Download Electromagnetic Induction

CHAPTER·
25
Electromagnetic
Induction
... . ... . .... .... . ... .
Chapter Outline
~ Go With the Flow
Aluminum is classified as a non-magnetic substance. Two
aluminum rings, one with a slit and one a continuous ring,
are placed over a magnetic field generator that is producing a constantly-changing magnetic field. Why does one
ring float but the other one does not?
25.1 CREATING ELECTRIC
CURRENT FROM
CHANGING MAGNETIC
FIELDS
·
·
·
·
Faraday's Discovery
Electromotive Force
Electric Generators
Alternating Current Generator
25.2 EFFECTS OF CHANGING
MAGNETIC FIELDS:
INDUCED EMF
· Lenz's Law
· Self-Inductance
· Transformers
•
VConcept Check
L
evitation? There is no superconductor or permanent magnet in this photograph. The ring is made of aluminum, a
non-magnetic conductor. The coil of wire around the central rod produces a continually changing magnetic field.
You may never have seen such a floating ring, but the physical principle that explains why it is levitated also explains
how the modern electrical distribution system works.
The following terms or
concepts from earl ier chapters
are important for a good
understanding of this chapter. If
you are not familiar with them,
you should review them before
studying this chapter.
. potential difference, electron
pump, current, resistance,
Chapter 22
. right-hand rules, electric
motor, Chapter 24
515
-
25.1
Objectives
· explain how a changing magnetic
field produces an electric current.
· define EMF; show an ability to
calculate EMF of wires moving in a
magnetic field and know the
limitations of the equation.
· explain how an electric generator
works and how it differs from a
motor.
· explain the difference between
peak and effective voltage and
current; use both in solving
problems.
To induce current, there must be
relative motion of a wire and the
magnetic field.
F. Y. I.
Michael Faraday left school at
age 14 to become an apprentice
to a bookbinder. He read most of
the books in the shop. Joseph
Henry left school at age 13 to
work for a watch maker. Later in
life, Faraday became director of
the Royal Institution in London,
founded by the American Benjamin Thomson (Count Rumford).
Henry became the director of the
Smithsonian Institution in Washington DC, founded by the Englishman James Smithson.
FIGURE 25-1. When a wire is moved
in a magnetic field, an electric
current flows in the wire, but only
while the wire is moving. The
direction of the current flow depends
on the direction the wire is moving
through the field. The arrows
indicate the direction of conventional
current flow.
516
Electromagnetic
Induction
..........................................
CREATING ELECTRIC CURRENT
FROM CHANGING MAGNETIC
FIELDS
I
n 1822, Michael Faraday wrote a goal in his notebook: "Convert
Magnetism into Electricity." After nearly ten years of unsuccessful experiments, he was able to show that a changing magnetic field could
produce electric current. In the same year, Joseph Henry, an American
high school teacher, made the same discovery.
Faraday's Discovery
Oersted had discovered that an electric current produces a magnetic
field. Faraday tried all combinations of field and wire without success
until he found he could induce current by moving the wire in a magnetic field. Figure 25-1 shows one of Faraday's experiments. A wire
loop that is part of a closed circuit is placed in a magnetic field. If the
wire moves up through the field, the current moves in one direction.
When the wire moves down through the field, the current moves in the
opposite direction. If the wire is held stationary or is moved parallel to
the field, no current flows. An electric current is generated in a wire
only when the wire cuts magnetic field lines.
To generate current, either the conductor can move through a magnetic field, or the magnetic field can move past a conductor. It is the
relative motion between the wire and the magnetic field that produces
the current. The process of generating a current through a circuit in this
way is called electromagnetic induction.
In what direction does the current move? To find the force on the
charges in the wire, use the third right-hand rule described in Chapter
24. Hold your right hand so that your thumb points in the direction in
which the wire is moving and your fingers point in the direction of the
magnetic field. The palm of your hand will point in the direction of the
conventional (positive) current flow, Figure 25-2.
Wire
moving up
(
Current
FIGURE 25-2. The right-hand rule
can be used to find the direction of
the forces on the charges in a
conductor that is moving in a
magnetic field.
B
F
s
~/IB_V_
N
Motion of the wire
v
••
Electromotive Force
When we studied electric circuits, we learned that a charge pump is
needed to produce a continuous current flow. The potential increase,
or voltage, given to the charges by the pump is called the electromotive
force, or EMF. Electromotive
force, however, is not a force; it is a potential increase and is measured in volts. Thus the term EMF is misleading. Like many other historical terms still in use, it originated before
electricity was well understood.
What creates the increase in potential that can cause an induced current to flow? When a wire is moved through a magnetic field, a force
acts on the charges and they move in the direction of the force. Work
is done on the charges. Their electrical potential energy, and thus their
potential, is increased. The increase in potential is called the induced
EMF. The EMF, measured in volts, depends on the magnetic field
strength, B, the length of the wire in the magnetic field, L, and the
velocity of the wire in the field, v. If B, v, and the direction of the length
of the wire are mutually perpendicular,
I EMF
=
Electromotive
volts.
force is measured
The EMF depends on magnetic field
strength, the length of the Wire, and its
velocity perpendicular to the field.
Coil
s
BLv·1
If the moving wire is part of a closed circuit, the EMF will cause a
current to flow in the circuit in the direction of the EMF.
If a wire moves through a magnetic field at an angle to the field, only
the component of the wire's velocity that is perpendicular to the direction of the field generates EMF.
A microphone is a simple application that depends on an induced
EMF. The "dynamic" microphone is similar in construction to a loudspeaker. The microphone in Figure 25-3 has a diaphragm attached to
a coil of wire that is free to move in a magnetic field. Sound waves
vibrate the diaphragm, which moves the coil in the magnetic field. The
motion of the coil, in turn, induces an EMF across the ends of the coil.
The voltage generated is small, typically 10-3 V, but it can be increased, or amplified, by electronic devices.
