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Phys 102 – Lecture 10
Phys 102 Lecture 10
Magnetic fields & forces
1
Today we will...
• Learn about the magnetism
Magnetic field B
Magnetic force F on moving charge
• Apply these concepts!
Charged particle motion in a magnetic field
Mass spectrometry
E h’
Earth’s magnetic field & northern/southern lights
i fi ld &
h /
h
li h
Phys. 102, Lecture 10, Slide 2
Electricity vs. magnetism
• Electricity
• Magnetism
Positive & negative charge
Opposite charges attract, like charges repel
–
+
+
N & S poles N & S always together as dipole (NO
“magnetic charge”)
Opposite poles attract, like poles repel
N
S
N
+
N
S
S
N
– –
S
N
N
S
DEMO
Phys. 102, Lecture 10, Slide 3
S
Electricity vs. magnetism
• Electric field
G
E
• Magnetic field
Vector at location in space
Points from positive & negative Q
Units: N/C = V/m
/
/
+
G
B
Vector at location in space
Points from N to S pole
Units: T (“Tesla”)
(
)
–
Electric dipole E field
Magnetic dipole B field
Phys. 102, Lecture 10, Slide 4
Sources of magnetic fields
There is no magnetic charge, so where do magnetic fields come from?
+
–
Moving electric charge (current)
–
Geodynamo
Intrinsic magnetic dipole (“spin”)
Phys. 102, Lecture 10, Slide 5
Magnetic force
Magnetic field B exerts a force on a moving charge q:
F = q vB sin θ
Speed of charge q
Magnetic field strength
“Right‐hand rule” (RHR)
G
v
G
B
θ
G
F
+
Angle between v and B
q
G
Thumb along vG
Fingers along
Fingers along B
G
F on + q is out of palm
G
F on – q is into palm
F is ⊥ to both v and B Phys. 102, Lecture 10, Slide 6
ACT: Right hand rule practice
A + charge moving to the right in a uniform B field experiences a force F up. Which way does the B
force F
up Which way does the B field point?
field point?
F
v
q
+
A.
B.
C.
D
D.
Up
Down
Into the page
O
Out of the page
f h
Phys. 102, Lecture 10, Slide 7
ACT: Right hand rule practice
A – charge moving out of the page in a uniform B field to the left experiences a force F in which direction?
experiences a force F in which direction?
B
–
q
v
A.
B.
C.
D
D.
Up
Down
Into the page
O
Out of the page
f h
DEMO
Phys. 102, Lecture 10, Slide 8
ACT: Moving charges
The three charges below have equal charge and speed, but are traveling in different directions in a uniform magnetic field. G
G
v
v
G
B
3
G
v
2
1
Which particle experiences the greatest magnetic force?
A. 1 B. 2 C. 3 D. All same
The force on charge 3 is in the same direction as the force on 1
A. True
B. False
Phys. 102, Lecture 10, Slide 9
Checkpoint 1.1
Each chamber has a unique magnetic field A positively charged particle field. A positively
charged particle
enters chamber 1 with velocity 75 m/s up, and follows the dashed trajectory.
v
1
+
2
v = 75 m/s q = +25 mC
What is the direction of the force
f
on the particle just as it p
j
enters region 1?
A. up
B down
B.
C. left
D. right
E. into page
F. out of page
Phys. 102, Lecture 10, Slide 10
Checkpoint 1.2
Each chamber has a unique magnetic field A positively charged particle field. A positively
charged particle
enters chamber 1 with velocity 75 m/s up, and follows the dashed trajectory.
v
1
+
2
v = 75 m/s q = +25 mC
What is the direction of the magnetic field
g
f
in region 1?
g
A. up
B. down
C left
C.
l f
D. right
E. into page
F. out of page
Phys. 102, Lecture 10, Slide 11
ACT: Checkpoint 1.4
Each chamber has a unique magnetic field A positively charged particle field. A positively
charged particle
enters chamber 1 with velocity 75 m/s up, and follows the dashed trajectory.
+
2
1
v = 75 m/s q = +25 mC
What is the direction of the magnetic field
g
f
in region 2?
g
A. up
B. down
C left
C.
l f
D. right
E. into page
F. out of page
Phys. 102, Lecture 10, Slide 12
ACT: Checkpoint 1.5
Each chamber has a unique magnetic field A positively charged particle field. A positively
charged particle
enters chamber 1 with velocity 75 m/s up, and follows the dashed trajectory.
