Transcript Lecture_14_mod

Chapter 29
Electromagnetic Induction
and Faraday’s Law
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29-3 EMF Induced in a Moving
Conductor
Example 29-7: Electromagnetic
blood-flow measurement.
The rate of blood flow in our
body’s vessels can be measured
using the apparatus shown,
since blood contains charged
ions. Suppose that the blood
vessel is 2.0 mm in diameter, the
magnetic field is 0.080 T, and the
measured emf is 0.10 mV. What
is the flow velocity of the blood?
Remind you of the Hall effect?
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29-3 EMF Induced in a Moving
Conductor
Example 29-8: Force on the rod.
To make the rod move to the right at speed v, you
need to apply an external force on the rod to the
right. (a) Explain and determine the magnitude of
the required force. (b) What external power is
needed to move the rod?
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ConcepTest 29.5 Rotating Wire Loop
If a coil is rotated as shown,
in a magnetic field pointing
to the left, in what direction
is the induced current?
1) clockwise
2) counterclockwise
3) no induced current
ConcepTest 29.5 Rotating Wire Loop
If a coil is rotated as shown,
in a magnetic field pointing
to the left, in what direction
1) clockwise
2) counterclockwise
3) no induced current
is the induced current?
As the coil is rotated into the B field,
the magnetic flux through it increases.
According to Lenz’s law, the induced B
field has to oppose this increase, thus
the new B field points to the right. An
induced counterclockwise current
produces just such a B field.
29-4 Electric Generators
A generator is the opposite of a motor – it
transforms mechanical energy into electrical
energy. This is an ac generator:
The axle is rotated by an
external force such as
falling water or steam.
The brushes are in
constant electrical
contact with the slip
rings.
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29-4 Electric Generators
If the loop is rotating with constant angular
velocity ω, the induced emf is sinusoidal:
For a coil of N loops,
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29-4 Electric Generators
Example 29-9: An ac generator.
The armature of a 60-Hz ac
generator rotates in a 0.15-T
magnetic field. If the area of the coil
is 2.0 x 10-2 m2, how many loops
must the coil contain if the peak
output is to be V0 = 170 V?
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ConcepTest 29.10 Generators
A generator has a coil of wire
rotating in a magnetic field.
If the rotation rate increases,
1) increases
2) decreases
how is the maximum output
3) stays the same
voltage of the generator
4) varies sinusoidally
affected?
ConcepTest 29.10 Generators
A generator has a coil of wire
rotating in a magnetic field.
If the rotation rate increases,
1) increases
2) decreases
how is the maximum output
3) stays the same
voltage of the generator
4) varies sinusoidally
affected?
The maximum voltage is the leading
term that multiplies sin wt and is
given by e0 = NBAw. Therefore, if
w increases, then e0 must increase
as well.
e  NBAw sin( wt )
29-5 Back EMF and Counter Torque;
Eddy Currents
d B
d
0  V  It R 
 V  I  t  R   A Bsin  
dt
dt

