Physics notes for references for references 2

37 Electromagnetic Induction
Magnetism can produce
electric current, and
electric current can
produce magnetism.

In 1831, two physicists,
Michael Faraday in
England and Joseph Henry
in the United States,
independently discovered
that magnetism could
produce an electric current
in a wire. Their discovery
was to change the world
by making electricity so
commonplace that it would
power industries by day
and light up cities by
night.

Electric current can be produced in a wire by simply
moving a magnet into or out of a wire coil.
37.1 Electromagnetic Induction

No battery or other voltage
source was needed to produce a
current—only the motion of a
magnet in a coil or wire loop.
Voltage was induced by the
relative motion of a wire with
respect to a magnetic field.

The production of voltage depends only on the relative motion
of the conductor with respect to the magnetic field.
Voltage is induced whether the magnetic field moves past a
conductor, or the conductor moves through a magnetic field.
The results are the same for the same relative motion.

The amount of voltage induced depends on how quickly the
magnetic field lines are traversed by the wire.
• Very slow motion produces hardly any voltage at all.
• Quick motion induces a greater voltage.
Increasing the number of loops of wire that move in a
magnetic field increases the induced voltage and the current
in the wire.
Pushing a magnet into twice as many loops will induce twice
as much voltage.

Twice as many loops as another means twice as much
voltage is induced. For a coil with three times as many loops,
three times as much voltage is induced.

We don’t get something
(energy) for nothing by simply
increasing the number of loops
in a coil of wire.
Work is done because the
induced current in the loop
creates a magnetic field that
repels the approaching magnet.
If you try to push a magnet into
a coil with more loops, it
requires even more work.

Work must be done to move the magnet.
a.Current induced in the loop produces a magnetic field
(the imaginary yellow bar magnet), which repels the bar
magnet.

Work must be done to move the magnet.
a.Current induced in the loop produces a magnetic field
(the imaginary yellow bar magnet), which repels the bar
magnet.
b.When the bar magnet is pulled away, the induced
current is in the opposite direction and a magnetic field
attracts the bar magnet.

The law of energy conservation applies here.
The force that you exert on the magnet multiplied by the
distance that you move the magnet is your input work.
This work is equal to the energy expended (or possibly
stored) in the circuit to which the coil is connected.

If the coil is connected to a resistor, more induced voltage in
the coil means more current through the resistor.
That means more energy expenditure.
Inducing voltage by changing the magnetic field around a
conductor is electromagnetic induction.

How can you create a current using a
wire and a magnet?

Faraday’s law states that the induced voltage in
a coil is proportional to the product of the
number of loops, the cross-sectional area of
each loop, and the rate at which the magnetic
field changes within those loops.
37.2 Faraday’s Law

Faraday’s law describes the relationship between
induced voltage and rate of change of a magnetic field:
The induced voltage in a coil is proportional to the product
of the number of loops, the cross-sectional area of each
loop, and the rate at which the magnetic field changes
within those loops.

The current produced by electromagnetic induction
depends upon
• the induced voltage,
• the resistance of the coil, and the circuit to
which it is connected.
For example, you can plunge a magnet in and out of
a closed rubber loop and in and out of a closed loop
of copper.
The voltage induced in each is the same but the
current is quite different—a lot in the copper but
almost none in the rubber.

think!
If you push a magnet into a coil connected to a resistor you’ll
feel a resistance to your push. For the same pushing speed,
why is this resistance greater in a coil with more loops?

think!
If you push a magnet into a coil connected to a resistor you’ll
feel a resistance to your push. For the same pushing speed,
why is this resistance greater in a coil with more loops?
Answer:
More work is required because more voltage is induced, producing more
current in the resistor and more energy transfer. When the magnetic fields
of two magnets overlap, the two magnets are either forced together or
forced apart. When one of the fields is induced by motion of the other, the
polarity of the fields is always such as to force the magnets apart. Inducing
more current in more coils increases the induced magnetic field and the
resistive force.

What does Faraday’s law state?

