Lecture 13.1 :
Electromagnetic Induction
Continued
Lecture Outline:
Lenz’s Law
Faraday’s Law
Induced Fields
Textbook Reading:
Ch. 33.4 - 33.6
April 9, 2013
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Announcements
•Homework #10 due on Monday, April 15, at 9pm.
•Exam #3 Results:
Average = 63.1% Standard Deviation = 16.8%.
•Brief outlook on next few weeks of class:
‣This week - continuing with Ch. 33.
‣Next week - Ch. 34 and Quiz #5.
‣April 23: Finish up Ch. 34.
‣April 26 : Quiz #6 and begin of Final Exam review.
‣April 30:
Review for Final Exam. Last day of lecture.
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Last Lecture...
Faraday observed that a changing magnetic field
creates an induced current.
3
Last Lecture...
There is an induced emf (a.k.a. motional emf)
in the moving conductor, with magnitude vlB.
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Last Lecture...
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
Φm
�
�
=A·B
Units of magnetic flux:
1 weber = 1 Wb = 1 Tm2
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Lenz’s Law
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Lenz’s Law
Brief reminder of the what the magnetic field of a
current-carrying loop looks like.
7
Lenz’s Law
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Lenz’s Law
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Clicker Question #1
The bar magnet is pushed toward the center of a
wire loop. Which is true?
There is a clockwise induced
current in the loop.
B. There is a counterclockwise
induced current in the loop.
C. There is no induced current in
the loop.
A.
1. Upward flux from magnet is increasing.
2. To oppose the increase, the field of the induced current points down.
3. From the right-hand rule, a downward field needs a cw current.
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Clicker Question #2
The current in the straight wire is decreasing.
Which is true?
A.
B.
C.
There is a clockwise
induced current in the loop.
There is a counterclockwise
induced current in the loop.
There is no induced current
in the loop.
1. The flux from wire’s field is into the screen and decreasing.
2. To oppose the decrease, the field of the induced current must point into
the screen.
3. From the right-hand rule, an inward field needs a cw current.
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Faraday’s Law
Lenz’s law lets us determine which direction an
induced current will flow. We still don’t know how
to quantify the magnitude of the induced emf.
We’ve observed that the magnitude of the emf
depends on a few things: strength of magnets;
rate of change of magnetic field; area of currentcarrying loop.
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Faraday’s Law
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Faraday’s Law
Demos:
1.) Rolling ball down a conductor.
2.) “Osheroff” Magnet
3.) Damped pendulum.
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Faraday’s Law
Magnetic Braking used to sort metals out of recyclable truck.
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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.
�·B
�
Φm = A
�
�
� ��
�
�
�
� dΦm � �
d
B
d
A
�
�·
�·
� = �B
E = ��
+
A
�
�
�
dt
dt
dt �
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Induced Fields
Magnetic forces alone cannot explain the current induced in
a stationary loop by a changing magnetic field.
We’ve seen that induced emf
develops since charge carriers in
moving conductor are subject to
a magnetic force (qv x B)
If the conductor is not moving,
but is in a changing magnetic
field, how does the emf develop?
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Induced Fields
We know from Lenz’s law that a conducting loop in a
changing magnetic field will develop an induced current to
counteract the changing flux. There must be an E-field
present to create this current in the loop.
In this changing magnetic field, the E-field is present
whether or not the loop is there!
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Induced Fields
In other words,
there are two ways to create an electric field:
non-Coulomb electric
field is created by
changing magnetic field.
Coulomb electric field is
created by charges.
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Clicker Question #3
The magnetic field is decreasing.
Which is the induced electric field?
The field is the same direction as induced
current would flow if there were a loop in the field.
E. There’s no induced field in this case.
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Reminders
•Read all of Ch. 33
•Homework #10 due on Monday, April 15.
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