1
+
2
v = 75 m/s q = +25 mC
How do the magnitudes of the B fields in region 1 and 2 compare?
A B1 > B
A.
> B2
B. B1 = B2
C. B1 < B2
Phys. 102, Lecture 10, Slide 13
Motion in uniform B field
Charged particle moves along x ⊥ to B field
Particle moves in a circle
Particle moves in a circle
+
F
B field does no work (since F ⊥ d)
v
R
y
B
x
Kinetic energy is constant
Speed is constant
DEMO
Phys. 102, Lecture 10, Slide 14
Mass spectrometer
Mass spectrometry uses a B field to analyze chemical compounds
Compound is vaporized into fragments & ionized, accelerated with Compound
is vaporized into fragments & ionized accelerated with
a E field into a B field Fragments separate according to mass to charge ratio (m/q) Phys. 102, Lecture 10, Slide 15
Calculation: Mass spectrometer
A mass spectrometer is used to separate different isotopes of carbon. Carbon ions are accelerated to a speed v
l
d
d = 10
105 m/s; /
assume all have charge +1e = 1.6×10–19 C. B = 0.2 T
02T
13C+
v = 105 m/s
Find which C isotope travels along the Find
which C isotope travels along the
green dotted path to the detector.
FA13 EX2
R = 6.8 cm
mv
qB
qBR 1.6 ×10−19 ⋅ 0.2 ⋅ 0.068
−26
=
=
2.18
×
10
kg = 13amu
m=
5
10
v
1amu = 1.67
1 67 ×10−27 kg
R=
Which way does the B field point?
13C+
Phys. 102, Lecture 10, Slide 16
ACT: Mass spectrometer I The mass spectrometer isolates three C isotopes a b c They
three C isotopes a, b, c. They move at a speed v = 105 m/s entering the B field and follow th d h d th
the dashed paths.
Magnet
C ion beam
v = 105 m/s
a
R
c
b
Detector
How do the speeds of the different isotopes a, b, c leaving the B field compare?
A. va > vb > vc
B. va = vb = vc
C. va < vb < vc
Phys. 102, Lecture 10, Slide 17
ACT: Mass spectrometer II The mass spectrometer isolates three C isotopes a b c They
three C isotopes a, b, c. They move at a speed v = 105 m/s entering the B field and follow th d h d th
the dashed paths.
Magnet
C ion beam
v = 105 m/s
a
R
c
b
Detector
How do the masses of the different isotopes a, b, c compare?
A. ma > mb > mc
B. ma = mb = mc
C. ma < mb < mc
Phys. 102, Lecture 10, Slide 18
3‐D motion in uniform B field
What if particle v has a component along B?
Charged
particle moves in x z plane
B field
along z
Charged particle moves in x‐z
plane, B
field along z
B
+
z
+
v⊥
F
B
z
B
=
y
v||
+
x
F = 0
Component || to B
remains constant
x
x
v
v٣
v||
+
R=
mv⊥
qB
y
F = qBv⊥
Component ⊥ to B
rotates in a circle
Charge moves in a helical trajectory
Phys. 102, Lecture 10, Slide 19
Aurora borealis & australis
Earth’s B field protects against stream of ions from sun (“solar wind”)
z
x
B
y
Aurora australis
“Southern lights”
B field directs ions to atmosphere in north and south hemispheres. Ions collide with particles in atmosphere and emit light: “aurora”
Phys. 102, Lecture 10, Slide 20
Summary of today’s lecture
Electric vs. magnetic forces
Force:
Electric
Source:
Charge
Act on:
Charge Magnitude: FE = q
Magnitude: F
=qE
Direction: || to E
Work
Work: WE = qEd
qEd cos(θ) cos(θ)
Magnetic
Moving charge
Moving charge
Moving charge
FB = q v B sin(θ)
= q v B sin(θ)
⊥ to v, B
WB = 0
0
Phys. 102, Lecture 10, Slide 21
B
v
v
F
B
F
v
F
B
v
F
B
Phys. 102, Lecture 10, Slide 22
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