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Chapter 10:
Magnetic Fields
Section 1
Understanding Magnetism
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Section 1
Understanding Magnetism
Main Idea :
Magnets and electric currents produce magnetic fields.
Essential Questions
What are some properties of magnets?
What causes an object to be magnetic?
What are the characteristics of magnetic fields?
What is the relationship between magnetic fields and electric currents?
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Properties of Magnets
Magnet:
An object that attracts iron and some other
materials
Properties of the magnets

Magnet is Polarized ( The magnets have north
and south poles)

Metals that are not attracted to magnets are
(Brass, copper, and aluminum) are common.

Magnets only attract some metals are (Iron,
nickel, and cobalt) are strongly attracted.
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Properties of Magnets
Properties of the magnets

All magnets have two singular
poles or Monopoles

When magnet is broken in half,
magnets orient themselves in a N
& S direction.
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Properties of Magnets
Types of the magnets
Temporary magnet :

That lose its magnetization by time or by removing the impact.

These objects have no poles. When a magnet touches one of these
objects, such as the nail, the magnet polarizes the object, making it a
temporary magnet. This process is called magnetization by induction.

Materials containing these elements, called ferromagnetic materials, can
become temporary magnets.

A steel nail can become a temporary magnet because it is made of iron
with tiny amounts of carbon and other materials.
Permanent magnet

That does not lose its magnetization by time such as natural magnets
and industrial magnets.
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Properties of Magnets
Earth’s magnetic field

The needle of a compass points in a north-south direction because
Earth itself is a giant magnet.

A compass’s north pole points to Earth’s geographic North Pole.

As you will read, however, a magnet's north pole is always attracted
to a magnetic south pole.

Therefore, what we call the North Pole is actually near Earth’s
magnetic south pole, and the South Pole is near Earth’s magnetic
north pole.

When magnet is broken in half, magnets orient themselves in a N &
S direction.
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Properties of Magnets
Earth’s magnetic field
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Properties of Magnets
Magnetic domains

Each atom in ferromagnetic materials acts
like a tiny magnet, each has two poles.

When the magnetic fields of the electrons in
a group of neighboring atoms are all aligned
in the same direction, the group is called a
domain.

When a piece of iron is not in a magnetic
field, the domains point in random directions,
and their magnetic fields cancel one another
out.
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Properties of Magnets
Magnetic domains

If, however, a piece of iron is placed in a
magnetic field, the domains tend to align
with the external field.

In the case of a temporary magnet, after
the external field is removed, the domains
return to their random arrangement.

In a permanent magnet, the iron has
been alloyed with other substances to
keep the domains aligned after the
external magnetic field is removed.
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Properties of Magnets
Creating permanent magnets

Heating an object contains ferromagnetic materials in the
presence of strong magnet.

Thermal energy frees the atoms in each of the object’s
domains.

The domains can rotate and align with the magnet’s poles.

The object is then cooled, and its atoms become less free to
rotate.
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Properties of Magnets
Magnetic field
 Magnetic Field is Created by the
Magnets
 A vector quantity, Symbolized by B
 Direction is given by the direction a
north pole of a compass needle points
in that location
 Magnetic field are fields that exist
in space where magnets would
experience a force.
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Properties of Magnets
Magnetic field Lines
Note that magnetic field lines, like electric field
lines, are imaginary.
They are used to help us visualize a field, and
they also provide a measure of the strength of
the magnetic field.
The number of magnetic field lines passing
through a surface is called the magnetic flux.
The flux per unit area is proportional to the
strength of the magnetic field.
The magnetic flux is most concentrated at the
poles; thus, this is where the magnetic field
strength is the greatest.
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Electromagnetism

How can current produce
a strong magnetic field?
Because the electric
current
creates
a
magnetic field around the
wire, that effects on the
compass needle.
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Electromagnetism
Magnetic fields from current-carrying wires

The field lines form closed loops around the
current-carrying wire.