 
Back EMF
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29-5 Back EMF and Counter Torque;
Eddy Currents
Induced currents can flow
in bulk material as well as
through wires. These are
called eddy currents, and
can dramatically slow a
conductor moving into or
out of a magnetic field.
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29-6 Transformers and Transmission
of Power
A transformer consists of two coils, either
interwoven or linked by an iron core. A
changing emf in one induces an emf in the
other.
The ratio of the emfs is equal to the ratio of
the number of turns in each coil:
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29-6 Transformers and Transmission
of Power
This is a step-up
transformer – the
emf in the secondary
coil is larger than the
emf in the primary:
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29-6 Transformers and Transmission
of Power
Energy must be conserved; therefore, in the
absence of losses, the ratio of the currents
must be the inverse of the ratio of turns:
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ConcepTest 29.12b Transformers
1) 1/4 A
Given that the intermediate
2) 1/2 A
current is 1 A, what is the
3) 1 A
current through the
4) 2 A
lightbulb?
5) 5 A
1 A
120 V
240 V
120 V
ConcepTest 29.12b Transformers
1) 1/4 A
Given that the intermediate
current is 1 A, what is the
current through the
lightbulb?
2) 1/2 A
3) 1 A
4) 2 A
5) 5 A
Power in = Power out
240 V  1 A = 120 V  ???
1 A
The unknown current is 2 A.
120 V
240 V
120 V
29-6 Transformers and Transmission
of Power
Example 29-12: Cell phone charger.
The charger for a cell phone contains a
transformer that reduces 120-V ac to 5.0-V ac
to charge the 3.7-V battery. (It also contains
diodes to change the 5.0-V ac to 5.0-V dc.)
Suppose the secondary coil contains 30 turns
and the charger supplies 700 mA. Calculate
(a) the number of turns in the primary coil, (b)
the current in the primary, and (c) the power
transformed.
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29-6 Transformers and Transmission
of Power
Transformers work only if the current is
changing; this is one reason why electricity
is transmitted as ac.
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29-6 Transformers and Transmission
of Power
Example 29-13: Transmission lines.
An average of 120 kW of electric power is sent
to a small town from a power plant 10 km away.
The transmission lines have a total resistance
of 0.40 Ω. Calculate the power loss if the power
is transmitted at (a) 240 V and (b) 24,000 V.
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29-7 A Changing Magnetic Flux
Produces an Electric Field
A changing magnetic flux induces an electric
field; this is a generalization of Faraday’s
law. The electric field will exist regardless of
whether there are any conductors around:
.
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29-7 A Changing Magnetic Flux
Produces an Electric Field
Example 29-14: E produced by
changing B
B.
A magnetic field B between the pole
faces of an electromagnet is nearly
uniform at any instant over a circular
area of radius r0. The current in the
windings of the electromagnet is
increasing in time so that B changes in
time at a constant rate dB/dt
B at each
point. Beyond the circular region (r > r0),
we assume B
B = 0 at all times. Determine
the electric field E at any point P a
distance r from the center of the
circular area due to the changing B
B.
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Summary of Chapter 29
• Magnetic flux:
• Changing magnetic flux induces emf:
• Induced emf produces current that
opposes original flux change.
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Summary of Chapter 29
• Changing magnetic field produces an electric
field.
• General form of Faraday’s law:
.
• Electric generator changes mechanical
energy to electrical energy; electric motor
does the opposite.
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Summary of Chapter 29
• Transformer changes magnitude of
voltage in ac circuit; ratio of currents is
inverse of ratio of voltages:
and
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Chapter 30
Inductance, Electromagnetic
Oscillations, and AC Circuits
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Units of Chapter 30
• Mutual Inductance
• Self-Inductance
• Energy Stored in a Magnetic Field
• LR Circuits
• LC Circuits and Electromagnetic Oscillations
• LC Circuits with Resistance (LRC Circuits)
• AC Circuits with AC Source
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Units of Chapter 30
• LRC Series AC Circuit
• Resonance in AC Circuits
• Impedance Matching
• Three-Phase AC
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30-1 Mutual Inductance
Mutual inductance: a changing current in one
coil will induce a current in a second coil:
And vice versa; note that the constant M,
known as the mutual inductance, is the same:
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30-1 Mutual Inductance
Unit of inductance: the henry, H:
1 H = 1 V·s/A = 1 Ω·s.
A transformer is an
example of mutual
inductance.
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30-1 Mutual Inductance
Example 30-1: Solenoid and coil.
A long thin solenoid of length l and cross-sectional
area A contains N1 closely packed turns of wire.
Wrapped around it is an insulated coil of N2 turns.
Assume all the flux from coil 1 (the solenoid)
passes through coil 2, and calculate the mutual
inductance.
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30-2 Self-Inductance
A changing current in a coil will also induce
an emf in itself:
Here, L is called the self-inductance:
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30-2 Self-Inductance
Example 30-3: Solenoid inductance.
(a) Determine a formula for the self-inductance
L of a tightly wrapped and long solenoid
containing N turns of wire in its length l and
whose cross-sectional area is A.
(b) Calculate the value of L if N = 100, l = 5.0 cm,
A = 0.30 cm2, and the solenoid is air filled.
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30-2 Self-Inductance
Conceptual Example 30-4: Direction of emf in
inductor.
Current passes through a coil from left to right
as shown. (a) If the current is increasing with
time, in which direction is the induced emf?
(b) If the current is decreasing in time, what
then is the direction of the induced emf?
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30-3 Energy Stored in a Magnetic Field
Just as we saw that energy can be stored in
an electric field, energy can be stored in a
magnetic field as well, in an inductor, for
example.
1
L  d 2 
 dI 
P  IV  E   I  L  dt    I  dt  LI 2
0
2
2 0  dt 
 dt 
Consider a solenoid: length , N turns, area A:

N 2 0 A
N B N   N  
N
  0   I  A 
B s  0   I  L s 
I   
I
 
1 2 1  N 2 0 A  2 1 A  02 N 2I 2  1 Bs2
 E  LI  
 Vol 


I 
2
2 0 
2
2
 2 0

Bs2
E

e 
Vol 2 0
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