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Exam I, Monday, Feb. 21, 7pm
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How do you study for a Phys 102 exam?
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Emphasize understanding concepts & problem solving, NOT
memorization
Review lecture notes, problem solver summary
Understand formula sheet (i.e. when to use and when NOT
to use an equation) & know what each symbol means
Do practice exam problems (time yourself!)
Go to office hours & review session
Physics 102: Lecture 8, Slide 1
Exam I, Monday, Feb. 21, 7pm
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What will exam cover?
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Lectures through #7 (RC circuits)
Homework through #4 (RC circuit problems only)
Discussions through #3
Labs through #3
Review, Sunday, Feb. 20, 3 PM, 141 Loomis
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I will go over Fall ‘10 exam problems
Physics 102: Lecture 8, Slide 2
Two more points
• Conflict exams
– There will be a conflict exam Monday, 5:15pm
– Can’t make that either? Contact before Thursday:
[email protected]
• Cheating
– DON’T DO IT!
– We will monitor the exams
– We will prosecute!
Physics 102: Lecture 8, Slide 3
Physics 102: Lecture 08
Magnetism
This material is NOT
on exam 1!
Physics 102: Lecture 8, Slide 4
Lecture Overview
• Magnetic fields
• Magnetic forces on moving charges
– Direction: “Right hand rule”
– Magnitude
Physics 102: Lecture 8, Slide 5
Magnets & magnetic fields
• North Pole and South Pole
– Opposites Attract
– Likes Repel
• Magnetic Field B
– Units = Tesla (T)
– Like E, vector at a location
– Points N to S
• Magnetic Field Lines
N
Physics 102: Lecture 8, Slide 6
S
– Arrows give direction
– Density gives strength
– Looks like dipole!
The Earth is a Magnet
Physics 102: Lecture 8, Slide 7
No Magnetic Charges
• N and S poles always go together
• 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)
Physics 102: Lecture 8, Slide 8
We’ll return to this in Lecture 25 & 26
Magnetic Fields and Forces
• Magnetic field B exerts force on moving charge
𝐹 = 𝑞𝑣𝐵 sin 𝜃
• Magnetic force is perpendicular to both B and v
• “Right-hand rule” (RHR):
– Thumb of right hand along v
– Fingers of right hand along B
– Out-of-palm points
• in the direction of F for + charge
• opposite to F for – charge
Physics 102: Lecture 8, Slide 9
Note: there are different versions of RHR
ACT: Direction of Magnetic
Force on + Moving Charge
Velocity
out of page
out of page
B
right
left
out of page
up
1) Up
2) Down
Physics 102: Lecture 8, Slide 10
3) Right
Force
up
down
4) Left
5) Zero
Direction of Magnetic Force on
Moving Charges
Velocity
out of page
out of page
out of page
out of page
Physics 102: Lecture 8, Slide 11
B
right
left
up
down
Force
up
down
left
right
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.
15%
3%
15%
36%
24%
8%
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
2) down
Particle is moving straight upwards
3) left
then veers to the right.
4) right
5) into page
6) out of page
Physics 102: Lecture 8, Slide 12
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.
11%
5%
9%
24%
20%
32%
B1
2
1
v = 75 m/s
q = +25 mC
What is the direction of the magnetic field in region 1?
1) up
2) down
3) left
4) right
5) into page
6) out of page
Physics 102: Lecture 8, Slide 13
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.
B2
2
1
v = 75 m/s
q = +25 mC
What is the direction of the magnetic field in region 2?
A) down
B) left
C) right
D) into page
E) out of page
Physics 102: Lecture 8, Slide 14
Magnitude of Magnetic Force on
Moving Charges
Force depends on magnitude of charge, velocity, and
magnetic field
𝐹 = 𝑞𝑣𝐵 sin 𝜃
= 𝑞𝑣⊥ 𝐵 = 𝑞𝑣𝐵⊥
180-q V
q
Only component of v ⊥ to B (or B ⊥ to v) matters
If v is parallel to B then F = 0
Does not matter whether you use q or 180 – q
Physics 102: Lecture 8, Slide 15
V⊥
B
B⊥
ACT: Moving Charges
The three charges below have equal charge and speed, but are traveling in
different directions in a uniform magnetic field.
3
B
2
1
F = qvBsin(q)
1) Which particle experiences the greatest magnetic force?
A) 1
B) 2
C) 3
D) All Same
2) The force on particle 3 is in the same direction as the force on particle 1.
A) True
B) False
Physics 102: Lecture 8, Slide 16
Comparison
Electric vs. Magnetic
Source:
Act on:
Magnitude:
Direction:
Physics 102: Lecture 8, Slide 17
Electric
Magnetic
Charges
Charges
F=qE
Parallel to E
Moving Charges
Moving Charges
F = q v B sin(q)
Perpendicular to v, B
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
v
FE
Electric force is down, so need magnetic force up.
By RHR, B must be into page
For straight line, need |FE |= |FB |
Physics 102: Lecture 8, Slide 18
q E= q v B sin(90)
B = E/v
E
Velocity Selector
Determine magnitude and direction of
magnetic field such that a negatively
charged particle with initial velocity v
travels straight through and exits the
other side.
E
v
ACT: Velocity Selector
What direction should B point if you want to select negative charges?
A) Into Page
Physics 102: Lecture 8, Slide 19
B) Out of page
C) Left
D) Right
FE would be up so FB must be down.
Motion of q in uniform B field
• Solve for R:
Recall circular motion from Phys 101
𝑣2
𝐹 = 𝑚 = 𝑞𝑣𝐵 sin 𝜃
𝑅
Physics 102: Lecture 8, Slide 20
𝑚𝑣
𝑅=
𝑞𝐵
x
x
x
x
x
x
x
x
x
x
x
x
x
v
x x
xR x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
F
v
– Motion is circular
– B does no work! (W=F d cos q)
– Speed is constant (W=DK.E.)
F
• Force is perpendicular to B,v
x x x x x x x
Uniform B into page
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?
9% 1) v2 < v1
63% 2) v2 = v1
27% 3) v2 > v1
Physics 102: Lecture 8, Slide 21
Magnetic force is always
perpendicular to velocity, 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
42% 1) B1 > B2
36% 2) B1 = B2
22% 3) B1 < B2
Physics 102: Lecture 8, Slide 22
𝑚𝑣
𝑅=
𝑞𝐵
Larger B, greater force, smaller R
ACT: 2 chambers
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
3) Q = 50 mC
Physics 102: Lecture 8, Slide 23
𝑚𝑣
𝑅=
𝑞𝐵
Summary
• We learned about magnetic fields B
• We learned about magnetic forces on
moving charged particles
Physics 102: Lecture 8, Slide 24