25.1
Creating
Electric
Current
Magnet
(also serves as
the supporting
frame)
.~
Connectlng
Air vent
wires
FIGURE 25-3. Schematic of a
moving coil microphone. The
aluminum diaphragm is connected to
a coil in a magnetic field. When
sound waves vibrate the diaphragm,
the coil moves in the magnetic field,
generating a current proportional to
the sound wave.
from Changing
Magnetic
Fields
517
POCKET
LAB
MAKING CURRENTS
Hook the ends of a 1 m length
of wire to the binding posts of a
galvanometer (or microammeter). Make several overlapping
loops in the wire. Watch the
readings on the wire as you
move a pair of neodymiummagnets (or a strong horseshoe
magnet) near the loops. Record
your observations.What can you
do to increase the current? Replace the 1 m length of wire with
a pre-formed coil and see how
much current you can produce.
Describeyour results.
Example Problem
Induced EMF
A straight wire 0.20 m long moves perpendicularly through a magnetic field of magnetic induction 8.0 x 10-2 T at a speed of
7.0 m/s. a. What EMF is induced in the wire? b. The wire is part of a
circuit that has a resistance of 0.50 D. What current flows in the
circuit?
Given: L
=
8
=
0.20 m
8.0 X 10-2 T
v = 7.0 mls
R = 0.500
Unknowns: a. EMF b. I
Basicequations: a. EMF = 8Lv
b. I = VIR
Solution: a. EMF
=
=
EMF
b. I
= 8Lv
(8.0 x 10-2 T)(0.20 m)(7.0 m/s)
(8.0 x 10-2 N/A·m)(0.20
m)(7.0 m/s)
= 0.11 (_N_)(m)(m)
A'm
= ~ =
R
0.11 V
0.500
s
= 0.11 W = 0.11 V
A
0.22 A
Practice Problems
1. A straight wire, 0.5 m long, is moved straight up through a O.4-T
magnetic field pointed in the horizontal direction at a speed of
20 m/s.
a. What EMF is induced in the wire?
b. The wire is part of a circuit of total resistance of 6.0 D. What is
the current in the circuit?
2. A straight wire, 25 m long, is mounted on an airplane flying at
125 m/s. The wire moves perpendicularly through Earth's magnetic
field (8 = 5.0 x 10-5 T). What EMF is induced in the wire?
3. A permanent horseshoe magnet is mounted so that the magnetic field
lines are vertical. If a student passesa straight wire between the poles
and pulls it toward herself, the current flow through the wire is from
right to left. Which is the N-pole of the magnet?
~ 4. A straight wire, 30.0 m long, moves at 2.0 mls perpendicularly
through a 1.0-T magnetic field.
a. What EMF is induced in the wire?
b. The total resistance of the circuit of which the wire is a part is
15.0 D. What is the current?
Electric Generators
The electric generator, invented by Michael Faraday, converts mechanical energy to electric energy. An electric generator consists of a
number of wire loops placed in a strong magnetic field. The wire is
wound around an iron form to increase the strength of the field. The
iron and wires are called the armature, similar to that of an electric
motor.
518
Electromagnetic Induction
FIGURE 25-4.
2
N
4
a
An electric current is
generated in a wire loop as the loop
rotates (a). The cross-sectional view
(b) shows the position of the loop
when maximum current is generated.
The numbered positions correspond
to the numbered points on the graph
in Figure 25-5.
1=0
b
The armature is mounted so that it can rotate freely in the field. As
the armature turns, the wire loops cut through the magnetic field lines,
inducing an EMF. The EMF, commonly called the voltage, developed
by the generator depends on the magnetic induction, B, the length of
wire rotating in the field, L, and v, the speed of the loops perpendicular
to the magnetic field. Increasing the number of loops in the armature
increases the wire length, L, increasing the induced EMF.
When a generator is connected in a closed circuit, current flows that
is proportional to the induced EMF. Figure 25-4 shows a single loop
generator. The direction of the induced current can be found from the
third right-hand rule. As the loop rotates, the strength and direction of
the current change. The current is greatest when the component of the
loop's velocity perpendicular to the field is largest. This occurs when
the motion of the loop is perpendicular to the magnetic field-when
the
loop is in the horizontal position. As the loop rotates from the horizontal
to the vertical position, it moves through the magnetic field lines at an
ever-increasing angle and current decreases. When the loop is in the
vertical position, the wire segments move parallel to the field and the
current is zero. As the loop continues to turn, the segment that was
moving up begins to move down, reversing the direction of the current
in the loop. This change in direction takes place each time the loop
turns through 180°. The current changes smoothly from zero to some
maximum value and back to zero during each half-turn of the loop.
Then it reverses direction. The graph of current versus time is shown in
Figure 25-5.
The strength and direction of the
induced current change as the
armature rotates.
FIGURE 25-5. This graph shows the
variation of current with time as the
loop in Figure 25-4b rotates. The
variation of EMF with time is given
by a similar graph.
25.1
Creating Electric Current from Changing Magnetic Fields
519
FIGURE 25-6. Alternating current
generators transmit current to an
external circuit by way of a brushslip-ring arrangement (a). The
alternating current varies with
time (b).
i:
o
JL---\.---I---\--f-
-/max
Brushes
a
b
Generators and motors are almost identical in construction but convert energy in opposite directions. A generator converts mechanical energy to electric energy while a motor converts electric energy to mechanical energy. In a generator, mechanical energy turns an armature
in a magnetic field. The induced voltage causes current to flow. In a
motor, a voltage is placed across an armature coil in a magnetic field.
The voltage causes current to flow in the coil and the armature turns,
producing mechanical energy from electrical energy.
The direction of current produced by
generators in electric utility companies
alternates from one direction to the
other and back 60 times each second.
HELP WANTED
ELECTRICIAN
Electrical contractor needs electricians who have successfully completed a 5-year apprenticeship program conducted by a union or
professional builder'S association.
You must be a high school grad, be
in good physical condition, have excellent dexterity and color vision, and
be willing to work when and where
there is work. You will do all aspects
of the job, including reading blueprints, dealing with all types of wires,
conduits, and equipment. Safety and
quality work must be your highest
priori'
.