Whereas a motor converts electrical energy into
mechanical energy, a generator converts
mechanical energy into electrical energy.
37.3 Generators and Alternating Current

A current can be generated by plunging a magnet into and out
of a coil of wire.
• As the magnet enters, the magnetic field strength inside
the coil increases and induced voltage in the coil is
directed one way.
• As the magnet leaves, the magnetic field strength
diminishes and voltage is induced in the
opposite direction.
• Greater frequency of field change induces
greater voltage.
• The frequency of the alternating voltage is the frequency
of the changing magnetic field within the loop.

It is more practical to move the coil instead of moving the
magnet, by rotating the coil in a stationary magnetic field.
A machine that produces electric current by rotating a coil
within a stationary magnetic field is called a generator.
A generator is essentially the opposite of a motor, converting
mechanical energy into electrical energy.

Simple Generators
Starting perpendicular to the field, the loop has the largest
number of lines inside.
As it rotates, the loop encircles fewer of the field lines until it
lies along the field lines, when it encloses none at all.
As rotation continues, it encloses more field lines, reaching a
maximum when it has made a half revolution.
The magnetic field inside the loop changes in cyclic fashion.

As the loop rotates, the magnitude and direction of the induced
voltage (and current) change. One complete rotation of the
loop produces one complete cycle in voltage (and current).

The voltage induced by the
generator alternates, and the current
produced is alternating current (AC).
The current changes magnitude and
direction periodically.
The standard AC in North America
changes magnitude and direction
during 60 complete cycles per
second—60 hertz.

Complex Generators
The generators used in power plants are much more
complex than the model discussed here.
Huge coils made up of many loops of wire are wrapped on
an iron core, to make an armature much like the armature of
a motor.
They rotate in the very strong magnetic fields of powerful
electromagnets.

The armature is connected externally to an assembly of paddle wheels
called a turbine.
While wind or falling water can be used to produce rotation of the turbine,
most commercial generators are driven by moving steam.
At the present time, a fossil fuel or nuclear fuel is used as the energy
source for the steam.

An energy source of some kind is required to operate
a generator.
Some fraction of energy from the source is converted to
mechanical energy to drive the turbine.
The generator converts most of this to electrical energy.
Some people think that electricity is a source of energy. It is
not. It is a form of energy that must have a source.

How is a generator different from a motor?

Moving charges experience a force that is
perpendicular to both their motion and the
magnetic field they traverse.
37.4 Motor and Generator Comparison

An electric current is deflected in a magnetic field,
which underlies the operation of the motor.
Electromagnetic induction underlies the operation of
a generator.
We will call the deflected wire the motor effect and
the law of induction the generator effect.

a. When a current moves to the right, there is a force on the
electrons, and the wire is tugged upward.

a. When a current moves to the right, there is a force on the
electrons, and the wire is tugged upward.
b. When a wire with no current is moved downward, the
electrons in the wire experience a force, creating current.

The motor effect occurs when a current moves through a
magnetic field.
• The magnetic field creates a perpendicular upward
force on the electrons.
• Because the electrons can’t leave the wire, the
entire wire is tugged along with the electrons.

In the generator effect, a wire with no current is moved
downward through a magnetic field.
• The electrons in this wire experience a force
perpendicular to their motion, which is along the wire.
• A current begins to flow.

A striking example of a device functioning as both motor and
generator is found in hybrid automobiles.
• When extra power for accelerating or hill climbing is
needed, this device draws current from a battery and
acts as a motor.
• Braking or rolling downhill causes the wheels to exert a
torque on the device so it acts as a generator and
recharges the battery.
• The electrical part of the hybrid engine is both a motor
and a generator.

How does a magnetic field affect a
moving charge?

