Grade 12 Unit 8
Grade 12 Unit 8
SCIENCE 1208 MAGNETISM
CONTENTS I. FIELDS AND FORCES. . . . . . . . . . . . . . . . . . .
2
FIELDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . FORCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 5
II. ELECTROMAGNETISM . . . . . . . . . . . . . . . . .
11
THE ELECTROMAGNETIC FIELD . . . . . . . . . . . . . . . . . . . . CURRENTS AND MAGNETISM . . . . . . . . . . . . . . . . . . . . . . ELECTROMAGNETIC INDUCTION . . . . . . . . . . . . . . . . . . . .
11 12 15
III. ELECTRON BEAMS . . . . . . . . . . . . . . . . . . . . .
21
MAGNETIC DEFLECTION . . . . . . . . . . . . . . . . . . . . . . . . . . THE CATHODE-RAY TUBE . . . . . . . . . . . . . . . . . . . . . . . . .
21 22
GLOSSARY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
Author:
James T. Coleman, Ph.D.
Editor:
Alan Christopherson, M.S.
Illustrations:
Alpha Omega Graphics
804 N. 2nd Ave. E., Rock Rapids, IA 51246-1759 © MM by Alpha Omega Publications, Inc. All rights reserved. LIFEPAC is a registered trademark of Alpha Omega Publications, Inc.
All trademarks and/or service marks referenced in this material are the property of their respective owners. Alpha Omega Publications, Inc. makes no claim of ownership to any trademarks and/or service marks other than their own and their affiliates’, and makes no claim of affiliation to any companies whose trademarks may be listed in this material, other than their own.
MAGNETISM Science LIFEPAC® 1207 dealt with the nature of electric current and was the second unit on electrophysics: the relation of the electrical nature of matter to physical systems. Science LIFEPAC 1208 will deal with the force laws for natural and man-made magnets, and with the subject of electromagnetism. The flow of the electrical charge is a current; when the current flows, a magnetic field is created. You will see that understanding of electromagnetism is being used daily, often without our knowledge. Electromagnetism generates the power that comes to our homes, and electromagnetic transformers send it from the generators over long distances to our homes. The laws of electromagnetic induction are so regular that an entire power distribution system may be designed for a city, including generators
and transformers; and its performance would be predictable before a single wire is connected. Such is the regularity of these electromagnetic laws. This LIFEPAC will introduce you to the electromagnetic world that the Lord has provided. God has power-generating stations around the earth in the upper regions of the ionosphere, about 100 kilometers above the earth’s surface. Above the equator the equatorial electrojet uses the tidal motion of the atmosphere to generate a 100,000 ampere current in that region. This electrojet is part of His invisible creation. Colossians 1:16 credits God with all Creation, which certainly includes electricity. We cannot see the flow of electrons, but we can the flow’s effect, including magnetism and electromagnetism.
OBJECTIVES Read these objectives. The objectives tell you what you will be able to do when you have successfully completed this LIFEPAC. When you have finished this LIFEPAC, you should be able to: 1.
Sketch various magnetic fields.
2.
Write the force law for magnetic pole interactions.
3.
Describe forces on charges in magnetic fields.
4.
Explain how electric and magnetic field effects interact.
5.
Describe the application of electromagnetic induction.
6.
Interpret electric and magnetic deflection of electron beams.
7.
Explain the operating principles of a cathode ray tube (CRT).
Survey the LIFEPAC. Ask yourself some questions about this study. Write your questions here.
1
I. FIELDS AND FORCES Magnetic fields are around us everywhere. The earth’s magnetic field is with us wherever we go, as is the gravitational field. We are more aware of the force of gravity, without which we could not walk across the street. The forces due to a magnetic field are more subtle, and we are exposed to these every day. When we walk under electrical power lines, we are exposed to both alternating magnetic
fields and the earth’s magnetic field. The effects of these fields on the body are not well understood, but their effects on electrical conductors and on currents of electrical charge are well known. This section will introduce the laws for forces between magnetic poles (magnets), and the forces on moving electrical charges in magnetic fields.