.
ct:
nternational Brotherhood of Electrical Workers, 1125 15th Street,
.w., Washington, DC 20005
520
Electromagnetic Induction
Alternating Current Generator
An energy source turns the armature of a generator in a magnetic field
at a fixed number of revolutions per second. In the United States, electric utilities use a 60-Hz frequency. The current goes from one direction, to the other, and back to the first, 60 times a second.
Figure 25-6 shows how an alternating current in an armature is transmitted to the rest of the circuit. The brush-slip-ring arrangement permits
the armature to turn freely while still allowing the current to pass into
the external circuit. As the armature turns, the alternating current varies
between some maximum value and zero. If the armature is turning rapidly, the light in the circuit does not appear to dim or brighten because
the changes are too fast for the eye to detect.
The power produced by a generator is the product of the current and
the voltage. Power is always positive because either / and V are both
positive or both negative. Because / and V vary, however, the power
associated with an alternating current varies and its average value is less
than the power suppl ied by a direct current with the same /max and VrnaxIn fact, the average AC power is
PAC
=1/2P
ACmax
= 1/2PDC'
It is common to describe alternating currents and voltages in terms of
effective currents and voltages. Recall that P = /2R. Thus, the average
AC power can be written in terms of the effective current,
PAC
= PeffR.
PAC
=
PeffR
=
1i2PDc
1i2(p maxlR
F. Y. I.
Jeff = y1/2J2max
Jeff = 0.707Jmax
Veff = 0.707Vmax
The voltage generally available at wall outlets is described as 120 V,
where 120 is the magnitude of the effective voltage, not the maximum
voltage.
Example Problem
Effective Voltage and Effective Current
An AC generator develops a maximum voltage of 34 V and delivers
a maximum current of 0.17 A to a circuit. a. What is the effective
voltage of the generator? b. What effective current is delivered to the
circuit? c. What is the resistance of the circuit?
Given: Vmax= 34 V
Jmax= 0.17 A
In an incandescent bulb, the
filament temperature cannot
change fast enough to keep up
with the changing voltage. However, a fluorescent lamp can.
Look at the blades of a fan in the
light of a fluorescent lamp. You
will see blue-looking blades from
the 120-Hz blue flashes of excited mercury vapor. The overall
yellowish light is from the phosphors on the inner surface of the
tube, which emit a more slowly
changing light.
Unknowns: a. Veffb. Jeffc. R
Basic equations: a. Veff = 0.707 Vmax
b. Jefl = 0.707 Jmax
c. R = Vefl
Jefl
Solution: a. Veff = o. 707(V max)
= 0.707(34 V) = 24 V
b. Jeff= 0.707(1max)
= 0.707(0.17 A) = 0.12 A
Veff
24 V
c R = = -= 2000=
•
Jeff
0.12 A
2.0 X 1020
Practice Problems
5. A generator in a power plant develops a maximum voltage of 170 V.
a. What is the effective voltage?
b. A 60-W light bulb is placed across the generator. A maximum
current of 0.70 A flows through the bulb. What effective current
flows through the bulb?
c. What is the resistance of the light bulb when it is working?
6. The effective voltage of a particular AC household outlet is 117 V.
a. What is the maximum voltage across a lamp connected to the
outlet?
b. The effective current through the lamp is 5.5 A. What is the maximum current in the lamp?
7. An AC generator delivers a peak voltage of 425 V.
a. What is the effective voltage in a circuit placed across the generator?
b. The resistance of the circuit is 5.0 x 102 O. What is the effective
current?
~ 8. If the average power dissipated by an electric light is 100 W, what is
the peak power?
25.1
POCKET
LAB
MOTOR AND GENERATOR
Make a series circuit with a
Genecon (or efficient DC motor),
a miniature lamp, and ammeter.
Rotate the handle (or motor
shaft) to try to light the lamp. Describe your results. Predict what
might happen if you connect
your Genecon to the Genecon
from another lab group and
crank yours. Try it. Describe
what happens. Can more than
two be connected?
Creating Electric Current from Changing Magnetic Fields
521
PHYSICSLABo
: The Pick Up
Purpose
To investigate changing magnetic fields with a telephone pickup coil.
Materials
· telephone pickup coil (Radio Shack #44-533
similar)
· mini audio amplifier (Radio Shack #277-1008
similar)
· strong permanent magnet
· iron or air core solenoid coil
· 9-V battery
· low-voltage AC power supply
· battery-powered car
· 1 meter of string
· masking tape
or
or
Procedure
1. Put the 9-V battery into the amplifier and plug
in the telephone pickup coil.
2. Place the strong permanent magnet on the table.
Slowly bring the pickup coil near the magnet.
3. Use the suction cup to stick the pickup coil on
the table. Attach the magnet to a string so that it
hangs just above the pickup coil.
4. Swing the magnet like a pendulum. Twist the
string so that as it untwists it will spin the magnet.
5. Attach the low-voltage AC power supply to the
solenoid coil. Turn the power supply to about
2-3 V.
6. Hold the pickup coil near the solenoid coil to
find where the sound is loudest. Listen to the
amplifier as the pickup coil is rotated.
Observations and Data
1. When does the pickup coil and amplifier make
a sound in Procedure 2-4?
2. Describe the sound as the pickup coil and amplifier approaches the solenoid coil.
Analysis
1. The pickup coil produces no signal when it is
held stationary near the permanent magnet. Explain this.
2. Explain why rotating the pickup coil (Procedure
6) changes the loudness of the signal.
3. Predict the sound that you would hear if the solenoid coil was connected to a battery. Explain
your prediction.
Mini audio
amplifier
Applications
Pickup coil
522
Electromagnetic Induction
1. Turn the battery-powered car on low speed and
bring the pickup coil near to "hear" the changing magnetic fields. Predict how the sound will
be different when the battery-powered car is on
high speed. Try it. What happened? Why?
........................
