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Section 13.3 Questions
Understanding Concepts
1. An electric current is travelling southward in a straight, horizontal
conductor. State the direction of the magnetic field
(a) below the conductor
(b) above the conductor
(c) east of the conductor
(d) west of the conductor
2. What is the direction of the magnetic field lines around a conductor with the electric current travelling (a) away from you, and
(b) toward you?
Figure 9
For question 3
3. The diagram in Figure 9 represents two parallel current-carrying
conductors. Determine whether the conductors attract or repel
one another. Explain your reasoning.
Reflecting
4. Why do you think the connection between electricity and magnetism was not discovered until the early 19th century? (Hint:
Research when magnetism, static electricity, and current electricity were discovered.)
13.4
Figure 1
electromagnet: object that exerts a magnetic force using electricity
solenoid: a coil of wire that acts like a
magnet when an electric current passes
through it
uniform magnetic field: the magnetic
field is the same strength and acts in the
same direction at all points
right-hand rule for a coil: If a coil is
grasped in the right hand with the curled fingers representing the direction of electric
current, the thumb points in the direction of
the magnetic field inside the coil.
482 Chapter 13
The Magnetic Field of a Coil
or Solenoid
In a junkyard, a crane lifts a pile of scrap metal to be compressed and eventually
recycled (see Figure 1). How is the scrap metal held up by the crane? You might
say by a magnet, but it couldn’t be a permanent magnet—otherwise how would
the metal be released? It is held by an electromagnet, a device that exerts a magnetic force using electricity.
The magnetic field around a straight conductor can be intensified by
bending the wire into a loop, as illustrated in Figure 2. The loop can be thought
of as a series of segments, each an arc of a circle, and each with its own magnetic
field (Figure 2(a)). The field inside the loop is the sum of the fields of all the segments. Notice that the field lines are no longer circles but have become more like
lopsided ovals (Figure 2(b)).
The magnetic field can be further intensified (Figure 3) by combining the
effects of a large number of loops wound close together to form a coil, or solenoid.
The field lines inside the coil are straight, almost equally spaced, and all point in
the same direction. We call this a uniform magnetic field; the magnetic field is
of the same strength and is acting in the same direction at all points.
If the direction of electric current through the coil is reversed, the direction
of the field lines is also reversed but the magnetic field pattern, as indicated by a
pattern of iron filings, looks the same as it did before. To help you remember the
relationship between the direction of electric current through a coil and the direction of the coil’s magnetic field, there is the right-hand rule for a coil (Figure 4).
Right-Hand Rule for a Coil
If a coil is grasped in the right hand with the curled fingers representing
the direction of electric current, the thumb points in the direction of the
magnetic field inside the coil.
13.4
(a)
N
S
electric current
Figure 4
The right-hand rule for a coil
(b)
current flowing up
Figure 5 shows the similarity between the magnetic fields of a bar magnet
(Figure 5(a)) and those of a coil (Figure 5(b)). Notice that the coil is wrapped
around an iron core, which helps to increase the strength of the magnetic field.
(a)
(b)
N
S
N
S
iron core
electric
current
Figure 5
The ends of a coil can be thought of as an N-pole and an S-pole, and the field within
the core resembles the field in the interior of a bar magnet, with its ferromagnetic
dipoles aligned so that they all point in the same direction.
current flowing down
Figure 2
Practice
Understanding Concepts
1. Copy Figure 6 into your notebook and indicate on each diagram the
direction of the electric current, the magnetic field lines around the
coil, and the north and south poles of the coil.
(a)
(b)
N
S
Figure 3
At both ends of the coil, the field is still
strong, but along the sides, the magnetic
field is weaker, as the field lines begin to
bend and spread out.
Figure 6
2. If two identical cardboard tubes are wound with wire in exactly the
same way and placed end-to-end with current passing through them
in the same direction, will the two tubes attract or repel each other?
Explain.
Electromagnetism 483
Activity 13.4.1
Magnetic Field of a Coil
Question
What are the characteristics of the magnetic field of a coil?
Materials
Figure 7
Setup for Activity 13.4.1
50 cm of bare 12-gauge copper wire
wooden dowel (about 15 cm long × 4 cm diameter)
stiff cardboard and scissors
battery (6 V–12 V) or DC power supply
connecting wires with alligator clips
iron filings
2 compasses
Procedure
One of the wires from the
conductor should be connected firmly to one of the
terminals; the other wire
should be touched momentarily to the other terminal.
The resistance of the bare
wire is very low. As a result, it
draws a large current. This
will cause the wire to get hot
and the battery to discharge
quickly if the terminals are
connected for too long a time.
Be careful not to get iron
filings in your eyes. Wash
your hands after handling
iron filings.