A transformer works by inducing a changing
magnetic field in one coil, which induces an
alternating current in a nearby second coil.
37.5 Transformers

Consider a pair of coils, side by side, one connected to a
battery and the other connected to a galvanometer.
It is customary to refer to the coil connected to the power
source as the primary (input), and the other as the
secondary (output).
37.5 Transformers

As soon as the switch is closed in the primary and current
passes through its coil, a current occurs in the secondary.
When the primary switch is opened, a surge of current again
registers in the secondary but in the opposite direction.
Whenever the primary switch is opened or closed, voltage is
induced in the secondary circuit.
37.5 Transformers

The magnetic field that builds up around the primary
extends into the secondary coil.
Changes in the magnetic field of the primary are sensed
by the nearby secondary.
These changes of magnetic field intensity at the
secondary induce voltage in the secondary, in accord
with Faraday’s law.
37.5 Transformers

If we place an iron core inside
both coils, alignment of its
magnetic domains intensifies the
magnetic field within the primary.
The magnetic field is
concentrated in the core, which
extends into the secondary, so
the secondary intercepts more
field change.
The galvanometer will show
greater surges of current when
the switch of the primary is
opened or closed.
37.5 Transformers

Instead of opening and closing a switch to produce the
change of magnetic field, an alternating current can
power the primary.
Then the rate of magnetic field changes in the primary
(and in the secondary) is equal to the frequency of the
alternating current.
Now we have a transformer, a device for increasing or
decreasing voltage through electromagnetic induction.
37.5 Transformers

If the iron core forms a complete loop, guiding all
magnetic field lines through the secondary, the
transformer is more efficient.
All the magnetic field lines within the primary are
intercepted by the secondary.
37.5 Transformers

Voltage
Voltages may be stepped up or stepped down with a
transformer.
Suppose the primary consists of one loop connected to a
1-V alternating source.
• Consider the arrangement of a one-loop secondary
that intercepts all the changing magnetic field lines of
the primary.
• Then a voltage of 1 V is induced in the secondary.
37.5 Transformers

If another loop is wrapped around the core, the
induced voltage will be twice as much, in accord
with Faraday’s law.
If the secondary has a hundred times as many turns
as the primary, then a hundred times as much
voltage will be induced.
This arrangement of a greater number of turns on
the secondary than on the primary makes up a step-
up transformer.
Stepped-up voltage may light a neon sign or
operate the picture tube in a television receiver.
37.5 Transformers

a. 1 V induced in the secondary equals the voltage of the primary.
37.5 Transformers

b. 1 V is induced in the added secondary also because it intercepts the
same magnetic field change from the primary.
37.5 Transformers

b. 1 V is induced in the added secondary also because it intercepts the
same magnetic field change from the primary.
c. 2 V is induced in a single two-turn secondary.
37.5 Transformers

If the secondary has fewer turns than the primary, the
alternating voltage in the secondary will be lower than that in
the primary.
The voltage is said to be stepped down.
If the secondary has half as many turns as the primary, then
only half as much voltage is induced in the secondary.
37.5 Transformers

The relationship between primary and secondary voltages with
respect to the relative number of turns is
37.5 Transformers

A practical transformer uses many coils. The relative
numbers of turns in the coils determines how much the
voltage changes.
37.5 Transformers

Power
You don’t get something for nothing with a transformer that
steps up the voltage, for energy conservation is always in
control.
The transformer actually transfers energy from one coil to the
other. The rate at which energy is transferred is the power.
The power used in the secondary is supplied by the primary.
37.5 Transformers

The primary gives no more power than the secondary uses.
If the slight power losses due to heating of the core are
neglected, then the power going in equals the power
coming out.
Electric power is equal to the product of voltage and current:
(voltage × current)primary
= (voltage × current)secondary
37.5 Transformers

If the secondary has more
voltage, it will have less current
than the primary.
If the secondary has less
voltage, it will have more
current than the primary.
37.5 Transformers