CONCEPT REVIEW
1.1 Could you make a generator by mounting permanent magnets on
the rotating shaft and having the coil stationary? Explain.
1.2 A bike generator lights the headlamp. What is the source of the
energy for the bulb when the rider travels along a flat road?
1.3 Consider the microphone shown in Figure 25-3. When the diaphragm is pushed in, what is the direction of the current in the coil?
1.4 Critical Thinking: A student asks: "Why doesn't AC dissipate any
power? The energy going into the lamp when the current is positive
is removed when the current is negative. The net is zero." Explain
why this argument is wrong .
25.2
.......................................
EFFECTS OF CHANGING
MAGNETIC FIELDS: INDUCED
Objectives
· state Lenz's law; explain back-EMF
and how it affects the operation of
motors and generators.
· explain the nature of selfinductance and its effects in
circuits.
· describe the transformer; explain
the connection of turns ratio to
voltage ratio; solve transformer
EMF
na generator, current flows when the armature turns through a magnetic field. We learned in Chapter 24 that when current flows through
a wire in a magnetic field, a force is exerted on the wire. Thus, a force
is exerted on the wires in the armature. In a sense, then, a generator is,
at the same time, a motor.
I
problems.
Lenis Law
In what direction is the force on the wires of the armature? The direction of the force on the wires opposes the original motion of the wires.
That is, the force acts to slow down the rotation of the armature. The
direction of the force was first determined in 1834 by H. F. E. Lenz and
is called Lenz's law.
Lenz's law states: The direction of the induced current is such that
According to Lenz's law, the direction of
the induced current is such that the
current's magnetic effects oppose the
changes that produced the current.
the magnetic field resulting from the induced current opposes the
change in the field that caused the induced current. Note that it is the
change in the field and not the field itself that is opposed by the induced
FIGURE 25-7. The magnet
approaching the coil causes an
induced current to flow. Lenz's law
predicts the direction of flow shown.
magnetic effects.
Figure 25-7 is a simple example of how Lenz's law works. The Npole of a magnet is moved toward the right end of a coil. To oppose
the approach of the N-pole, the right end of the coil must also become
N
25.2
s
Effects of Changing Magnetic Fields: Induced EMF
523
POCKET
LAB
SLOW MAGNETS
Lay the 1 m length of copper
tube on the lab table. Try to pull
the copper with a pair of neodymium magnets. Can you feel
any force on the copper? Hold
the tube by one end so that it
hangs straight down. Drop a
small steel marble through the
tube. Use a stopwatch to measure the time needed for the
marble and then for the pair of
magnetsto fall through the tube.
Catch the magnets in your hand.
If they hit the table or floor they
will break. Devise a hypothesis
that would explain the strange
behavior and suggest a method
of testing your hypothesis.
FIGURE 25-8. Sensitive balances
use eddy current damping to control
oscillations of the balance beam (a).
As the metal plate on the end of the
beam moves through the magnetic
field, a current is generated in the
metal. This current, in turn, produces
a magnetic field that opposes the
motion that caused it, and the
motion of the beam is dampened (b).
>
Pivot
524
.;...-~""""
Electromagnetic Induction
an N-pole. In other words, the magnetic field lines must emerge from
the right end of the coil. Use the second right-hand rule you learned in
Chapter 24. You will see that if Lenz's law is correct, the induced current must flow in a counterclockwise direction. Experiments have
shown that this is so. If the magnet is turned so an S-pole approaches
the coil, the induced current will be in a clockwise direction.
If a generator produces only a small current, then the opposing force
on the armature will be small, and the armature will be easy to turn. If
the generator produces a larger current, the force on the larger current
will be larger, and the armature will be more difficult to turn. A generator supplying a large current is producing a large amount of electrical
energy. The opposing force on the armature means that an armature of
mechanical energy must be supplied to the generator to produce the
electrical energy, consistent with the law of conservation of energy.
Lenz's law also applies to motors. When a current-carrying wire
moves in a magnetic field, an EMF is generated. This EMF, called the
back-EMF, is in a direction that opposes the current flow. When a motor
is first turned on, a large current flows because of the low resistance of
the motor. As the motor begins to turn, the motion of the wires across
the magnetic field induces the back-EMF that opposes the current flow.
Therefore, the net current flowing through the motor is reduced. If a
mechanical load is placed on the motor, slowing it down, the backEMF is reduced and more current flows. If the load stops the motor,
current flow can be so high that wires overheat.
The heavy current required when a motor is started can cause voltage
drops across the resistance of the wires that carry current to the motor.
The voltage drop across the wires reduces the voltage across the motor.
If a second device, such as a light bulb, is near the motor in a parallel
circuit with it, the voltage at the bulb will also drop when the motor is
started. The bulb will dim. As the motor picks up speed, the voltage
will rise again and the bulb will brighten.
When the current to the motor is interrupted by turning off a switch
in the circuit or by pulling the motor's plug from a wall outlet, the
sudden change in the magnetic field generates a back-EMF that can be
large enough to cause a spark across the switch or between the plug
and the wall outlet.
A sensitive balance, Figure 25-8, such as the kind used in chemistry
laboratories, uses Lenz's law to stop its oscillation when an object is
placed on the pan. A piece of metal attached to the balance arm is
Wire coil
Wire coil
Wire coil
Wire coil
located between the poles of a horseshoe magnet. When the balance
arm swings, the metal moves through the magnetic field. Currents,
called eddy-currents, are generated in the metal. These currents produce a magnetic field that acts to oppose the motion that caused the
currents. Thus the metal piece is slowed down. The force opposes the
motion of the metal in either direction, but does not act if the metal is
still. Thus it does not change the mass read by the balance. This effect
~
is called "eddy-current damping."
The magnetic field caused by the induced EMF causes the ring in the
chapter-opening photo to float. The coil is driven by AC, so the magnetic field is constantly changing, and this change induces an EMF in
the ring. The resulting ring current produces a magnetic field that opposes the change in the generating field, the ring is pushed away. The
lower ring has been sawed through. There is an EMF generated, but no
current flow, and hence no magnetic field is produced by the ring.