SECTION OBJECTIVES Review these objectives. When you have completed this section, you should be able to: 1.
Sketch various magnetic fields.
2.
Write the force law for magnetic pole interactions.
3.
Describe forces on charges in magnetic fields.
VOCABULARY Study these words to enhance your learning success in this section. aurora borealis
ionosphere
magnetic pole
electrojet
left hand rule
solenoid
field line
magnetic field
FIELDS The region around a magnetic pole (magnet) in which a bit of iron experiences a force is called a magnetic field. It is the magnet’s “sphere of influence.” The magnetic field has direction, as defined by the force on a test north pole at any point in the field. The path followed by the test north pole describes a magnetic line of force, or a magnetic field line. Magnetic fields, such as the earth’s magnetic field, occur in nature and around such man-made objects as the bar magnet and the solenoid.
N. Magnetic Pole
S. Geographic Pole
Natural fields. Magnets have been known to man since the dawn of history. They were probably first regarded with an air of mystery; later they were used as navigational tools. The earth’s magnetic field is used as a direction-finding aid. Suspended magnetic needles, acting as compasses, follow the direction of the earth’s field lines.
N. Geographic Pole
S. Magnetic Pole
The magnetic field of the earth extends from the center of the earth, up through the oceans, and
2
into outer space. It influences the outer atmosphere in particular (the ionosphere) and has a strong influence on the flow of currents in that region. At great distances from the earth, the earth’s magnetic field controls the flow of electrical currents that come from the surface of the sun. The current systems closer to the earth are called electrojets. One exists in the region near the North Pole and is called the auroral electrojet, which helps to produce the northern lights of high latitudes. Another high current system is near the equator and is called the equatorial electrojet. Both current systems are controlled and, to a degree, are generated by the earth’s magnetic field. An estimated 1 million amperes of current flow every night in the auroral electrojet. The Inuit depend upon the northern lights to enable them to see at night. The northern lights (aurora borealis) are a marvelous display of multicolored and beautifully formed sheets of light in the sky. Currents from outer space funnel down the earth’s magnetic field lines to form these beautiful displays. Thus the natural magnetic field of the earth has a profound influence on nature and the outer atmosphere. You will study this field and will discover some of its properties and attributes.
toward the earth’s north pole. The poles behave somewhat like electric charges: Like poles repel and unlike poles attract. The form of the magnetic field around a bar magnet will be found by experiments you will perform. The direction of the field lines can be traced and will generally be considered to “flow” from the north pole outside the magnet to the south pole. In other words, the presence of a magnetic field is sensed by a test north pole. The similarity to the case of two opposite electric charges ends at this point, because when a bar magnet is cut in half, two new smaller magnets are formed, each complete with a north pole and a south pole. A magnetic field is formed when a current flows in a wire. A compass brought near a current-carrying wire will align itself as shown in Figure 1.
Man-made fields. A simple example of a man-made magnetic field is the bar magnet. The magnet has two poles. The pole that points toward the earth’s north pole is termed the north-seeking pole, or simply the north pole, of the magnet. If the magnet is floated in water on a piece of cork, it will again align itself with the earth’s field, with its north pole pointing
The magnetic field B will form as indicated by the compass needle’s direction. The needle aligns with the magnetic field. When the wire is wound into a coil, the fields around the wires add to form a solenoid. A solenoid is a coil of wire designed to produce a magnetic field by means of a current passed through its windings. The field around the solenoid will be similar to the one around a bar magnet, with north and south poles as shown. This field is termed an electromagnet. Increasing the electric current will produce a stronger magnetic field.
A
I B compass
FIGURE 1
S I
e–
B
B a. Bar Magnet Field
b. Bar Magnet Cut in Half
N
BAR MAGNET FIELDS
3
✍
Choose the correct answer.