The magnetic field around a current-carrying
wire is always perpendicular to that wire.

Just as field lines around permanent
magnets form closed loops, the field lines
around current-carrying wires also form
closed loops.

The circular pattern of iron filings shown in
the top panel of Figure represents these
loops.
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The factors that the strength of
magnetic field depends on:
directly
proportional to
the current in
the wire
proportional
inversely with
the distance
from the wire.
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Direction of magnetic field for loop coil
How to determine the direction of
the magnetic field around a current
carrying wire?
 By using the right-hand rule:
 Thumb points in the direction of the
current.
 The fingers of the hand encircling
the wire points in the direction of
the magnetic field.
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I
I
B
N
B
B
I
N
N
B
X
I
B
B
I
N
I
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Direction of magnetic field
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Examples of magnetic field for coil loops
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Examples of magnetic field for coil loops
A compass shows the direction of the field lines.
If you reverse the direction of
the current, the compass
needle also reverses its
direction, as shown in the
figure at right.
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Electromagnetism

A wire connected to a circuit and coiled
into many spiral loops is a solenoid.

When current is turned on in a solenoid,
each loop produces its own magnetic
field.

The fields are all in the same direction,
so they add together.

This magnetic field is similar to the field of
a permanent magnet.

The solenoid is an electromagnet, which is a magnet whose
magnetic field is produced by electric current.
https://www.twig-world.com/experiment/makingan-electromagnet-4154/
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The factors that the strength of
magnetic field a solenoid:
proportional to the
current in the
solenoid’s loops.
Increased by
placing an ironcontaining rod
inside it.
Proportional to The
number of the
solenoid loops.
The spaces between
the solenoid loops.
(invers proportional)
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Direction of magnetic field for solenoid
How to determine the
direction of the solenoid
magnetic field?
By using the right-hand rule:
 Thumb points in the direction of
the magnetic field direction.
 The fingers curling with the
current direction.
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5- How does the strength of a magnetic field, 1 cm
from a current-carrying wire, compare with each of
the following?
A. The strength of the field that is 2 cm from the wire
B. The strength of the field that is 0.5 cm from the wire
SOLUTION:
a)
Because magnetic field strength varies inversely with
distance from the wire, the magnetic field at 1 cm will be
twice as strong as the magnetic field at 2 cm.
b)
Because magnetic field strength varies inversely with
distance from the wire, the magnetic field at 1 cm will be
three times as strong as the magnetic field at 3 cm.
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6. A long, straight current-carrying wire lies in a
north-south direction.
a) The north pole of a compass needle placed above
this wire points toward the east. In what direction
is the current?
a) from south to north
b) If a compass were placed underneath this wire, in
which direction would the compass needle point?
b) west
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7- A student makes a magnet by winding wire around
a nail and connecting it to a battery, as shown in the
figure.
Which end of the nail- the pointed end or the headwill be the north pole?
SOLUTION:
the pointed end
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8. You have a battery, a spool of wire, a glass rod,
an iron rod, and an aluminum rod.
Which rod could you use to make an electromagnet
that can pick up steel objects? Explain.
SOLUTION:
•
Use the iron rod. Iron would be attracted to a permanent
magnet and take on properties of a magnet, whereas
aluminum or glass would not.
•
This effect would support the magnetic field in the wire coil
and thus make the strongest electromagnet.
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9. Challenge The electromagnet in the previous
problem works well, but you would like to make the
strength of the electromagnet adjustable by using a
potentiometer as a variable resistor.
Is this possible? Explain.
SOLUTION:
•
Yes.
•
Connect the potentiometer in series with the power supply
and the coil.
•
Adjusting the potentiometer for more resistance will
decrease the current and the field strength.
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Section Check
Question 1
What happens when the North Pole of one magnet is
brought near the South Pole of another magnet?
A. The magnets attract each other.
B. There will be no effect.
C. The magnets repel each other.
D. The magnets partially attract and partially repel each other.
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Section Check
Question 2
What is the direction of a magnetic field line (imaginary line) of a bar
magnet?
A. Outside the magnet, magnetic field lines emerge from the magnet at its
North Pole and enter the magnet at its South Pole; they do not travel
inside the magnet.
B. Outside the magnet, magnetic field lines emerge from the magnet at its
South Pole and enter the magnet at its North Pole; they do not travel
inside the magnet.
C. Outside the magnet, magnetic field lines emerge from the South Pole and
enter the magnet at its North Pole. Inside the magnet, the magnetic field
lines travel from the North Pole to the South Pole.
D. Outside the magnet, magnetic field lines emerge from the North Pole and
Continued
enter the magnet at its South Pole. Inside the magnet, the magnetic field
lines travel from the South Pole to the North Pole.
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Section Check
Question 3
What will happen if you lay a wire across the top of a small compass
and connect the ends of a wire to complete an electrical circuit?
A. The needle of the compass will point in the same direction of
the current in the wire.
B. The needle of the compass will point in the opposite direction of
the current in the wire.
C. The needle of the compass will point in the direction
perpendicular to the direction of the current in the wire.
D. The needle of the compass will point in the direction making an
angle of 45° with the direction of the current in the wire.
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Chapter 10:
Magnetic Fields
Section 2
Applying Magnetic Forces
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Big Idea
Many devices, including earbuds and electric motors, rely on forces
from magnetic fields in order to work.
Essential Questions