Self-Inductance
Back-EMF
can be explained another way. As Faraday showed, EMF
is induced whenever a wire cuts magnetic field lines. Consider the coil
of wire shown in Figure 25-9. The current through the wire increases
as we move from left to right. Current generates a magnetic field, shown
by magnetic field lines. As the current and magnetic field increase, new
lines are created. As the lines expand, they cut through the coil wires,
generating an EMF to oppose the current changes. This induction of
EMF in a wire carrying changing current is called self-inductance. The
size of the EMF is proportional to the rate at which field lines cut
through the wires. The faster you try to change the current, the larger
the opposing EMF, and the slower the current change. If the current
reaches a steady value, the magnetic field is constant, and the EMF is
zero. When the current is decreased, an EMF is generated that tends to
prevent the reduction in magnetic field and current.
Because of self-inductance, work has to be done to increase the current flowing through the coil. Energy is stored in the magnetic field. This
is similar to the way a charged capacitor stores energy in the electric
field between its plates.
25.2
FIGURE 25-9. As the current in the
coil increases from left to right, the
EMF generated by the current also
increases.
.
Go With The Flow
F. Y. I.
Many modern automobiles
have an electronic ignition system that varies the magnetic
field. An aluminum armature with
4, 6, or 8 protrusions (depending
on the number of spark plugs)
spins. Each protrusion in turn
passes through the magnetic
field, causing it to vary.
Effects of Changing Magnetic Fields: Induced EMF
525
Transformers
POCKET
Inductance between coils is the basis for the operation of a transformer. A transformer is a device used to increase or decrease AC voltages. Transformers are widely used because they change voltages with
essentially no loss of energy.
Self-inductance produces an EMF when current changes in a single
coil. A transformer has two coils, electrically insulated from each other,
but wound around the same iron core. One coil is called the primary
coil. The other coil is called the secondary coil. When the primary coil
is connected to a source of AC voltage, the changing current creates a
varying magnetic field. The varying magnetic field is carried through the
core to the secondary coil. In the secondary coil, the varying field induces a varying EMF. This effect is called mutual inductance.
The EMF induced in the secondary coil, called the secondary voltage,
is proportional to the primary voltage. The secondary voltage also depends on the ratio of turns on the secondary to turns on the primary.
LAB
SLOW MOTOR
Make a series circuit with a
miniature DC motor, an ammeter, and a DC power supply.
Hook up a voltmeter in parallel
across the motor. Adjust the setting on the power supply so that
the motor is running at medium
speed. Make a data table to
show the readings on the ammeter and voltmeter. Predict
what will happen to the readings
on the circuit when you hold the
shaft and keep it from turning.
Try it. Explain the results.
secondary voltage
number of turns on secondary
primary voltage
number of turns on primary
I~;~ z;1
Ns
Vs = -Vp
Np
A transformer uses two coupled coils to
increase or decrease the voltage in an
AC circuit.
If the secondary voltage is larger than the primary voltage, the transformer is called a step-up transformer. If the voltage out of the transformer
is smaller than the voltage put in, then it is called a step-down transformer.
In an ideal transformer, the electric power delivered to the secondary
circuit equals the power supplied to the primary. An ideal transformer
dissipates no power itself. Since P = VI,
Vp Ip
=
v,
Is.
The current that flows in the primary depends on how much current
is required by the secondary circuit.
Is
Ip
FIGURE 25-10. For a transformer,
the ratio of input voltage to output
voltage depends upon the ratio of
the number of turns on the primary
to the number of turns on the
secondary.
Primary
100V
-
lOA
L
~3
-------r-rl
1000W.
I
~
5 turns
20 turns
Core
Electromagnetic
Induction
I
Secondary
200V
400 V
--
__
1000V
2.5A
.
Vp _ Np
v, Ns
Primary
-'I' ---
Step-up transformer
a
526
Secondary
=
lOA
2A
2000W
1000W
2000W
b
Step-down transformer
A step-up transformer increases voltage; the current in the primary circuit is greater than that in the secondary. In a step-down transformer,
the current is greater in the secondary circuit than it is in the primary.
FIGURE25-11. If the input voltage is
connected to the coils on the left,
with the larger number of turns, the
transformer functions as a stepdown transformer. If the input
voltage is connected at the right, it is
a step-up transformer.
Example Problem
Step-Up Transformer
A certain step-up transformer has 2.00 x 102 turns on its primary
coil and 3.00 x 103 turns on its secondary coil. a. The primary coil
is supplied with an alternating current at an effective voltage of
90.0 V. What is the voltage in the secondary circuit? b. The current
flowing in the secondary circuit is 2.00 A. What current flows in the
primary circuit? c. What is the power in the primary circuit? in the
secondary circuit?
Given:
Np = 2.00
Unknowns: a. v, b.
Basicequations:
x 102
3
Ns
Vp
=
=
3.00 X 10
90.0 V
Is
=
2.00 A
v,
a.-=-
v,
b. Vp/p
Ip
c.
P
Ns
Np
=
Vs/s
Solution:
V
N
= -'2 or V = VpNs
Ns
Np
a. -E
v,
(90.0 V)(3.00 x 103) _
3
2.00 X 102
- 1.35 x 10 V
b V
.
c.
I
pp
=
V I or I
ssp
=
Vs/s
Vp
=
(1350 V)(2.00 A) 90.0 V
- 30.0 A
Pp = Vp Ip = (90.0 V)(30.0 A)
r, = v, Is =
(1350 V)(2.00 A)
=
2.70 x 103 W
2.70 x 103 W
Practice Problems
In all problems,
effective
currents
and voltages are indicated.
9. A step-down transformer has 7500 turns on its primary and 125
turns on its secondary. The voltage across the primary is 7200 V.
a. What voltage is across the secondary?
b. The current in the secondary is 36 A. What current flows in the
primary?