This transformer lowers 120 V to
6 V or 9 V. It also converts AC to
DC by means of a diode that acts
as a one-way valve.
37.5 Transformers

think!
When the switch of the primary is opened or
closed, the galvanometer in the secondary
registers a current. But when the switch remains
closed, no current is registered on the
galvanometer of the secondary. Why?
37.5 Transformers

think!
When the switch of the primary is opened or
closed, the galvanometer in the secondary
registers a current. But when the switch remains
closed, no current is registered on the
galvanometer of the secondary. Why?
Answer:
A current is only induced in a coil when there is a
change in the magnetic field passing through it.
When the switch remains in the closed position,
there is a steady current in the primary and a
steady magnetic field about the coil.
37.5 Transformers

think!
If the voltage in a transformer is stepped up, then the current is
stepped down. Ohm’s law says that increased voltage will produce
increased current. Is there a contradiction here, or does Ohm’s Law
not apply to transformers?
37.5 Transformers

think!
If the voltage in a transformer is stepped up, then the current is
stepped down. Ohm’s law says that increased voltage will produce
increased current. Is there a contradiction here, or does Ohm’s Law
not apply to transformers?
Answer:
Ohm’s law still holds, and there is no contradiction. The voltage
induced across the secondary circuit, divided by the load
(resistance) of the secondary circuit, equals the current in the
secondary circuit. The current is stepped down in comparison with
the larger current that is drawn in the primary circuit.
37.5 Transformers

How does a transformer work?
37.5 Transformers

Almost all electric energy sold today is in the
form of alternating current because of the ease
with which it can be transformed from one
voltage to another.
37.6 Power Transmission

Power is transmitted great
distances at high voltages and
correspondingly low currents.
This reduces energy losses
due to the heating of the wires.
Power may be carried from
power plants to cities at about
120,000 volts or more, stepped
down to about 2400 volts in the
city, and finally stepped down
again to 120 volts.

Power transmission uses transformers to increase voltage for
long-distance transmission and decrease it before it reaches
your home.

Energy, then, is transformed from
one system of conducting wires
to another by electromagnetic
induction.
The same principles account for
sending energy from a radio-
transmitter antenna to a radio
receiver many kilometers away.
The effects of electromagnetic
induction are very far-reaching.

Why is almost all electrical energy sold today in
the form of alternating current?

A magnetic field is created in any region of space in
which an electric field is changing with time.
37.7 Induction of Electric and Magnetic Fields

Electromagnetic induction has thus far been discussed in
terms of the production of voltages and currents.
The more fundamental way to look at it is in terms of the
induction of electric fields.
The electric fields, in turn, give rise to voltages and currents.

Induction takes place whether or not a conducting wire or
any material medium is present.
Faraday’s law states that an electric field is created in
any region of space in which a magnetic field is changing
with time.
The magnitude of the created electric field is proportional
to the rate at which the magnetic field changes.
The direction of the created electric field is at right angles
to the changing magnetic field.

If electric charge happens to be present where the
electric field is created, this charge will experience a
force.
• For a charge in a wire, the force could cause it to
flow as current, or to push the wire to one side.
• For a charge in the chamber of a particle
accelerator, the force can accelerate the charge to
high speeds.

There is a second effect, which is
the counterpart to Faraday’s law.
It is just like Faraday’s law, except
that the roles of electric and
magnetic fields are interchanged.

A magnetic field is created in any region of space in
which an electric field is changing with time.
• The magnitude of the magnetic field is proportional
to the rate at which the electric field changes.
• The direction of the created magnetic field is at right
angles to the changing electric field.

How can an electric field
create a magnetic field?

An electromagnetic wave is composed of
oscillating electric and magnetic fields that
regenerate each other.
37.8 Electromagnetic Waves

Shake the end of a stick back and forth in still water and you
will produce waves on the water surface.
Similarly shake a charged rod back and forth in empty space
and you will produce electromagnetic waves in space.

The shaking charge can be considered an electric current.
• A magnetic field surrounds an electric current.
• A changing magnetic field surrounds a changing
electric current.
• A changing magnetic field creates a changing electric
field.
• The changing electric field creates a changing
magnetic field.

An electromagnetic wave is composed of oscillating electric and magnetic fields that
regenerate each other.
No medium is required. The oscillating fields emanate from the vibrating charge.
At any point on the wave, the electric field is perpendicular to the magnetic field.
Both are perpendicular to the direction of motion of the wave.