How is the direction of the force on a current-carrying wire related
to the direction of the magnetic field?

What affects the force on a current-carrying wire in a magnetic
field?

What are the characteristics of the design and operation of an
electric motor?

What affects the force on a charged particle moving in a magnetic
field?
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Forces on Current-Carrying Wires
When you put a magnet in a magnetic
field, the magnet can move.
What happens when you put a currentcarrying wire in a magnetic field?
Michael Faraday, who performed many
electricity and magnetism experiments
during
the
nineteenth
century,
discovered that a magnetic field
produces a force on a current-carrying
wire.
The force on the wire is always at right angles to both the direction of the
magnetic field and the direction of current, as shown in the left part of
Figure.
When current changes direction, so does the force.
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Forces on Current-Carrying Wires
Direction of force
You can use a right-hand rule to
determine the direction of force on
a
current-carrying
wire
in
a
magnetic field.
Thumb is in the direction of the
wire’s conventional (+) current.
Fingers are in the direction of B
Palm is in the direction of FB
–On a positive particle
–You can think of this as your
hand pushing the particle
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Forces on Current-Carrying Wires
Arrows in three dimensions

The relationship among magnetic field, electric current, and force is
three-dimensional.

How do you accurately represent directional arrows in three dimensions
on a two-dimensional piece of paper? Imagine an archer shooting an
arrow toward you.

The arrow looks like a dot. Now imagine the same arrow going away
from you.

