CHAPTER 29 ELECTROMAGNETIC INDUCTIONpeople.physics.tamu.edu/adair/phys208/chapt29/CHAPTER 29.pdf1...
Transcript of CHAPTER 29 ELECTROMAGNETIC INDUCTIONpeople.physics.tamu.edu/adair/phys208/chapt29/CHAPTER 29.pdf1...
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CHAPTER 29
ELECTROMAGNETIC
INDUCTION
BASIC CONCEPTS
Faraday’s Law
Lenz’s Law
Motional emf
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Chapter 21: We saw:
Electric Charge Produces an
Electric Field
Chapter 27: We saw:
Moving Electric Charge Produces a
Magnetic Field
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Now Changing Magnetic Field Produces an
εmf
a potential difference (voltage)
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What is changing and causing
the emf is the magnetic flux.
In Chapter 22 defined Electric
Flux
Magnetic Flux is similar
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Flux through an area
We will define a vector to
represent area. The direction
of the vector will be
perpendicular to the surface.
The length of the vector will be
the area of the surface. The
vector will be .
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The flux will be
First, flat area perpendicular to
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For a surface parallel to
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And for in between
If this flux changes an emf will
be induced in the area.
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Consider a copper coil with one
loop
For N loops
B A
r
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B A
r
N loops
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FARADAY’S LAW
The emf induced in a circuit is
directly proportional to the
time rate of change of the
magnetic flux through the
circuit.
Or
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If changes with time an emf,
, will be produced.
Coil in magnetic field.
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Flux through coil
Flux can change:
1. Magnitude of changes.
2. Area of loop changes.
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3. The angle changes.
4. Any combination of the
three.
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Example:
Consider a coil with 200 turns
on a rectangular frame, 20 cm
by 30 cm. The resistance of the
coil is 2 Ω.
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If increases uniformly from
zero to in 0.8 s
what is the current in the coil?
At
At
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The current will be
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Lenz’s Law
A changing magnetic flux will
cause an emf and if the emf is
in a conductor there will be a
current.
What will be the direction of
the current?
Lenz’s Law will answer that
question.
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The polarity of the induced emf
is such that it tends to produce
a current that will create a
magnetic flux to oppose the
change in magnetic flux
through the loop.
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a. Magnet moves toward loop.
Magnet field is down and
increasing. Induced emf and
thus current will be ccw to
oppose the increase.
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b. Magnet moves away from
loop. Magnetic field is up and
but decreasing.
Induced current gives magnetic
field to oppose the decrease.
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Motional emf
dx
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In time dt the rod will move dx.
The area covered in dt will be
Faraday’s Law
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A conducting rod moving in a
magnetic field will have an emf
Induced across it given by this
equation.
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Example: My airplane
Luscombe 8E
Built 1947
Wingspan 22 feet = 6.7m
Speed 100 mph = 44.7 m/s
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If I am flying it at a point on
earth where the vertical
magnetic field is what
is the voltage drop across the
wings?
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Book example (A more interesting
problem):
The small segment is moving in the
magnetic field .
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What we have learned
So the contribution to the emf
for the small segment is
Angular velocity and velocity
are related by
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Add them up – integrate:
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Consider a loop around a long solenoid.
The current in the solenoid is increasing
so the flux through the loop is
increasing.
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An emf is induced in the loop by
Faraday’s Law
Also from Chapter 23 we know the
potential difference between two points
is
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If we integrate around the loop from the
galvanometer back to the galvanometer
in a counter‐clockwise direction we get
the emf induced in the loop
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But also
Therefore
One of Maxwell’s Equations.