2006 Physics 2112 Fundamentals of Physics Chapter 28 1
Fundamentals of Physics
Chapter 29 Magnetic Fields
1. The Magnetic Field2. B3. Crossed Fields: Discovery of the Electron4. Crossed Fields: the Hall Effect
5. A Circulating Charged Particle6. Cyclotrons & Synchrotrons
7. Magnetic Force on a Current-Carrying Wire8. Torque on a Current Loop9. The Magnetic Dipole Moment
Review & SummaryChapter QuestionsExercises & Problems
2006 Physics 2112 Fundamentals of Physics Chapter 28 2
Magnetism in Ancient Times
>2000 years ago Ancient Greeks - magnetite orenamed for the Magnesia region of Asia Minor
Attracts small bits of iron
Magnetite can magnetize an iron bar.
Ancient Chinese discovered the compass.
The Chinese compass seen at the right uses a piece of magnetite shaped like a spoon. The handle of the spoon points south.
2006 Physics 2112 Fundamentals of Physics Chapter 28 3
Magnetism in Ancient Times
11th Century
An elongated piece of magnetite suspended from a thread turns to the earth s north-south direction.
lodestone - a leading stone
1269 ad Peter Peregrinus (Pierre de Maricourt) was an engineer in the army of the King of Sicily.
A piece of magnetite has 2 poles (Latin polus)Every magnet has a north and a south pole.How the north and south poles attract or repel
He also described how to make a perpetual motion machine using magnets.
People are still trying this (unsuccessfully) today!
2006 Physics 2112 Fundamentals of Physics Chapter 28 4
Magnetism in Ancient Times
William Gilbert, 1544-1603The Earth is a magnet
William Gilbert published De Magnete (On the Magnet) in 1600.
first to distinguish the electric force (named for the Greek word for amber) from the magnetic force.
debunked many folk myths about the curative properties of magnets.
Based on his observations of the preferred directions of thin iron needles near spherical lodestones, and the similarity of this phenomenon to the tendency of compass needles to tilt with respect to the horizontal plane as well as point north-south, Gilbert deduced that the earth itself must be a giant magnet.
The Earth s North Pole is actually a south magnetic pole.
2006 Physics 2112 Fundamentals of Physics Chapter 28 5
Ben Franklin again!: lightning can magnetize iron.
Oersted, Ampere, Gauss, Weber & Faraday (1810-1830)
Force of a Magnetic Field
Right-Hand Rule for Cross Products
sinBvqF
BvqF
B
B
Magnets are surrounded by a magnetic field:
B = Magnetic Field (aka magnetic-flux density &magnetic induction )
Experimentally, the force on charge q moving with velocity v :
2006 Physics 2112 Fundamentals of Physics Chapter 28 6
The Magnetic Field B
Units: Tesla (T) = 1 (N/C) / (m/s) = 1 N/(A m)Gauss = T / 10,000
Earth s magnetic field ~ 0.6 gauss
Iron magnet ~ 0.5 TFermilab electro-magnets ~ 1-2 T
BvqFB
2006 Physics 2112 Fundamentals of Physics Chapter 28 7
Checkpoint 1
Direction of B ?
2006 Physics 2112 Fundamentals of Physics Chapter 28 8
Example 1
B = 1.2 mT vertically outward
proton KE = 5.3 MeV enters moving South to NorthWhat deflecting force acts on proton(m = 1.67 x 10-27 kg)
2006 Physics 2112 Fundamentals of Physics Chapter 28 9
The Definition of B
A magnetic field surrounds magnets.Magnetic Field Lines
Tangent gives the direction of the B fieldSpacing of the lines is proportional to the magnitude of B
Magnets have a North Pole and a South PoleOpposite poles attract each other, and like poles repel.No magnetic monopoles have been observed (a la +/- charges).
2006 Physics 2112 Fundamentals of Physics Chapter 28 10
Charged Particle Moving in Crossed Electric & Magnetic Fields
BE FFF
BvqEqF
B
Ev
Velocity Selector: adjust the fields so that there is no deflection (F = 0):
2006 Physics 2112 Fundamentals of Physics Chapter 28 11
Crossed Fields: Discovery of the Electron
Cathode Ray Tube:
Discovery of the Electron - J. J. Thomson (Cambridge) 1897
2006 Physics 2112 Fundamentals of Physics Chapter 28 12
q /m for Electrons - J. J. Thomson (1897)
p. 864
Add a crossed magnetic field adjusted to cancel out the deflection y:
B
Ev
tvtvL
a
x
x 0
221 tay
EqamF
y
yy
Consider the deflection of a charged particle moving through an electric field:
2
2
2 vm
LEqy
Ey
LB
q
m
2
22
2006 Physics 2112 Fundamentals of Physics Chapter 28 13
Checkpoint 2
positively charged particle velocity Vrank 1, 2, 3 for net forcewhich direction could lead to zero deflection?
2006 Physics 2112 Fundamentals of Physics Chapter 28 14
Crossed Fields: the Hall Effect
Use a magnetic field to deflect the charge carriers inside a conductor:
This creates an electric field across the conductor, generating a potential difference:
V = E dE grows until it balances the effect of the B-field.
e E = e vd BCurrent in a conductor
i = n e A vd = n e d l vd
Number density of the charge carriers:
elV
iBn
BvqFB
2006 Physics 2112 Fundamentals of Physics Chapter 28 15
Crossed Fields: the Hall Effect
Positive Charge Carriers Negative Charge Carriers
A calibrated Hall effect probe is also used to measure magnetic fields.
