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Physics 122 – Class #28 (4/28/15) –
●Announcements
●Torque on an electric motor●Motional EMF●Faraday's Law●Flux
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RecitationThis week recitation introduces Flux and Faraday's Law.
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Reading Assignments
Chapter 32, EXCEPT section 32.10
Chapter 33. Omit 33.6, 33.9, 33.10You need to really understand Faraday's
law and Lenz's law as well as generators and transformers. We will also understand the equation for potential across an inductor, but you will not be responsible for RL or LC circuits.
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Extra Credit Opportunity
Show up in recitation this week and take the same electricity quiz you took at beginning of term.
Eval FormsTuesday recitation 66714Thursday afternoon 66808Thursday evening 66956 Delivery person??
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Final Homework
Written homework #10. 33.49, 33.54. Slide from class #29 (explain why the magnet in the copper tube falls slowly)
MP Assignment #1333.1, 33.3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 18, 19, 28, 29, 30, 31, 39, 41, 42, 50, 60
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Torque
Only the part of theForce at right anglesTo the “moment arm”Twists the bolt
τ⃗= r⃗×F⃗
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=×B
=I A=I A
Torque on a current loop is proportional to magnetic moment.
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=×B
=I A
Torque on a current loop is proportional to magnetic moment.
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Slide 32-154
A Simple Electric Motor
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If released from rest, the current loop will
Slide 32-152
Clicker
A. Move upward.
B. Move downward.
C. Rotate clockwise.
D. Rotate counterclockwise.
E. Do something not listed here.
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Electric Motor demonstrations
DC Electric Motor
Homopolar motor “The simplest motor of the world”
http://www.youtube.com/watch?v=zOdboRYf1hM&NR=1
http://www.youtube.com/watch?v=Xi7o8cMPI0E&feature=fvw
http://www.youtube.com/watch?v=FjNnRyLexNM
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A Uniform Magnetic Field Exerts a Torque on a Square Current Loop
and are opposite eachother and cancel.
Both and exert a force of magnitude F = IlB around a moment arm d = ½lsin.
Slide 32-150
F⃗front F⃗back
F⃗top
F⃗front
F⃗bottom
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The total torque is:
= 2Fd = (Il2)Bsin = Bsinwhere = Il2 = IA is the loop’s magnetic dipole moment.
Although derived for a square loop, the result is valid for a loop of any shape:
A Uniform Magnetic Field Exerts a Torque on a Square Current Loop
Slide 32-151
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Why is magnetic dipole moment a useful concept?
It's good for understanding motors.
Protons and electrons have dipole moments. This is particularly surprising since electrons have zero size. Even at the quantum level, particles act like
spinning balls of charge!
MRI works by flipping over every proton in the Watermolecules in your body!
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MRI Used to be called “Nuclear ←Magnetic Resonance” (NMR)
Protons are flipped by a resonant magnetic field.They flip back to align with the large axial (solenoid) field. The time it takes them to flip back is converted to shades of grey in the MRI image.The time is weakly affected by the type of tissue that surrounds them.
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An electric motor is made from 100 turns ofCopper wire in a rectangle 10 cm on a side.It is placed in a 10 milliTesla magnetic field.What is the maximum torque with a 100 amp current?
(A) 0.001 Nm(B) 0.01 Nm(C) 0.1 Nm(D) 1 Nm(E) 10 Nm
=×B
=I A
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Physics 122 – Class #28 (4/28/15) –
●Announcements
●Torque on an electric motor●Motional EMF●Faraday's Law●Flux
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F=q v×B
There is a force on charges wheneverV cross B is not zero. Magnetic force >on a chargeMagnetic force >on all chargesIn a volume AL
F⃗=nAq L v⃗d×B⃗
F⃗=I L⃗×B⃗
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The battery creates a current, andThe Bfield pushes back on the wire.
F⃗=I L⃗×B⃗
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What if there was no battery and youPulled the wire out of the Bfield?
F⃗ per electron=q ⃗vpull×B⃗
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Here there is no battery … the Bfield pushes on the electronsWhen the crossbar moves … and makes a current.Slidewire generator
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Any time you change the magnetic fieldIn a loop, you cause a current
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Motional emf
Slide 33-24
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Slide 33-25
Motional emf
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Slide 33-26
Motional emf
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The magnetic force on the charge carriers in a moving conductor creates an electric field of strength E = vB inside the conductor.
But Voltage is E L so ...
For a conductor of length l, the motional emf perpendicular to the magnetic field is:
Slide 33-27
Motional emf
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A metal bar moves through a magnetic field. The induced charges on the bar are
Slide 33-30
Clicker
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A metal bar moves through a magnetic field. The induced charges on the bar are
Clicker
Slide 33-28
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F=qvBE=F /q=vBε=EL=vBL
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ε=v lB=
dAdt
B=dΦB
dtΦB=A⃗⋅⃗B
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Faraday's Law
Changing magnetic fluxes produce electric fields and hence voltages (also called emfs).
ε=−dΦB
dt← Faraday 's Law (of induction)
ΦB=B⃗⋅A⃗← Flux for B const. ovr space
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Faraday's Law – Why?
Changing magnetic fluxes produce electric fields and hence voltages.
If only electric fields
If elec. And magnetic fields
Units check out ...
ε=−dΦB
dt¿
ε=−∫ E⃗⋅d r⃗
ε=−∫(E⃗+ v⃗×B⃗)⋅d r⃗
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An induced current flows clockwise as the metal bar is pushed to the right. The magnetic field points
A. Up.
B. Down.
C. Into the screen.
D. Out of the screen.
E. To the right.
Slide 33-37
Clicker F⃗=q ⃗vpush×B⃗
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What is magnetic flux?
Flux – flow – like water through a river,or magnetic field lines through a surface.
For B uniform over area A:
B=B⋅A
B=∫ B⋅d A
ΦE=∫ E⃗⋅d A⃗
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Work done by magnetic force on electrons in a moving wire
Slidewire generator
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Ways to change flux
Let be uniform over the loop. Then
ΦB=∫ B⃗⋅d A⃗→ B⃗⋅A⃗
B⃗
dΦB
dt=dB⃗dt
⋅A⃗+d A⃗dt
⋅⃗B
Can move loop into stronger or weaker B.Can increase/decrease B.Can rotate B.Can increase/decrease size of loop.Can rotate loop.
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