1.1
.
The earth’s magnetic field extends
1.2
a.
from the earth’s surface to the upper atmosphere
b.
from the center of the earth to the sun
c.
from the earth’s core to outer space
The earth’s magnetic field captures the flow of current from
1.3
a.
the moon
c. the sun
b.
Saturn
d. the center of the earth
High natural currents flow above the earth’s atmosphere in
1.4
a.
the aurora
c. outer space
b.
upper clouds
d. the asthenosphere
Two north poles will
1.5
.
.
a.
attract each other
c. experience neither attraction nor repulsion
b.
repel each other
d. cancel each other .
A north compass needle points to the
1.6
.
a.
north magnetic pole
c. north geographic pole
b.
south magnetic pole
d. south geographic pole
The field around a solenoid is a.
similar to a bar magnet
b.
unipolar
. c. nonsymmetical
Try this activity to investigate the nature of magnetic fields.
These supplies are needed: 2 bar magnets 3 sheets of stiff cardboard iron filings
✍
Follow these directions and complete the activities. Place a check in the box after each step is completed.
❏ 1. Place the sheet of stiff cardboard over one of the bar magnets so that the cardboard is level. ❏ 2. Sprinkle the iron filings on the cardboard. ❏ 3. Tap the cardboard to help the filings align with the magnetic field lines. 1.7
Sketch the magnetic field lines or take a Polaroid™ photograph.
1.8
Indicate where the magnetic field lines appear to be concentrated.
❏ ❏ ❏ ❏
4. Place the north pole of one magnet 1 inch from the south pole of the other magnet. 5. Place the second cardboard over the two magnets. 6. Sprinkle iron filings on the cardboard. 7. Tap the cardboard.
1.9
Sketch the field lines or take a Polaroid™ photograph.
1.10
Indicate where the magnetic field lines appear to be concentrated.
4
❏ ❏ ❏ ❏
8. Place the north pole of one magnet 2 inches away from the north pole of the second magnet. 9. Place the third cardboard over the two magnets. 10. Sprinkle iron filings on the cardboard. 11. Tap the cardboard.
1.11
Sketch the field lines or take a Polaroid™ photograph.
1.12
Indicate the concentration of field lines and where the field lines seem to be opposing rather than adding.
✍
Answer these questions.
1.13
Where are the magnetic field lines concentrated in Activity 1.7?
1.14
Are the magnetic field lines continuous between the poles in Activity 1.9?
1.15
Are the lines of force continuous between the poles in Activity 1.11?
Without the magnet, the filings are without any order. When the magnet is brought near, the filings themselves become little magnets, having magnetism induced into them. The filings have north poles and south poles, similar to the big bar magnet. FORCES Forces are pushes and pulls. Magnets both attract and repel each other through empty space. Magnetism is one of the three forces that operate without an intervening medium, the others being gravity and electrostatics. Magnets also produce currents in conductors and exert forces on current-carrying conductors.
south magnet pairs are formed. Each will be similar to the unbroken magnet. A force of attraction exists between the two magnet halves. The unlike poles (north and south) of the two magnet ends will attract each other. Individual magnetic poles cannot exist. A north pole cannot exist without a corresponding south pole. In other words, a separate north pole cannot be moved completely away from its south pole. The two opposite poles always exist in pairs. The force of attraction between two magnetic poles is expressed in a form similar to Coulomb’s law:
Forces of attraction or repulsion. The laws of attraction and repulsion for magnetic poles are similar to Coulomb’s law for electrical charges. The force will be repulsive if the poles are alike, and will be attractive for dissimilar poles. An example is the splitting of a bar magnet. When a bar magnet is cut in half, two new north-
FM = K M1M2 r2 M1 is the strength of magnetic pole M1, M2 is the strength of magnetic pole M2, r is the separation between M1 and M2, and K is a constant that is dependent upon the units used in the formula (usually the metric system). The sign of the pole is used in the formula, as in Coulomb’s law. Like poles repel and unlike poles attract. The product of M1 and M2 will be negative for attraction and positive for repulsion, similar to Coulomb’s law.