484 Chapter 13
1. Make a coil by winding the bare copper wire around the dowel as many
times as possible. Spread the loops out so that they are about 0.5 cm apart.
Remove the dowel.
2. Using scissors, cut a piece of cardboard to fit snugly into the core of the
coil, as shown in Figure 7. Insert the cardboard into one end of the coil,
and support the coil so that the cardboard is horizontal.
3. Connect one end of the coil to one of the terminals of the battery using a
wire with an alligator clip. Connect another wire with a clip to the other
end of the coil, but do not connect the wire to the battery.
4. Lightly sprinkle iron filings on the cardboard, both inside and outside the
coil. Momentarily touch the loose wire to the other terminal of the battery,
and tap the cardboard gently. Once the iron filings have assumed a pattern,
disconnect the battery and sketch the pattern, including the coil. From the
battery terminals you used, determine in which direction the electric current was moving through the coil, and mark the direction on your sketch.
5. Place the compasses on the cardboard, one at each end of the coil.
Reconnect the battery and note the directions in which the compasses
point. Add these directions to your sketch of the iron filings.
6. Without moving the compasses, reverse the connections to the battery.
Make another sketch. Show the direction in which the electric current is
moving.
Observations
(a) Describe the direction, shape, and spacing of the magnetic field lines in the
core of the coil.
(b) What happens to these magnetic field lines at the ends of the coil?
(c) Describe the magnetic field in the region at either side of the coil.
(d) Compare the compass direction pattern obtained in step 5 to that obtained
in step 6. Does the right-hand rule provide an adequate description of
these patterns? Explain.
13.4
Factors Affecting the Magnetic Field of a Coil
A coil with an electric current flowing through it has a magnetic field that can be
plotted in the same way as for a bar magnet; however, it can be much more useful
than a bar magnet. A bar magnet is able to pick up small pieces of iron but it
cannot release them, and its strength cannot be varied. A coil, on the other hand,
has a magnetic field that can be turned on and off and altered in strength.
The strength of a magnetic field is related to the degree of concentration of
its magnetic field lines. To increase the strength of the magnetic field in a coil,
you must increase the number of magnetic field lines or bring them closer
together. The magnetic field strength in a coil depends on the following factors.
Current in the Coil
Since the electric current flowing through the coil creates the magnetic field in
the core of the coil, the more electric current there is, the greater the concentration of magnetic field lines in the core. In fact, in an air core coil (a coil with no
material inside it), the magnetic field strength varies directly with the current in
a coil: doubling the current doubles the magnetic field strength.
Number of Loops in the Coil
Each loop of wire produces its own magnetic field, and since the magnetic field
of a coil is the sum of the magnetic fields of all its loops, the more loops that are
wound in the coil, the stronger its magnetic field. Magnetic field strength varies
directly as the number of loops per unit length in a coil: doubling the number of
loops in a coil doubles the magnetic field strength.
Type of Core Material
The material that makes up the core of a coil can greatly affect the coil’s magnetic
field strength. For example, if a cylinder of iron—rather than air—is used as the
core for a coil, the coil’s magnetic field strength can be several thousand times
stronger than with air. An aluminum core will have almost no effect on the
strength.
The core material becomes an induced magnet, as its atomic dipoles align
with the magnetic field of the coil. As a result, the core itself becomes an induced
magnet and the magnetic field strength increases.
The factor by which a core material increases the magnetic field strength is
called the material’s relative magnetic permeability (K). The permeability is the
ratio of the magnetic field strength in a material to the magnetic field strength
that would exist in the same region if a vacuum replaced the material.
magnetic field strength in material
K = magnetic field strength in vacuum
relative magnetic permeability: (K )
the factor by which a core material increases
the magnetic field strength that would exist
in the same region if a vacuum replaced the
material
For example, a material with a relative magnetic permeability of 3 will make
the field in a coil three times as strong as it would be in a vacuum.
The magnetic field strength of a coil varies directly as the permeability of its
core material: doubling the relative magnetic permeability of the core doubles
the magnetic field strength.
Electromagnetism 485
Ferromagnetism, Paramagnetism, and Diamagnetism
paramagnetic: material that magnetizes
very slightly when placed in a coil and
increases the field strength by a barely measurable amount
diamagnetic: materials that cause a very
slight decrease in the magnetic field of a coil
DID YOU KNOW ?
Applying Paramagnetism and
Diamagnetism
One of the uses of paramagnetism is to analyze the components of materials such as
powders and glasses. This application is performed using “electron paramagnetic resonance” apparatus. An interesting use of
diamagnetism is found in levitation devices,
such as a frictionless bearing in which a diamagnetic material is used in conjunction with
a ferromagnetic material.
Core materials are divided into three groups according to their relative magnetic
permeability.