Move the sample in the opposite direction of the drift until a velocity is found that makes the potential difference disappear -
the magnitude of the drift velocity!
The sign of the side-to-side potential difference gives the sign of the drifting charges inside the conductor.
2006 Physics 2112 Fundamentals of Physics Chapter 28 16
Example 2
d =1.5 cmmoving uniformly in +y directionv = 4.0 ms
B = .050 T towards +za) which face is at lower electric potential
b) what is potential difference
2006 Physics 2112 Fundamentals of Physics Chapter 28 17
A magnetic field does no work on moving charged particles, but it does deflect their velocity:
A Circulating Charged Particle
BvqFB
Bq
vmr
r
vmBvqF
2
Circular Motion:
Period:Bq
m
v
rT
22
(r ~ momentum)
(independent of v!)
2006 Physics 2112 Fundamentals of Physics Chapter 28 18
Example 3
Mass Spectrometer:
Energy:
x = 2 r
momentum:
Bq
vmr
Vqvm 22
1
V
xqBm
8
22
B = 80.000 mT
V = 1000.0 Vq = 1.6 x 10-19 C
x = 1.6254 mmass m in amu s (1 u = 1.6605 x 10-27 kg)
Mass
Momentum
2006 Physics 2112 Fundamentals of Physics Chapter 28 19
A Circulating Charged Particle
Helical Paths:
z
y
x
BvqF xyxy
constantzv0zF
kBB z Uniform circular motion
in xy-plane
2006 Physics 2112 Fundamentals of Physics Chapter 28 20
29-5 A Circulating Charged Particle
Magnetic Bottle: Charged particles spiraling in a non-uniform magnetic field.
reflectionreflection
2006 Physics 2112 Fundamentals of Physics Chapter 28 21
A Circulating Charged Particle
Van Allen Belts - Earth s magnetic bottle
2006 Physics 2112 Fundamentals of Physics Chapter 28 22
Van Allen Belts
Protons & electrons boiling off the Sun are trapped in the Earth s magnetic bottle:
The Northern (& Southern) Lights!
2006 Physics 2112 Fundamentals of Physics Chapter 28 23
The Cyclotron
Constant BElectric potential difference between the Dees accelerates particles across the gap.
larger momentum larger radiusNo E inside the Dee.Orbital period in B is independent of energy.
Constant frequency oscillator.
Acceleration continues until particles reach the radius of the Dee; then deflected out.
Bq
m
v
rT
22
2006 Physics 2112 Fundamentals of Physics Chapter 28 24
Magnetic Force on a Current-Carrying Wire
outB
2006 Physics 2112 Fundamentals of Physics Chapter 28 25
Magnetic Force on a Current-Carrying Wire
The force that a magnetic field exerts on the charge carriers inside a conductor is transmitted to a conducting wire itself.
BLiF
eqAvqni
LAnBvqF
Bvqf
B
d
dB
dB
)626(
Or: and integrate.BdLiFd B BdLiFd B
2006 Physics 2112 Fundamentals of Physics Chapter 28 26
Example 6
I = 28 A
Magnitude and direction of minimum magnetic field B to suspend the wire.
= 46.6 g/m
2006 Physics 2112 Fundamentals of Physics Chapter 28 27
Torque on a Current Loop
BLiF
2006 Physics 2112 Fundamentals of Physics Chapter 28 28
Torque on a Current Loop
Forces on all 4 sides of a current loop in a magnetic field.
Suppose that the current loop can only rotate about a horizontal axis.
2006 Physics 2112 Fundamentals of Physics Chapter 28 29
Torque on a Current Loop
BLiF
cos90sin 02 BbiBbiF
BaiF1
24 FF
Sides 1 & 3 are perpendicular to B:
31 FF
Sides 2 & 4 are not:
2006 Physics 2112 Fundamentals of Physics Chapter 28 30
Torque on a Current Loop
cos24 BbiFF
sin
sinsin2
2 1
BAiN
BAib
F
Produce a net torque.
BaiFF 31
No torque produced.
2006 Physics 2112 Fundamentals of Physics Chapter 28 31
Torque on a Current Loop
A Motor: Reverse the current every half turn.
Force reversesConstant torque direction
2006 Physics 2112 Fundamentals of Physics Chapter 28 32
Simple DC Motor
2006 Physics 2112 Fundamentals of Physics Chapter 28 33
Magnetic Dipole Moment
AiNB where
sinBAiN
Magnetic Dipole Moment
2006 Physics 2112 Fundamentals of Physics Chapter 28 34
The Magnetic Dipole Moment
Magnetic Moment:
AiNB where
BU
2006 Physics 2112 Fundamentals of Physics Chapter 28 35
Example 8
circular coil with 250 turnsA = 2.52 x 10-4 m2
current = 100 mAB = 0.85 T, with dipole moment m initially aligned with Ba) direction of current in coil?b) how much work would the torque from an external agent have to do on the coil to rotate it 900 from its original orientation so the m is perpendicular to B and the coil is at rest again?
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