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PHY2054: Chapter 19 1
Chapter 19: Magnetic Fields
PHY2054: Chapter 19 2
Magnetic Fields Magnetic field (units, field lines)
Magnetic field of the earth and other astronomical objects
Effects of magnetic fields on charges and currentsForce on a moving chargeForce on a currentTorque on a current loopPath followed by particle in magnetic field
Generating magnetic fieldsLong wireCurrent loopSolenoid
InstrumentsMass spectrometersCyclotrons and synchrotrons
PHY2054: Chapter 19 3
Reading QuizThe magnetic force on a moving charged particle is:
(1) Perpendicular to the velocity(2) Parallel to the velocity(3) Parallel to the B field(4) Independent of the velocity(5) None of the above
PHY2054: Chapter 19 4
Reading QuizWhen I cut a magnet into two pieces I get:
An isolated north and south magnetic poleTwo smaller magnetsThe two pieces are no longer magnets
PHY2054: Chapter 19 5
Reading QuizConsider +q moving relative to a B field as shown. What is the direction of the magnetic force?
Force is parallel to vForce is parallel to BForce is into the pageForce is out of the page B
+q
PHY2054: Chapter 19 6
Reading QuizConsider +q moving relative to a B field as shown. What is the direction of the magnetic force?
Force is parallel to vForce is parallel to BForce is into the pageForce is out of the page B
+q
PHY2054: Chapter 19 7Fig. 19-1, p.625
PHY2054: Chapter 19 8
Bar MagnetsTwo poles: “north” and “south”
Like poles repel
Unlike poles attract
Magnetic poles cannot be isolated
NS
Similar to dipole field from electrostatics
PHY2054: Chapter 19 9
Interaction of Magnetic Poles
N – SAttract
N – NRepel
1 magnet
PHY2054: Chapter 19 10
Magnetic Monopoles?Can any isolated magnetic charge exist?
We would call this a “magnetic monopole”It would have a + or – magnetic charge
How can we isolate this magnetic charge?Cut a bar magnet in half? NO!
Magnetic monopoles have never been seen!
What you getis a bunch oflittle magnets!
PHY2054: Chapter 19 11
Searches for Magnetic Monopoles
PHY2054: Chapter 19 12
Earth is a big magnet!!
The North pole of a small magnet (compass) points towards geographic North because Earth’s magnetic South pole is up there!!
Particles moving along field lines cause Aurora Borealis.http://science.nasa.gov/spaceweather/aurora/gallery_01oct03.html
PHY2054: Chapter 19 13Fig. 19-4, p.626
PHY2054: Chapter 19 14
What Causes Magnetism?What is the origin of magnetic fields?
Electric charge in motion!For example, a current in a wire loop produces a field very similar to that of a bar magnet (as we shall see).
Understanding the source of bar magnet field lies in understanding currents at the atomic level within matter
Orbits of electrons about nuclei
Intrinsic “spin” of electrons (more important effect)
PHY2054: Chapter 19 15
Magnetic Field UnitsFrom the expression for force on a current-carrying wire:
B = Fmax / I LUnits: Newtons/A⋅m ≡ Tesla (SI unit)Another unit: 1 gauss = 10-4 Tesla
Some sample magnetic field strengths:Earth: B = 0.5 gauss = 0.5 x 10-4 TGalaxy: B ∼ 10-6 gauss = 10-10 TBar magnet: B ∼ 100 – 200 gaussStrong electromagnet: B = 2 TSuperconducting magnet: B = 5 – 10 TPulse magnet: B ∼ 100 TNeutron star: B ∼ 108 – 109 TMagnetar: B ∼ 1011 T
PHY2054: Chapter 19 16
PulsarsRapidly Rotating Neutron Stars
Enormous Magnetic Fields
Beam off Beam on
Crab PulsarR = 10 kmM = 1.4 solar massB ≈ 108 TPeriod = 1/30 sec
PHY2054: Chapter 19 17
Magnetic Force on Moving ChargeMagnetic force acts only on moving charge
Force direction is perpendicular to both B and vRight hand rule (next slide)
Force direction depends on sign of chargeForce is in opposite direction from positive charge
Force magnitude depends on direction of v relative to Bv is parallel to B ⇒ sinφ = 0v is perpendicular to B ⇒ sinφ = 1v is at angle 45° to B ⇒ sinφ = 0.71
sinF qvB φ=
F qvB=0F =
sin 45F qvB=
PHY2054: Chapter 19 18
Direction of Magnetic Force
F perpendicular to v and B
PHY2054: Chapter 19 19
Right Hand Rule For Magnetic ForceFirst point fingers in direction of velocity
Curl fingers toward B field⇒ Thumb points toward force
F
v
B
B
+q
v
F is into page
PHY2054: Chapter 19 20
ExampleParticle with m = 2.0 g, q = −2μC moves with v = 2,000 m/s through B field of 2.5 T at an angle of 30° to the field.
Magnitude of force
Direction of force: up out of the page. Use RHR and take opposite direction because of −q
B
−q
v
F is up out of page
( )( )( )( )6
2
sin 2 10 2000 2.5 0.5 0.005N
/ 0.005/ 0.002 2.5m/s
F qvB
a F m
φ −= = × =
= = =
PHY2054: Chapter 19 21
QuizA charged particle moves in a straight line through some region of space. Can you conclude that B = 0 here?
(1) Yes(2) No
A B field can exist since if v || Bthere is no magnetic force
PHY2054: Chapter 19 22
A negative particle enters a magnetic field region. What path will it follow?
(1) A(2) B(3) C(4) D(5) E
x x x x x x x x x x x xx x x x x x x x x x x xx x x x x x x x x x x xx x x x x x x x x x x xx x x x x x x x x x x xx x x x x x x x x x x xx x x x x x x x x x x x
Magnetic Force
AB
C
D
E
(1) RHR says it bends down (− charge)(2) But force cannot instantaneously change v
and the velocity vector bends continuously(3) So the answer is D, not E
PHY2054: Chapter 19 23
Magnetic Force on Current-Carrying WireMagnitude of force on current
Direction of force: RHR
( ) ( )( ) ( ) ( )force on one charge # of charges
sin sin sind e e d
F
ev B n AL en v A BL iBLφ φ φ
= ×
= × = =
=i
PHY2054: Chapter 19 24
F
F
PHY2054: Chapter 19 25
ExampleA 4 m long wire carries current of 500A in NE direction
Magnitude of force (B = 0.5 gauss = 5 × 10-5 T, pointing N)φ = 45°
Direction of force: Upwards, from RHR
Can adjust current in wire to balance against gravityCalculate mass from density, length and cross-sectional area
siniBL mgφ =
( )( )( )( )5sin 45 500 5 10 4 0.71 0.071NF iBL −= ° = × =
density volumem LAρ= = ×
sinAgi
Bρ
φ=