10. The secondary of a step-down transformer has 500 turns. The primary has 15 000 turns.
a. The EMF of the primary is 3600 V. What is the EMF of the secondary?
b. The current in the primary is 3.0 A. What current flows in the
secondary?
25.2
F.Y.I.
The transformerswith the largest power rating in the world
changes765 kV to 345 kV. Their
power handlingcapacity is 1 500
OOOW.
Effects of Changing Magnetic Fields: Induced EMF
527
FIGURE 25-12. Transformers are
used to reduce voltages to consumer
levels at the points of use.
HISTORY
CONNECTION
In the late 1800s, there was
much debate in the United
States over the best way to
transmit power from power
plants to consumers. The existing plants transmitted direct current (DC), but DC had serious
limitations. A key decision was
made to use alternating current
(AC) in the new hydroelectric
power plant at Niagara Falls.
With the first successful transmission of AC to Buffalo, New
York in 1896, the Niagara Falls
plant paved the way for the development of AC power plants
across the country. It literally
provided the spark for the rapid
growth of United States cities
and industries that followed.
528
Electromagnetic
Induction
11. An ideal step-up transformer's primary circuit has 500 turns. Its secondary circuit has 15 000 turns. The primary is connected to an AC
generator having an EMF of 120 V.
a. Calculate the EMF of the secondary.
b. Find the current in the primary if the current in the secondary is
3.0 A.
c. What power is drawn by the primary? What power is supplied
by the secondary?
~ 12. A step-up transformer has 300 turns on its primary and 90 000
4
(9.000 X 10 ) turns on its secondary. The EMF of the generator to
which the primary is attached is 60.0 V.
a. What is the EMF in the secondary?
b. The current flowing in the secondary is 0.50 A. What current
flows in the primary?
As was discussed in Chapter 23, long-distance transmission of electric
energy is economical only if low currents and very high voltages are
used. Step-up transformers are used at power sources to develop voltages as high as 480 000 V. The high voltage reduces the current flow
required in the transmission lines, keeping /2R losses low. When the
energy reaches the consumer, step-down transformers provide appropriately low voltages for consumer use.
There are many other important uses of transformers. Television picture tubes require up to 25 kV, developed by a transformer within the
set. The spark or ignition coil in an automobile is a transformer designed
to step up the 12 V from the battery to thousands of volts. The "points"
interrupt the DC current from the battery to produce the changing magnetic field needed to induce EMF in the secondary coil. Some arc welders require currents of 104 A. Large step-down transformers are used to
provide these currents, which can heat metals to 3000°C or more.
CONCEPT REVIEW
2.1 You hang a coil of wire with its ends joined so it can swing easily.
If you now plunge a magnet into the coil, the coil will swing.
Which way will it swing with respect to the magnet and why?
2.2 If you unplug a running vacuum cleaner from the wall outlet, you
are much more likely to see a spark than if you unplug a lighted
lamp from the wall. Why?
2.3 Frequently, transformer windings that have only a few turns are
made of very thick (low-resistance) wire, while those with many
turns are made of thin wire. Why is this true?
2.4 Critical Thinking; Would permanent magnets make good transformer cores? Explain.
P
hysics and
society
WEAK ELECTROMAGNETIC
FIELDS-A HEALTH
CONCERN?
A
lternating currents, such as
those in household wiring,
produce electric and magnetic
fields. The very low AC frequency is call Extremely Low
Frequency, or ELF. The many
sources of ELF electric and
magnetic fields include power
lines, home wiring, electric
clocks, electric blankets, televisions and computer terminals.
Twenty years ago, most scientists would have claimed that
very weak electric and magnetic
fields produced by ELFs could
not affect living systems. Electric
fields do exert forces on the ions
in cellular fluids, and changing
magnetic fields can induce such
electric fields. Fields normally
present in cells, however, are
much larger than fields induced
by ELFs, and, unlike ultraviolet
radiation,
ELFs can't break
chemical bonds.
Recently, however, experiments have shown that cells are
sensitive to even very weak ELF
fields. They can affect flow of
ions across cell membranes,
synthesis of DNA, and the response of cells to hormones.
Abnormal
development
of
chick embryos has been seen.
The experimental results, however, are very complex. Some
effects of ELFs occur only at
certain frequencies or amplitudes. Others occur only if the
fields are turned on or off
abruptly. Finally, for most environmental health hazards the
larger the exposure, or dose,
the larger the effect. For ELFs,
there is no clear way to define
or measure dose.
Some action has already
been taken to reduce ELFfields.
Electric
blankets
producing
much lower magnetic fields are
now sold. Several computer
manufacturers
sell terminals
that produce smaller fields.
Without knowing how to measure dose, however, it is not
clear if such changes are
enough to solve the problem.
Is there an association between cancer and exposure to
ELF? Some studies found small
increases in leukemia, breast
cancer, and brain cancer. Studies of users of electric blankets
have shown no effects on men,
but increases in cancers and
brain tumors in children whose
mothers slept under electric
blankets while pregnant. Studies to find the causes will take
years and may not have conclusive results. In the meantime,
what should be done?
DEVELOPING A
VIEWPOINT
Read articles about ELFs and
come to class ready to discuss
the following questions.
1. What do you think should be
done? Should no action be
taken until there is conclusive
evidence of health hazards of
ELFs?Or, is there enough reason for concern to take measures to limit exposure to ELFs?
2. Suppose a study finds many
cancer cases among people
who live near power lines.
Would this prove that ELF fields
from power lines cause cancer?
3. What steps could you take to
reduce exposure to ELF?
4. What could utility companies do to reduce ELF fields?
SUGGESTED READINGS
Noland, David. "Power Play."
10 (12), 62-68, December, 1989.
Pool, Robert. "Electromagnetic
Fields: The Biological
Evidence." Science 249, 13781381, September 21, 1990.
Raloff, Janet. "EPA Suspects ELF
Fields Can Cause Cancer." Science
News
137, 404-405,
June 30, 1990.
