Lecture 13.1 :!
Electromagnetic Induction
Continued
Lecture Outline:!
Faraday’s Law!
Induced Fields!
Applications!
Textbook Reading:!
Ch. 33.5 - 33.7
April 7, 2015
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Announcements
!
•Homework #10 due on Tuesday, April 14, at 9am.!
•Finish reading Ch. 33 this week.!
•Questions? Concerns? Want to work on some practice problems?
Come see me during office hours today from 3-5pm, or make
arrangements for another day/time.!
•Final MidTerm (#3) of the semester is on Thursday, April 16, and
will cover Ch. 32 and 33. Don’t delay your studying!
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Last Lectures...
Faraday observed that a changing magnetic field
creates an induced current.
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Last Lectures...
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
m
=A·B
Units of magnetic flux:!
1 weber = 1 Wb = 1 Tm2
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Last Lecture…
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Clicker Question #1
The bar magnet is pushed toward the center of a
wire loop. Which is true?
A. 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.
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. 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.
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
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: Demos
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.
https://
www.youtube.com/
watch?v=ek6npHC4jD8
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Applications
Generators, such as those in hydroelectric dams, use
induction to generate power (AC power).
Changing flux through
one loop of N-loop
generator coil.
Ecoil =
N
m
⇤·B
⇤ = AB cos = AB cos ⇥t
=A
d
m
dt
=
d
ABN (cos t) = ABN sin t
dt
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Faraday’s Law: Example Problem
Two 20-turn coils are tightly wrapped around the same 2.0 cm diameter
cylinder with 1.0mm diameter wire. The current through coil 1 is shown
in the graph. Determine the current in coil 2 at t= 0.05s, and t=0.25s.
Assume that a positive current is into the page at the top of the loop.
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Applications
Transformers allow voltages to be “stepped-up” or “stepped-down”.
N2
V2 =
V1
N1
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Applications
Another method of generating power…
Motion of magnet on a spring, surrounded by a coil, leads to induced
current that charges a battery.
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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 Tuesday, April 8.!
•Please take advantage of office hours, TAs, clinic
etc…
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