As you have learned, ferromagnetic materials become strong induced magnets when placed in a coil; that is, they have very high relative magnetic permeability. Iron, nickel, cobalt, and their alloys are ferromagnetic.
Paramagnetic materials magnetize very slightly when placed in a coil and
increase the field strength by a barely measurable amount. As a result, they have
a relative magnetic permeability only slightly greater than 1. Oxygen and aluminum are paramagnetic.
Diamagnetic materials cause a very slight decrease in the magnetic field of a
coil and, as a result, their relative magnetic permeabilities are slightly less
than 1. Copper, silver, and water are diamagnetic.
The crane in Figure 1 of this section uses a huge electromagnet to lift the car.
The electromagnet has a ferromagnetic core that passes through the coil and
almost completely surrounds it. When the electromagnet is activated the core
becomes completely magnetized. When the electromagnet is deactivated the core
loses its magnetism and the car is released. (Even when the current is completely
shut off, the magnet will not lose all of its strength because the core becomes a
temporary magnet.)
Sample Problem
Calculate the effect on the strength of the magnetic field in a coil when each of
the following separate changes is made:
(a) the current in the coil is increased from 2.0 A to 5.0 A;
(b) the number of loops in the coil is changed from 4400 to 1100; the length of
the coil is unchanged;
(c) the core is changed from steel with a relative magnetic permeability of
3.0 × 103 to iron with a relative magnetic permeability of 8.0 × 103.
Solution
(a) Magnetic field strength varies directly with current.
magnetic field after change
5.0 A
= magnetic field before change 2.0 A
= 2.5
The magnetic field strength is 2.5 times as great.
(b) Magnetic field strength varies directly with number of loops per unit
length.
magnetic field after change
1100
= magnetic field before change 4400
= 0.25
The magnetic field strength is 0.25 times as great.
(c) Magnetic field strength varies directly with permeability of core.
magnetic field after change
8.0 × 103
= 3
magnetic field before change 3.0 × 10
= 2.7
The magnetic field strength is 2.7 times greater.
486 Chapter 13
13.4
Practice
switch: a device that is used to make or
break an electric circuit
Understanding Concepts
3. An electromagnet is able to exert a force of 1.5 × 102 N when lifting
an object. The electromagnet has 1000 turns, a current of 1.5 A, and a
material in the core with a relative magnetic permeability of 2.0 × 103.
What force will the electromagnet exert if the following changes are
made, each considered separately?
(a) The current is increased to 6.0 A.
(b) The number of turns in the coil is increased to 1400 without
increasing the length of the coil.
(c) All of the above changes are considered simultaneously.
Answers
(a) 6.0 × 102 N
(b) 2.1 × 102 N
(c) 8.4 × 102 N
Applications of Electromagnetism
Many appliances, tools, vehicles, and machines use a current-carrying coil to
create a magnetic field. In most cases, the magnetic field is used to cause another
component to move by magnetic attraction. A few examples will illustrate how
electromagnets are used.
Lifting Electromagnet
Large steel plates, girders, and pieces of scrap iron can be lifted and transported
by a lifting electromagnet (Figure 8). A soft ferromagnetic core of high relative
magnetic permeability is wound with a copper conductor. The ends of the coil
are connected to a source of electric potential through a switch. Closing the
switch causes an electric current in the coil, and the soft iron core becomes a very
strong induced magnet.
When the switch is opened and the electric current stops, the soft iron core
becomes demagnetized and releases its load. A U-shaped core is often used, with
a coil wrapped around each leg of the device. If the coils are wound in opposite
directions, the legs become oppositely magnetized and the lifting ability of the
magnet is doubled.
soft
iron
core
battery
switch
N
S
S
N
Figure 8
A lifting electromagnet
soft iron core
switch
spring
Electromagnetic Relay
A relay is a device in which a switch is closed by the action of an electromagnet
(Figure 9). A relatively small current in the coil of the electromagnet can be used
to switch on a large current without the circuits being electrically linked.
A pivoted bar of soft iron, called an armature, is held clear of the contact
point by a light spring. There is no current in the left-hand circuit, and the lamp
is off. When the switch is closed, there is a current in the right-hand circuit, and
the soft iron U-shaped core becomes magnetized. The magnetized core attracts
the armature and pulls it to the right until it touches the contact point, completing the circuit. Now there is a current in the left-hand circuit, and the lamp
goes on.
When the switch is opened, the electric current drops to zero, the core
becomes demagnetized, and the armature is released. When the spring pulls the
armature away from the contact point, current drops to zero in the left-hand circuit and the lamp goes off.