Discover
25.2
Effects of Changing Magnetic Fields: Induced EMF
529
CHAPTER
25 REVIEW····························
------------~~=---~~~~~~~~~
SUMMARY
25.1 Creating Electric
Magnetic Fields
KEY TERMS
Current from Changing
· Michael Faraday and Joseph Henry discovered
that if a wire moves through a magnetic field, an
electric current can be induced in the wire.
· The direction that current flows in a wire moving
through a magnetic field depends upon the direction of the motion of the wire and the direction of the magnetic field.
· The current produced depends upon the angle
between the velocity of the wire and the magnetic field. Maximum current occurs when the
wire is moving at right angles to the field.
· Electromotive force, EMF, is the increased potential of charges in the moving wire. EMF is
measured in volts.
· The EMF in a straight length of wire moving
through a uniform magnetic field is the product
of the magnetic induction, B, the length of the
wire, L, and the component of the velocity of the
moving wire, v, perpendicular to the field.
· An electric generator consists of a number of
wire loops placed in a magnetic field. Because
each side of the coil moves alternately up and
down through the field, the current alternates direction in the loops. The generator develops alternating voltage and current.
· A generator and a motor are similar devices. A
generator converts mechanical energy to electric
energy; a motor converts electric energy to mechanical energy.
25.2 Effects of Changing
Induced EMF
MagnetiC Fields:
· Lenz's law states: An induced current is always
produced in a direction such that the magnetic
field resulting from the induced current opposes
the change in the field that is causing the induced current.
· A transformer has two coils wound about the
same core. An AC current through the primary
coil induces an alternating EMF in the secondary
coil. The voltages in alternating current circuits
may be increased or decreased by transformers.
530
Electromagnetic Induction
electromagnetic induction
electromotive force
electric generator
Lenz's law
self-inductance
transformer
primary coil
secondary coil
mutual inductance
step-up transformer
step-down
transformer
REVIEWING CONCEPTS
1. How are Oersted's and Faraday's results similar? How are they different?
2. Matt has a coil of wire and a bar magnet. Describe how Matt could use them to generate
an electric current.
3. What does EMF stand for? Why is the name
inaccurate?
4. What is the armature of an electric generator?
5. Why is iron used in an armature?
6. What is the difference between a generator
and a motor?
7. List the major parts of an AC generator.
8. Why is the effective value of an AC current
less than the maximum value?
9. Water trapped behind Hoover Dam turns turbines that rotate generators. List the forms of
energy between the stored water and the final
electricity produced.
10. State Lenz's law.
11. What produces the back-EMF of an electric
motor?
12. Why is there no spark when you close a
switch, putting current through an inductor,
but there is a spark when you open the
switch?
13. Why is the self-inductance of a coil a major
factor when the coil is in an AC circuit but a
minor factor when the coil is in a DC circuit?
14. Explain why the word "change" appears so
often in this chapter.
15. Upon what does the ratio of the EMF in the
primary of a transformer to the EMF in the
secondary of the transformer depend?
APPLYING CONCEPTS
1. What is the difference between the current
generated in a wire when the wire is moved
up through a horizontal magnetic field and the
current generated when the wire is moved
down through the same field?
2. Substitute units to show that the unit of BLv is
volts.
3. If the strength of a magnetic field is fixed, in
what three ways can you vary the size of the
EMF you can generate?
4. When a wire is moved through a magnetic
field, resistance of the closed circuit affects
a. current only.
c. both.
b. EMF only.
d. neither.
5. As Logan slows his bike, what happens to the
EMF produced by his bike's generator?
6. A hand-cranked generator is dropped, weakening the permanent magnet. How does this
affect the speed at which the generator must
be cranked to keep the same EMF?
7. The direction of AC voltage changes 120
times each second. Does that mean a device
connected to an AC voltage alternately delivers and accepts energy?
8. A wire segment is moved horizontally between the poles of a magnet as shown in Figure 25-13. What is the direction of the induced current?
12.
13.
14.
15.
16.
present AC system. What are the reasons the
Westinghouse system was adopted?
A transformer
is connected to a battery
through a switch. The secondary circuit contains a light bulb. Which of these statements
best describes when the lamp will be lighted?
a. as long as the switch is closed
b. only the moment the switch is closed
c. only the moment the switch is opened
Explain.
An inventor claims that a very efficient transformer will step up power as well as voltage.
Should we believe this? Explain.
Suppose a magnetic field is directed vertically
downward. You move a wire at constant
speed, first horizontally, then downward at
45°, then directly down.
a. Compare the induced EMF for the three
motions.
b. Explain the variations in voltage.
The direction of Earth's magnetic field in the
northern hemisphere is downward and to the
north. If an east-west wire moves from north
to south, in which direction does the current
flow?
Steve is moving a loop of copper wire down
through a magnetic field B, as shown in Figure 25-16.
a. Will the induced current move to the right
or left in the wire segment in the diagram?
b. As soon as the wire is moved in the field,
a current appears in it. Thus, the wire segment is a current-carrying wire located in a
magnetic field. A force must act on the
wire. What will be the direction of the force
acting on the wire due to the induced current?
FIGURE 25-13. Use with Applying
Concept S.
9. M.artha makes an electromagnet by winding
wire around a large nail. If she connects the
magnet to a battery, is the current larger just
after she makes the connection or several
tenths of seconds after the connection is
made? Or is it always the same? Explain.
10. A wire segment is moving downward through
the poles of a magnet as shown in Figure 2514. What is the direction of the induced current?
11. Thomas Edison proposed distributing electrical energy using constant voltages (DC).
George Westinghouse proposed using the
Down
FIGURE 25-14. Use with Applying
Concepts 10 and 16.
17. Steve, a physics instructor, drops a magnet
through a copper pipe, Figure 25-15. The
magnet falls very slowly and the class concludes that there must be some force opposing gravity.
Chapter 25 Review
531
a. What is the direction of the current induced
in the pipe by the falling magnet if the
S-pole is toward the bottom?
b. The induced current produces a magnetic
field. What is the direction of the field?
c. How does this field reduce the acceleration
of the falling magnet?
