Chapter 19: Magnetic Fields
PHY2054: Chapter 19
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Magnetic Fields
ÎMagnetic
field (units, field lines)
‹ Magnetic
ÎEffects
field of the earth and other astronomical objects
of magnetic fields on charges and currents
‹ Force
on a moving charge
‹ Force on a current
‹ Torque on a current loop
‹ Path followed by particle in magnetic field
ÎGenerating
magnetic fields
‹ Long
wire
‹ Current loop
‹ Solenoid
ÎInstruments
‹ Mass
spectrometers
‹ Cyclotrons and synchrotrons
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Reading Quiz
ÎThe
magnetic force on a moving charged particle is:
‹ (1)
‹ (2)
‹ (3)
‹ (4)
‹ (5)
Perpendicular to the velocity
Parallel to the velocity
Parallel to the B field
Independent of the velocity
None of the above
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Reading Quiz
Î
Consider +q moving relative to a B field as shown. What
is the direction of the magnetic force?
Force
‹ Force
‹ Force
‹ Force
‹
is
is
is
is
parallel to v
parallel to B
into the page
out of the page
B
+q
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Reading Quiz
ÎWhen
I cut a magnet into two pieces I get:
‹ An
isolated north and south magnetic pole
‹ Two smaller magnets
‹ The two pieces are no longer magnets
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Bar Magnets
ÎTwo
poles: “north” and “south”
ÎLike
poles repel
ÎUnlike
poles attract
ÎMagnetic
S
poles cannot be isolated
N
Similar to dipole field from electrostatics
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Magnetic Monopoles?
ÎCan
any isolated magnetic charge exist?
‹ We
would call this a “magnetic monopole”
‹ It would have a + or – magnetic charge
ÎHow
can we isolate this magnetic charge?
‹ Cut
a bar magnet in half? NO!
What you get
is a bunch of
little magnets!
Magnetic monopoles have never been seen!
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Searches for Magnetic Monopoles
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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
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What Causes Magnetism?
ÎWhat
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).
ÎUnderstanding
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)
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Magnetic Field Units
ÎFrom
the expression for force on a current-carrying wire:
‹B
= Fmax / I L
‹ Units: Newtons/A⋅m ≡ Tesla (SI unit)
‹ Another unit: 1 gauss = 10-4 Tesla
ÎSome
sample magnetic field strengths:
‹ Earth:
B = 0.5 gauss = 0.5 x 10-4 T
‹ Galaxy: B ∼ 10-6 gauss = 10-10 T
‹ Bar magnet: B ∼ 100 – 200 gauss
‹ Strong electromagnet: B = 2 T
‹ Superconducting magnet: B = 5 – 10 T
‹ Pulse magnet: B ∼ 100 T
‹ Neutron star: B ∼ 108 – 109 T
‹ Magnetar: B ∼ 1011 T
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Pulsars
Rapidly Rotating Neutron Stars
Enormous Magnetic Fields
Beam off
Beam on
Crab Pulsar
R = 10 km
M = 1.4 solar mass
B ≈ 108 T
Period = 1/30 sec
PHY2054: Chapter 19
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Magnetic Force on Moving Charge
ÎMagnetic
force
F = qvB sin φ
ÎSign
of charge
‹ Force
is in opposite direction from positive charge
ÎForce
magnitude depends on direction of v relative to B
‹ v is parallel to B
⇒ sinφ = 0
F =0
F = qvB
‹ v is perpendicular to B
⇒ sinφ = 1
F = qvB sin 45
‹ v is at angle 45° to B
⇒ sinφ = 0.71
ÎForce
direction is perpendicular to both B and v
‹ Right
hand rule (next slide)
PHY2054: Chapter 19
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Right Hand Rule For Magnetic Force
ÎFirst
point fingers in direction of velocity
‹ Curl
fingers toward B field
‹ ⇒ Thumb points toward force
v
F
B
v
+q
B
F is into page
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Example
with m = 1.5 g, q = −2μC moves with velocity
2,000 m/s through a magnetic field of 2.5 T at an angle of
30° to the field.
ÎParticle
‹ Magnitude
of force
(
)
F = qBv sin φ = 2 × 10−6 ( 2.5)( 2000 )( 0.5) = 0.005 N
‹ Direction
of force: up out of the page. Use RHR and take opposite
direction because of −q
v
B
−q
F is up out of page
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Quiz
ÎA
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 || B
there is no magnetic force
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Magnetic Force
ÎA
negative particle enters a magnetic field region. What
path will it follow?
‹ (1)
‹ (2)
‹ (3)
‹ (4)
‹ (5)
A
B
C
D
E
x x x x x x x x x x x x
A
x x x x x x x x x x x x
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 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 x x x x
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
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Magnetic Force on Current-Carrying Wire
ÎMagnitude
of force on current
F = ( force on one charge ) × ( # of charges )
= ( evd B sin φ ) × ( ne AL ) = ( ene vd A ) BL sin φ = iBL sin φ
ÎDirection
of force: RHR
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Example
ÎA
4 m long wire carries current of 500A in NE direction
‹ Magnitude
‹φ
of force (B = 0.5 gauss = 5 × 10-5 T, pointing N)
= 45°
(
)
F = iBL sin 45° = ( 500 ) 5 × 10−5 ( 4 )( 0.71) = 0.071N
‹ Direction
ÎCan
of force: Upwards, from RHR
adjust current in wire to balance against gravity
‹ Calculate
mass from density, length and cross-sectional area
iBL sin φ = mg
m = ρ LA = density × volume
ρ Ag
i=
B sin φ
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Magnetic Force
ÎA
vertical wire carries a current and is in a vertical
magnetic field. What is the direction of the force on the
wire?
‹ (a)
left
‹ (b) right
‹ (c) zero
‹ (d) into the page
‹ (e) out of the page
B
I is parallel to B, so
no magnetic force
I
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