Speed of Electromagnetic Waves
For electromagnetic radiation, there is only
one speed—the speed of light—no matter
what the frequency or wavelength or intensity
of the radiation.
The changing electric field induces a
magnetic field. The changing magnetic field
acts back to induce an electric field.
Only one speed could preserve this
harmonious balance of fields.

If the wave traveled at less than the speed of light, the fields
would rapidly die out.
The electric field would induce a weaker magnetic field, which
would induce a still weaker electric field.
If the wave traveled at more than the speed of light, the fields
would build up in a crescendo of ever greater magnitudes.
At some critical speed, however, mutual induction continues
indefinitely, with neither a loss nor a gain in energy.

From his equations of electromagnetic induction,
Maxwell calculated the value of this critical speed
and found it to be 300,000 kilometers per second.
He used only the constants in his equations
determined by simple laboratory experiments with
electric and magnetic fields.
He didn’t use the speed of light. He found the speed
of light!

Nature of Light
Maxwell quickly realized that he had discovered the
solution to one of the greatest mysteries of the universe
—the nature of light.
Maxwell realized that radiation of any frequency would
propagate at the same speed as light.

This radiation includes radio waves, which can be
generated and received by antennas.
• A rotating device in the sending antenna alternately
charges the upper and lower parts of the antenna
positively and negatively.
• The charges accelerating up and down the antenna
transmit electromagnetic waves.
• When the waves hit a receiving antenna, the electric
charges inside vibrate in rhythm with the variations of
the field.

What makes up an
electromagnetic wave?

1. A voltage will be induced in a wire loop when the magnetic field within
that loop
a. changes.
b. aligns with the electric field.
c. is at right angles to the electric field.
d. converts to magnetic energy.
Assessment Questions

1. A voltage will be induced in a wire loop when the magnetic field within
that loop
a. changes.
b. aligns with the electric field.
c. is at right angles to the electric field.
d. converts to magnetic energy.
Answer: A

2. If you change the magnetic field in a closed loop of wire, you induce in
the loop a
a. current.
b. voltage.
c. electric field.
d. all of these

2. If you change the magnetic field in a closed loop of wire, you induce in
the loop a
a. current.
b. voltage.
c. electric field.
d. all of these
Answer: D

3. The essential concept in an electric motor and a generator is
a. Coulomb’s law.
b. Ohm’s law.
c. Faraday’s law.
d. Newton’s second law.

3. The essential concept in an electric motor and a generator is
a. Coulomb’s law.
b. Ohm’s law.
c. Faraday’s law.
d. Newton’s second law.
Answer: C

4. A motor and a generator are
a. similar devices.
b. very different devices with different applications.
c. only found in hybrid cars.
d. energy sources.

4. A motor and a generator are
a. similar devices.
b. very different devices with different applications.
c. only found in hybrid cars.
d. energy sources.
Answer: A

5. A step-up transformer in an electrical circuit can
a. increase voltage.
b. decrease energy.
c. increase current.
d. increase energy.

5. A step-up transformer in an electrical circuit can
a. increase voltage.
b. decrease energy.
c. increase current.
d. increase energy.
Answer: A

6. To keep heat losses down when power is carried across the
countryside, it is best that current in the wires is
a. low.
b. high.
c. not too low and not too high.
d. replaced with voltage.

6. To keep heat losses down when power is carried across the
countryside, it is best that current in the wires is
a. low.
b. high.
c. not too low and not too high.
d. replaced with voltage.
Answer: A

7. According to James Clerk Maxwell, if the magnitude of the created
magnetic field increases, the change in the electric field will
a. stay the same.
b. increase.
c. decrease.
d. always disappear.

7. According to James Clerk Maxwell, if the magnitude of the created
magnetic field increases, the change in the electric field will
a. stay the same.
b. increase.
c. decrease.
d. always disappear.
Answer: B

8. Electricity and magnetism connect to form
a. mass.
b. energy.
c. ultra high-frequency sound.
d. light.

8. Electricity and magnetism connect to form
a. mass.
b. energy.
c. ultra high-frequency sound.
d. light.
Answer: D

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