI)

Detects energy difference between nuclear spins (ex: 1H) parallel and anti-parallel to B field7Magnetic force on currentRecall: B field exerts a force on a moving charge qCurrent I is flow of + chargeMagnitude DirectionRight-hand rule (RHR)

CurrentB field strengthAngle between I and B

Thumb along I

Fingers along

on I is out of palm

Phys. 102, Lecture 11, Slide 8Length of wire

+

+IL8CheckPoint 2.1

A rectangular loop of wire is carrying current I as shown. There is a uniform magnetic field parallel to the sides ab and cd.What is the direction of the force on section ab of the wire?Iabcdforce is zero out of the pageinto the page ...on section cd of the wire?Phys. 102, Lecture 11, Slide 9ACT: CheckPoint 2.2

A rectangular loop of wire is carrying current I as shown. There is a uniform magnetic field parallel to the sides ab and cd.What is the direction of the force on section bc of the wire?Iabcdforce is zero out of the pageinto the page

Phys. 102, Lecture 11, Slide 1010ACT: Force on loop

A rectangular loop of wire is carrying current I as shown. There is a uniform magnetic field parallel to the sides ab and cd.What is the direction of the force on section da of the wire?Iabcdforce is zero out of the pageinto the page

Phys. 102, Lecture 11, Slide 11CheckPoints 2.3 & 2.4Phys. 102, Lecture 11, Slide 12

IabcdwSo, does the loop move?Compare magnitudes of forces:DEMO12

Torque on current loopPhys. 102, Lecture 11, Slide 13Top viewSide view

abcdab

LLwFFLoop area

Loop spins in B fieldB field generates a torque on the loopElectric motorsDC motors use a clever arrangement of current carrying coils and permanent magnets to turn a shaft:

DEMOPhys. 102, Lecture 11, Slide 1414NS

Current loop & magnetic dipolePhys. 102, Lecture 11, Slide 15Top viewSide view

abcdab

NS

Current loop behaves the same as magnetic dipole to loop planeB field exerts torque on loopConvenient to define a normal vector to loop plane, || to dipole moment normalnormalTorque aligns normal vector || to B fieldMagnetic dipole & current loopA current loop behaves the same as a magnetic dipoleEquivalent magnetic dipole moment:=

DirectionAnother right hand rule:NSPhys. 102, Lecture 11, Slide 16=IMagnitudeCurl fingers along I

along thumbATrue for flat loop of any shape

IFor a loop with N turns of wire16ACT: Current loop practice

A loop is placed in a uniform B field. A current I flows around the loop as shown. Phys. 102, Lecture 11, Slide 17

ClockwiseCounterclockwiseThe loop does not rotateWhich way does loop rotate?IACT: Torque on a loopPhys. 102, Lecture 11, Slide 18

Compare the torque on loop 1 and 2, which have identical area A, and current I. 1 > 2 1 = 2 1 < 2

Para- & ferromagnetismPhys. 102, Lecture 11, Slide 19

NSNSNSNSNSNSNSNSNSIn some materials, unpaired electron (spin & orbit) give atoms net magnetic momentIn paramagnets, atomic dipoles are randomly orientedApply a B field and dipoles align!Material now behaves as a magnet In ferromagnets, atomic dipoles interact and align togetherMaterial is a permanent magnetNSNSNSNSNSNSNSNSNS19

ACT: Magnetic materials Phys. 102, Lecture 11, Slide 20

DEMOThe N pole of a permanent magnet is brought near a paramagnetic ball bearing. What happens next?The ball moves toward the magnetThe ball moves away from the magnetThe ball does not move

20Summary of todays lecture B fields exert torque on magnetic dipoles

B fields exert force on current-carrying wire

Current loops are equivalent to magnetic dipolePhys. 102, Lecture 11, Slide 21=

NS=

IAN

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