Please put away everything except
a pen/pencil and a calculator (if
you brought one).
!
No talking, and no using phones/computers
during Quiz! If you finish early, please sit
quietly until time is up.
Sourav Bhabesh
Kazage Utuje
Lecture 12.2 :!
Electromagnetic Induction
Lecture Outline:!
Motional emf!
Magnetic Flux!
Lenz’s Law!
Faraday’s Law!
!
Textbook Reading:!
Ch. 33.2 - 33.5
April 2, 2015
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Announcements
!
•HW #9 due on Tue., April 7, at 9am.!
•Having trouble with any material related to this course?
Please
come see me…don’t wait until the next midterm, or the Final Exam.
3
Last Lecture…
Faraday observed that a changing magnetic field
creates an induced current.
Changing magnetic field can also be due to relative motion.
4
Last Lecture…
5
Last Lecture…
Recall what happens to the bar if we add a potential
(battery) across the two rails, as shown.
It would appear such a scheme will accelerate the bar
arbitrarily fast...making a “rail gun”! There are limitations
to the speed, which we will discuss soon.
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Magnetic Flux
It is once again useful to introduce the idea of the “flux” of
field (magnetic) passing through a current loop.
For a uniform
magnetic field
m
=A·B
Units of magnetic flux:!
1 weber = 1 Wb = 1 Tm2
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Clicker Question #1
Which loop has the larger
magnetic flux through it? !
!
Φm = L2B
A. Loop A.!
B. Loop B.!
C. The fluxes are the same.!
D. Not enough information
! to tell.
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Lenz’s Law
We’ve seen that a changing magnetic flux through a loop
induces a current in that loop, but we don’t yet have a way
of defining the direction the induced current flows.
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Lenz’s Law
10
Lenz’s Law
11
Lenz’s Law
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Clicker Question #2
The magnetic field shown is pointing out of the
page, but decreasing in magnitude as a function
of time. The induced current in the loop is: !
!
A. Clockwise!
B. Counterclockwise!
C. There is no current
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Lenz’s Law
There is a clockwise induced current in the conducting loop
shown below. Is the magnetic field inside the loop
increasing in strength, decreasing in strength, or steady?
The magnetic field must be decreasing.
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Revisit Clicker Question from Lecture 12-1
An induced current flows
clockwise as the metal bar is pushed to the right. The
magnetic field points
!
A.
B.
C.
D.
E.
Up.
Down.
Into the screen.
Out of the screen.
To the right.
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Lenz’s Law
The jumping ring. Explain this behavior in terms of induced currents.
What things can we do to make the ring jump higher?
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Faraday’s Law
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Faraday’s Law
All induced currents are associated with a changing
magnetic flux. Two ways flux can change:!
1.Geometry: Loop can expand, contract, or rotate.!
2.Magnetic field can change.
m
E=
d
m
dt
=A·B
dB
dA
+A·
= B·
dt
dt
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Faraday’s Law: Example!
A 20 cm x 20 cm square loop of wire lies in the xy-plane with its bottom edge
on the x-axis. The resistance of the loop is 0.50 Ohms. A magnetic field parallel
to the z-axis is given by B=0.80y2t, where B is in tesla, y is in meters, and t is
seconds. What is the size of the induced current in the loop at t=0.50s?
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Reminders
!
•Read Ch. 33!
•HW #9 due next Tue. (April 7) at 9am.!
!
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