FIGURE 25-15. Use with Applying
Concepts 17.
18. Why is a generator more difficult to rotate
when it is connected to a circuit and supplying
current than it is when it is standing alone?
PROBLEMS
25.1 Creating Electric
Magnetic Fields
Current
From Changing
1. A wire segment, 31 m long, moves straight up
through a 4.0 x 1O-2-T magnetic field at a
speed of 15.0 m/s. What EMF is induced in
the wire?
2. A wire, 20.0 m long, moves at 4.0 m/s perpendicularly through a 0.50-T magnetic field.
What EMF is induced in the wire?
FIGURE 25-16. Use with Problem 2.
3. An airplane traveling at 950 km/h passes over
a region where Earth's magnetic field is 4.5 x
10-5 T and is nearly vertical. What voltage is
induced between the plane's wing tips, which
are 75 m apart?
532
Electromagnetic Induction
4. A straight wire, 0.75 m long, moves upward
through a horizontal 0.30- T magnetic field at
a speed of 16 m/s.
a. What EMF is induced in the wire?
b. The wire is a part of a circuit with a total
resistance of 11 D. What current flows in
the circuit?
~
5. A 40-cm wire is moved perpendicularly
through a magnetic field of 0.32 T with a velocity of 1.3 m/s. If this wire is connected into
a circuit of 10-D resistance, how much current
is flowing?
~
6. Jennifer connects both ends of a copper wire,
total resistance 0.10 D, to the terminals of a
galvanometer. The galvanometer has a resistance of 875 D. Jennifer then moves a
10.0-cm segment of the wire upward at
1.0 m/s through a 2.0 x 1O-2-T magnetic
field. What current will the galvanometer indicate?
~
7. The direction of a 0.045-T magnetic field is
60° above the horizontal. A wire, 2.5 m long,
moves horizontally at 2.4 m/s.
a. What is the vertical component of the magnetic field?
b. What EMF is induced in the wire?
8. An EMF of 0.0020 V
wire when it is moving
a uniform magnetic
4.0 m/s. What is the
field?
is induced in a 10-cm
perpendicularly across
field at a speed of
size of the magnetic
9. At what speed would a 0.2-m length of wire
have to move across a 2.5- T magnetic field to
induce an EMF of 10 V?
10. An AC generator develops a maximum EMF
of 565 V. What effective EMF does the generator deliver to an external circuit?
11. An AC generator develops a maximum voltage of 150 V. It delivers a maximum current
of 30.0 A to an external circuit.
a. What is the effective voltage of the generator?
b. What effective current does it deliver to the
external circuit?
c. What is the effective power dissipated in
the circuit?
12. An electric stove is connected to an AC
source with effective voltage of 240 V.
a. Find the maximum voltage across one of
the stove's elements when it is operating?
b. The resistance of the operating element is
11 n. What effective current flows through
it?
~ 13. A generator at Hoover Dam can supply
375 MW (375 x 106 W) of electrical power.
Assume that the turbine and generator are
85% efficient.
a. Find the rate which falling water must supply energy to the turbine.
b. The energy of the water comes from a
change in potential energy, mgh. What is
the needed change in potential energy
each second?
c. If the water falls 22 m, what is the mass of
the water that must pass through the turbine each second to supply this power?
25.2 Effects of Changing Magnetic Fields:
Induced EMF
14. The primary of a transformer has 150 turns. It
is connected to a 120-V source. Calculate the
number of turns on the secondary needed to
supply these voltages.
a. 625 V
b. 35 V
c. 6.0 V
15. A step-up transformer has 80 turns on its primary. It has 1200 turns on its secondary. The
primary is supplied with an alternating current
at 120 V.
a. What voltage is across the secondary?
b. The current in the secondary is 2.0 A.
What current flows in the primary circuit?
c. What is the power input and output of the
transformer?
16. A portable computer requires an effective
voltage of 9.0 volts from the 120 -V line.
a. If the primary of the transformer has 475
turns, how many does the secondary
have?
b. A 125-mA current flows through the computer. What current flows through the
transformer's primary?
17. In a hydroelectric plant, electricity is generated at 1200 V. It is transmitted at 240 000 V.
a. What is the ratio of the turns on the primary to the turns on the secondary of a
transformer connected to one of the generators?
b. One of the plant generators can deliver
40.0 A to the primary of its transformer.
What current is flowing in the secondary?
18. A hair dryer uses 10 A at 120 V. It is used
with a transformer in England, where the line
voltage is 240 V.
a. What should be the ratio of the turns of the
transformer?
b. What current will it draw from the 240-V
line?
19. A step-up transformer is connected to a generator that is delivering 125 V and 95 A. The
ratio of the turns on the secondary to the
turns on the primary is 1000 to 1.
a. What voltage is across the secondary?
b. What current flows in the secondary?
~ 20. A 150-W transformer has an input voltage of
9.0 V and an output current of 5.0 A.
a. Is this a step-up or step-down transformer?
b. What is the ratio of output voltage to input
voltage?
~ 21. A transformer has input voltage and current of
12 V and 3.0 A respectively, and an output
current of 0.75 A. If there are 1200 turns on
the secondary side of the transformer, how
many turns are on the primary side?
~ 22. Scott connects a transformer to a 24-V
source and measures 8.0 V at the secondary.
If the primary and secondary were reversed,
what would the new output voltage be?
USING LAB SKILLS
1. After doinq the Pocket Lab on page 518, predict what will happen if the magnet is kept stationary and the coil moves. Try it. What happens if the coil and magnet move together? Try
it.
THINKING PHYSIC-LY
1. A bike's headlamp is powered by a generator
that rubs against a wheel. Why is it harder to
pedal when the generator is lighting the lamp?
2. Suppose an "anti-Lenz's
law" existed that
meant a force was exerted to increase the
change in magnetic field. Thus, when more
electrical energy was demanded from a generator, the force needed to turn it would be reduced. What conservation law would be violated by this new "law"? Explain.
Chapter 25 Review
533