If the contact points were on the opposite side of the armature from the electromagnet, the relay would operate in reverse. Closing the switch would then
turn the left-hand circuit off, and vice versa.
battery
soft iron
armature
contact point
soft iron core
Figure 9
An electromagnetic relay
relay: a device in which a switch is closed
by the action of an electromagnet
armature: a pivoted bar of soft iron
Electromagnetism 487
Electric Bell
switch
spring
battery
soft iron
armature
N
contact
adjusting
screw
soft
iron
core
S
contact
bell
Figure 10
An electric bell
In an electric bell, a small hammer is attached to the armature. The armature is
vibrated back and forth several times a second, striking a metal bell. Figure 10
shows the circuit that causes the armature to move.
When a button is pushed, the switch is closed. An electric current flows
through the contacts and the spring to the coils, and the soft iron cores become
magnetized. The cores attract the iron armature, which moves toward the electromagnet, causing the hammer to strike the bell. As the hammer strikes the bell,
the movement of the armature opens the contacts. The electric current stops
flowing to the coils and the soft iron cores become demagnetized, releasing the
armature. A spring pulls the armature back to re-establish contact, thereby completing the circuit, and the entire cycle begins again. Small sparks, evidence of
charge jumping across the gap, can be observed at the contact points as the circuit is alternately completed and broken.
Try This
Activity
Testing an Electromagnet
Perform an activity in which you can use an electromagnet to lift iron
objects, such as washers. The coil of the electromagnet can be connected to a variable DC power supply. Remember not to leave the current flowing for more than a few seconds at a time. Test the
electromagnet both with and without the core, and with various currents
and numbers of loops. Summarize your findings in tabular form.
Practice
Understanding Concepts
Answers
4. Figure 11 shows coils of wire wound on cardboard cylinders. Copy
the diagrams into your notebook, and on each diagram mark the
direction of electric current, the direction of the field lines at each end
of the coil, and the N-pole and S-pole of the coil.
5. (a) 60.0 N
(b) 45.0 N
(c) 90.0 N
(a)
5. A coil with an iron core is used as an electromagnet. With 500 loops
and a current of 1.5 A, it can exert a lifting force of 30.0 N. What force
will it be able to lift if the following changes are made?
(a) The current is increased to 3.0 A.
(b) The number of loops is increased to 750 without increasing the
length of the coil.
(c) Both the above changes are made together.
(b)
–
+
(c)
6. In both electromagnetic relays and doorbells, soft iron cores are used
in the electromagnets. If a hard iron core is used, explain what would
happen in
(a) a relay that is used to turn a light on and off
(b) an electric bell
(d)
+
–
–
+
Figure 11
For question 4
488 Chapter 13
Making Connections
7. Describe some commercial or industrial applications in which electromagnets are better than permanent magnets. Describe some applications in which permanent magnets are better than electromagnets.
13.4
(a)
SUMMARY
The Magnetic Field of a Coil or Solenoid
• The magnetic field around a coil is the sum of the magnetic fields of each
of its segments.
• The right-hand rule for a coil states that if a coil is grasped in the right
hand with the curled fingers representing the direction of electric current,
the thumb points in the direction of the magnetic field inside the coil.
• The magnetic field strength of a coil depends on the current in the coil, the
number of loops in the coil, and the type of core material.
compass
(b)
conductor
Section 13.4 Questions
(c)
Understanding Concepts
1. Each empty circle in Figure 12 represents a compass near one
end of a coiled conductor. Redraw the diagrams, label the ends of
the coils N or S, and show the direction of the compass needle in
each case.
2. Two soft iron rods are placed inside a coiled conductor as shown
in Figure 13. Determine whether the rods will attract or repel
each other when the switch is closed.
3. Is insulation necessary for the conducting wires of a tightly
wound coil? Explain.
4. Determine the polarity of the poles of the electromagnet in
Figure 14.
5. State the relationship between the strength of the magnetic field
of a coil or solenoid and:
(a) the amount of current in the coil
(b) the number of loops in the coil
(c) the type of core material in the coil
Figure 12
For question 1
6. A coil of 600 turns, wound using 90.0 m of copper wire, is connected to a 6.0-V battery and is just able to support the weight of
a toy truck. If 200 turns are removed from the coil but the wire is
uncoiled and left in the circuit, what battery voltage would be
needed in order to support the truck?
7. Explain the series of events involved in the operation of a
doorbell.
8. The circuit for an electric bell is just a slight variation of the circuit for an electromagnetic relay. How are the circuits the same?
Describe how the circuits are different.
Figure 13
For question 2
Making Connections
9. Describe how to construct a very strong lifting electromagnet.
10. Find out more about the uses of diamagnetic and paramagnetic
materials. Write a brief report on what you discover. Follow the
links for Nelson Physics 11, 13.4.
GO TO
www.science.nelson.com
Figure 14
For question 4
Electromagnetism 489