Download Magnetism

Physics 102: Lecture 08
Review, Sunday Feb. 17
3 PM, 141 Loomis
•
•
I will go over a past exam
Vote for which exam
a)
b)
c)
d)
e)
Fall 2007
Spring 2007
Fall 2006
Spring 2006
Fall 2005
Today’s Lecture: Magnetism
This material is NOT on exam 1
•
•
Magnetic fields
Magnetic force on charged
particles
Magnets are Cool!
• North Pole and South Pole
-
– Opposites Attract
– Likes Repel
+
• Magnetic Field Lines
– Arrows give direction
– Density gives strength
– Looks like dipole!
Lets Break it!
15
S
N
S
N
S
N
Field Lines of Bar Magnet
S
N
Magnetic field lines don’t start or stop.
There are no magnetic charges (monopoles)
18
Preflight 8.1
1
Which drawing shows the correct
field lines for a bar magnet?
(1) 10%
(2) 30%
S
N
S
N
S
N
2
(3) 60%
• Magnetic field lines are continuous
• Arrows go from N to S outside the
magnet (S to N inside).
3
The Earth is a Magnet
S
N
Comparison:
Electric Field Lines vs. Magnetic Field Lines
• Similarities
– Density gives strength
– Arrow gives direction
• Leave +, North
• Enter -, South
• Differences
– Start/Stop on electric charge
– No Magnetic Charge, lines are continuous!
• FYI
– x x x x x x x INTO Page
– • • • • • • • • • OUT of Page
20
No Magnetic Charges
• Magnetic Fields are created by
moving electric charge!
• Where is the moving charge?
Orbits of electrons about nuclei
Intrinsic “spin” of
electrons (more
important effect)
21
Magnetic Fields and Forces
• Magnetic fields exert forces on moving
charge
• We will discuss the magnitude of the force
shortly
• Direction of force is given by a “right-hand
rule”
Direction of Magnetic Force on
Moving Charges
• Magnetic force is perpendicular to both B
and v
• Right-hand rule:
– Thumb of right hand points in v direction
– Orient hand so that forefinger points in B
direction
– Then normal to palm points in direction of F
• Outward normal for + charge
• Opposite for – charge
B
v
F
25
25
Direction of Magnetic Force on
Moving Charges
Velocity
out of page
out of page
B
right
left
out of page
up
Force
up
down
B
v
F
ACT:
1) Up
2) Down
3) Right
4) Left
5) Zero
25
Direction of Magnetic Force on
Moving Charges
Velocity
out of page
out of page
out of page
out of page
B
right
left
up
down
Force
up
down
left
right
B
F
v
25
Preflight 8.3
Each chamber has a unique magnetic
field. A positively charged particle
enters chamber 1 with velocity 75 m/s
up, and follows the dashed trajectory.
21%
7%
9%
30%
24%
9%
2
1
v = 75 m/s
q = +25 mC
What is the direction of the force on the particle just as it
enters region 1?
1) up
Particle is moving straight upwards
2) down
then veers to the right.
3) left
4) right
5) into page
6) out of page
27
Preflight 8.4
Each chamber has a unique magnetic
field. A positively charged particle
enters chamber 1 with velocity 75 m/s
up, and follows the dashed trajectory.
17%
6%
8%
22%
20%
26%
2
1
v = 75 m/s
q = +25 mC
What is the direction of the magnetic field in region 1?
_
1) up
2) down v (thumb) points up, F(palm) points
right: so B(fingers) must point out.
3) left
_
4) right
5) into page
6) out of page
27
ACT: 2 Chambers
Each chamber has a unique magnetic
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 in region 2?
A) down
v (thumb) points right, F(palm) points
B) left
up, B(fingers) point in.
C) right
D) into page
E) out of page
29
Magnitude of Magnetic Force on
Moving Charges
• The magnetic force on a charge depends on
the magnitude of the charge, its velocity,
and the magnetic field.