The arrow looks like a cross. You can use dots to represent magnetic
fields that go into a piece of paper, and crosses to represent fields that
go out of the paper, as shown in Figure on the opposite page.
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Forces on Current-Carrying Wires
• A magnetic field exerts a force on a current-carrying
wire.
• The force on the wire is always at right angles to both
the direction of the magnetic field and the direction of
current.
• When current changes direction, so does the force.
The size of the force depends on:
• the current,
• the length of wire in the field,
• the strength of the magnetic field, and
• the angle between the current and the magnetic
field.
Force on a Current-Carrying Wire in a
Magnetic Field
F   L B s in  
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Forces on Current-Carrying Wires
The strength of a magnetic field, B, is measured in tesla, T.
1 T is equivalent to 1 N/Aּm.
Note that if the wire is not perpendicular to the magnetic field, a factor of
sin θ is introduced in the above equation, resulting in
F = ILB sin θ.
As the wire becomes parallel to the magnetic field, the angle θ becomes
zero, and the force is reduced to zero. When θ = 90°, the equation is
again F = ILB.
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Forces on Current-Carrying Wires
Loudspeakers
One use of the force on a current-carrying wire in a magnetic field is in a
loudspeaker.
A loudspeaker changes electric energy to sound energy using a coil of fine
wire mounted on a paper cone and placed in a magnetic field.
The amplifier driving the loudspeaker sends a current through the coil.
The magnetic field from the permanent magnet is oriented radially so it is
perpendicular to both the coil of wire and the direction of motion of the
coil.
A music player sends current through an earbud's wires.
The current enters the coil, changing direction between 40 and 40,000
times each second, depending on the pitches of the tones it represents.
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Forces on Current-Carrying Wires
Loudspeakers
The force from the magnetic field on the coil pushes the coil in and out,
depending on the direction of current.
This causes the membrane to vibrate, thereby producing sound waves.
Each time the current changes direction twice, the membrane vibrates
back and forth once.
Most loudspeakers and headphones work in a similar way. A magnetic
field exerts a force on a coil of wire mounted on a paper or plastic cone.
As the wire moves, it pushes the coil into and out of the field. This motion
causes the cone to vibrate and produce sound waves.
A force exerted on the coil, because it is in a magnetic field, pushes the
coil either into or out of the field, depending on the direction of the
current.
The motion of the coil causes the cone to vibrate, thereby creating sound
waves in the air.
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Forces on Current-Carrying Wires
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Forces on Current-Carrying Wires
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Forces on Current-Carrying Wires
Galvanometers
A galvanometer is a device used to
measure very small currents, and
therefore, it can be used as a
voltmeter or an ammeter. Current in
the wire loop shown in the left of
Figure passes in one end of the loop
and out the other.
As it does, the force on the loop
pushes one side of the loop down and
the other side up.
The resulting torque causes the loop
to rotate. The magnitude of the torque
on the loop is proportional to the
magnitude of the current. This is the
principle used in a galvanometer.
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Forces on Current-Carrying Wires
Galvanometers
The resistance of the coil of wire in a sensitive
galvanometer is about Ω.
To measure larger currents, a galvanometer
can be converted into an ammeter by placing
a resistor with resistance smaller than the
galvanometer in parallel with the meter.
Most of the current, Is, passes through the
resistor, called the shunt, because the current
is inversely proportional to resistance;
whereas only a few microamps, Im, flow
through the galvanometer.
The resistance of the shunt is chosen according to the desired
deflection scale.
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Forces on Current-Carrying Wires
Galvanometers
A galvanometer also can be connected as a voltmeter.
To make a voltmeter, a resistor, called the multiplier, is placed in
series with the meter, as shown in the figure.
The galvanometer measures
the current through the
multiplier.
The current is represented by I
= V/R, where V is the voltage
across the voltmeter and R is
the effective resistance of the
galvanometer and the
multiplier resistor.
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Forces on Current-Carrying Wires
Electric Motor
An electric motor is an apparatus that converts electrical energy into
mechanical energy.
The wire coil in an electric motor is called the armature.
The armature is made of many loops mounted on a shaft or axle.
The total force acting on the armature is proportional to nILB, where n is
the total number of turns on the armature, B is the strength of the
magnetic field, I is the current, and L is the length of wire in each turn that
moves perpendicular to the magnetic field, and B is the strength of the
magnetic field.
The magnetic field is produced either by a permanent magnet or by an
electromagnet (called a field coil).
The torque on the armature is controlled by varying the current through
the motor.
The larger the torque, the faster the armature turns.
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Forces on Current-Carrying Wires
Electric Motor
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Forces on Single Charged Particle
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The signals used to determine the direction
of the magnetic field
Up ( Toward the positive y axis)
Towards the north
Right (Toward the positive x axis)
Towards the east
Perpendicular into page: inward
(Toward the negative Z axis)
Down ( Toward the negative y axis)
Towards the south
left ( Toward the negative x axis )
Towards the west
Perpendicular out of page: outward
(Toward the positive Z axis)
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Forces on Single Charged Particles
Use with Example Problem 2.
Problem
KNOWN
F = 2.810−14 N
v = 1.7106 m/s
q = e = 1.60210−19 C
θ = 90°
UNKNOWN
B=?
An engineer is designing a deflection system
for an electron-beam device and needs a force
of 2.810−14 N on each electron in the beam,
SOLVE FOR THE UNKNOWN
which travels at 1.7106 m/s. Determine the
• Use the relationship among the magnetic
required field strength.
field, force, charge, and speed.
F
Response
B 
qv sin  
SKETCH AND ANALYZE THE PROBLEM
• Sketch the
2.810 14 N