F = q v B sin(q)
– Direction from RHR
V
q
B
• Thumb (v), fingers (B), palm (F)
– Note if v is parallel to B then F=0
30
ACT: Moving Charges
The three charges below have equal charge and speed, but are traveling in
different directions in a uniform magnetic field.
1) Which particle experiences the greatest magnetic force?
A) 1
B) 2
C) 3
D) All Same
F = q v B sin(q)
2) The force on particle 3 is in the same direction as the force on particle 1.
A) True
B) False
B
3
Thumb (v), fingers (B), palm (F)
into page!
2
1
33
Comparison
Electric vs. Magnetic
Source:
Act on:
Magnitude:
Direction:
Electric
Magnetic
Charges
Charges
F = Eq
Parallel to E
Moving Charges
Moving Charges
F = q v B sin(q)
Perpendicular to v,B
34
Velocity Selector
Determine magnitude and direction of
magnetic field such that a positively
charged particle with initial velocity v
travels straight through and exits the
other side.
FB
E
v
FE
Electric force is down, so need magnetic force up.
By RHR, B must be into page
For straight line, need |FE |= |FB |
q E= q v B sin(90)
B = E/v
What direction should B point if you want to select
negative charges? FE would be up so FB must be down.
A) Into Page
B) Out of page
C) Left
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D) Right
Motion of Q in uniform B field
• Force is perpendicular to B,v
– B does no work! (W=F d cos q ) x x x
– Speed is constant (W=D K.E. ) x x x
x x x
v
– Circular motion
F
x x x x
x x x x x x
x
x x x x x x
F
x
v
• Solve for R:
x x x x
R
x x x x
x x x x x x x
Uniform B into page
41
Motion of Q in uniform B field
• Force is perpendicular to B,v
– B does no work! (W=F d cos q ) x x x
– Speed is constant (W=D K.E. ) x x x
x x x
v
– Circular motion
v2
F m
R
v2
qvBsin(q )  m
R
F
x x x x
x x x x x x
x
x x x x x x
F
x
v
• Solve for R:
x x x x
R
x x x x
x x x x x x x
Uniform B into page
mv
R
qB
41
Preflight 8.6
Each chamber has a unique magnetic
field. A positively charged particle enters
chamber 1 with velocity v1= 75 m/s up,
and follows the dashed trajectory.
2
1
v = 75 m/s
q = +25 mC
What is the speed of the particle when it leaves
chamber 2?
17% 1) v2 < v1
46% 2) v2 = v1
36%
3) v2 > v1
Magnetic force is always perpendicular to velocity,
43
so it changes direction, not speed of particle.
Preflight 8.8
Each chamber has a unique magnetic
field. A positively charged particle enters
chamber 1 with velocity v1= 75 m/s up,
and follows the dashed trajectory.
2
1
v = 75 m/s
q = +25 mC
Compare the magnitude of the magnetic field in
chambers 1 and 2
37% 1) B1 > B2
38% 2) B1 = B2.
26% 3) B1 < B2
mv
R
qB
Larger B, greater force, smaller R
45
ACT
Each chamber has a unique magnetic
field. A positively charged particle enters
chamber 1 with velocity v1= 75 m/s up,
and follows the dashed trajectory.
2
1
v = 75 m/s
q = ?? mC
A second particle with mass 2m enters the chamber and
follows the same path as the particle with mass m and
charge q=25 mC. What is its charge?
1) Q = 12.5 mC
2) Q = 25 mC
mv
R
qB
3) Q = 50 mC
48
extra questions to try
B
1.
Which angle do you use to determine the
magnitude of the force on the charged
particle? (q1, q2 , either one).
V
q1
q2
Either one sin(q) = sin(180-q)
2.
Below I have drawn the trajectory for two
charged particles traveling through a
magnetic field. Is particle 1 positive or
negatively charged?
Positive
3.
If particles 1 and 2 have the same mass and
velocity, which has the largest charge?
Particle 1
x
x x x 1x x x
x
x x x
x x x
x
x x x
x x x
x
x x x
x x x
2
Summary
• We learned about magnetic fields B
• We learned about magnetic forces on
moving charged particles
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