situation.
19
1.60210 C 1.7106 m/s sin 90
• List the knowns
 0.10 T
and unknowns.



EVALUATE THE ANSWER
• 0.10 T is reasonable for a magnetic field
in an deflection system.
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Force on a Charged Particle in a Magnetic Field
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Synchrotrons
Because the direction of force is always perpendicular to a
charged particle’s velocity in a magnetic field, magnets can be
used to direct a charged particle’s path.
For example, accelerating particles in a synchrotron, such as
the Large Hadron Collider (LHC), move in a circle as they
maintain their velocity at right angles to a uniform magnetic
field.
You can see several segments of the 27-km-long tunnel
housing the LHC in Figure.
As the particles gain speed, the magnetic field in the tunnel is
increased to keep the radius of the circle constant.
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Synchrotrons
Additional magnets provide horizontal and vertical forces to
focus the beam.
Additional segments along the LHC tunnel add fixed amounts
of energy that accelerate the particles.
Because charged particles go through many accelerators in
multiple passes around the synchrotron, the particles can
reach extremely high energies.
The LHC was designed to give accelerating protons enough
energy to travel against a potential difference of 7.2 trillion
volts. To reduce electrical power needs, the magnets in the
LHC use superconducting wires
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25. In what direction is the force on an electron if that electron is
moving east through a magnetic field that points north?
SOLUTION:
down
26. What are the magnitude and direction of the force acting on the
proton shown in Figure 20?
SOLUTION:
F = qvB
= (+1.60×10−19 C)(4.0×107 m/s)(0.50 T)
= 3.2×10−12 N
The direction of force is up.
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27. A stream of doubly ionized particles (missing two
electrons and thus carrying a net charge of two elementary
charges) moves at a velocity of 3.0×104 m/s perpendicular
to a magnetic field of 9.0×10−2 T. How large is the force
acting on each ion?
SOLUTION:
F = qvB
= (2)(1.60×10−19 C) (3.0×104 m/s)(9.0×10−2 T)
= 8.6×10−16 N
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28. Triply ionized particles in a beam carry a net positive
charge of three elementary charge units. The beam enters
a magnetic field of 4.0×10−2 T. The particles have a speed
of 9.0×106 m/s and move at right angles to the field. How
large is the force acting on each particle?
SOLUTION:
F = qvB
= (3)(1.60×10−19 C)(9.0×106 m/s)(4.0×10−2 T)
= 1.7×10−13 N
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Galvanometer A galvanometer deflects full-scale
for a 50.0-μ A current. What must be the total
resistance of the series resistor and the
galvanometer to make a voltmeter with 10.0-V fullscale deflection?
R= v/I
= 10 / 50 * 10-6
= 200 *103 Ω
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Section Check
A current-carrying wire is kept in a magnetic field such that the direction
of the flow of conventional current is perpendicular to the direction of
the magnetic field. In which direction will the wire experience the force?
A. In the direction of the magnetic field.
B. In a direction opposite to the magnetic field.
C. In a direction perpendicular to both the direction of the magnetic
field and the direction of the conventional current.
D. In a direction perpendicular to both the direction of the magnetic
field and the direction opposite to the direction of the
conventional current.
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Section Check
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Section Check
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Section Check
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