5
If the distance between the two poles is cut in half the force FM will be increased four times, the result of the inverse square relationship in the formula. Similarly, if we cause the distance between two magnetic poles to be tripled, the force between them will be reduced to one-ninth of its previous value.
(positive) charge flow. The force, or thrust, is then in the direction of the thumb. (Note: If electron flow is considered instead, v is reversed, q is then negative, which gives the same direction for F.)
F The Biot-Savart force law. Consider an electric charge in motion in a magnetic field. The moving charge will experience a magnetic force FM. The magnitude of the force will depend on the magnitude of the charge, its velocity, and the direction in which the charge moves relative to the field direction. Experiments determine the relationship between these quantities. B B v
q
FM = O v
LEFT HAND RULE
Another way to remember the directions is the motion for turning a right-hand screw. ZERO FORCE CONDITION A charge q moving parallel to the field experiences no force because no field lines are crossed. If the opposite condition is chosen and a charge is moved normal to the field lines, the force on the charge is the maximum force Fmax.
v
screw
B
a.
B
b. v
B FIGURE 2 v
FM = Fmax
In Figure 2a the velocity of the positive conventional charge flow is in the direction of v, and the magnetic field is in the direction B. If we arrange the velocity of vector v (translate it to just meet B) as shown in Figure 2b, then a screw turned the clockwise direction formed by v and B would move into the paper, the force being into the paper in agreement with the left-hand rule. The vectors v and B in the figure define a plane. Vectors in a plane can always be translated in position (but not in direction) so that they will meet at some point in the plane. The direction of the force will then be perpendicular to this x-y plane, as indicated above. If the vectors v and B are not perpendicular to each other but pass through the same point, the rule can still be applied.
q
MAXIMUM FORCE CONDITION The force FM will be perpendicular to both the directions of the velocity v and the field B. The magnitude of the force FM is given by Fmax = qvB The direction of the force can be found by using the left-hand rule. To use the left-hand rule, align the first finger of the left hand with the field and the second finger with the speed of a conventional
6
B is the magnetic field, L is the length of wire, and I is the current in wire. The force F will be in a direction found from using the left-hand rule: It results from the flow of electrical charge perpendicular to the magnetic field. The geometry for the force on the wire is given in Figure 4.
v B
a.
B b.
v 0
F
FM Fmax
I FIGURE 3: NONPERPENDICULAR CASE In Figure 3a velocity v is not perpendicular to the field B. In Figure 3b the vectors can be made to intersect at a point, but the angle θ between them is not 90°. To find the equivalent of mutually perpendicular v and B vectors, multiply by the sine of the angle θ . The force will then be indicated:
B
FM = qvB sin θ FIGURE 4
This more general form of the Biot-Savart force law will apply to all velocity and field directions. If the velocity is in the same direction as the field, then the force FM is zero, since θ would be zero and the sine of θ is zero. The formula Fmax given previously assumes θ is 90°, a condition giving the maximum force. The preceding expression for FM is the more general case. The force on a long, straight, current-carrying wire in a magnetic field B is given by
Apply the left-hand rule to this figure, and the force FM will be in the direction shown. If the magnetic field is not perpendicular to the current in the wire, the force will be given by FM = B L I sin θ where θ is the angle between the vectors I and B, as before.
FM = B I L.
✍
Complete these sentences. .
1.16
The laws of attraction and repulsion for magnetic poles are similar in form to
1.17
The force between two magnetic poles is repulsive if the poles are
1.18
A bar magnet cut in half will form a total of
1.19
The equation that relates two poles to the force between them and their separation is the square law.
1.20
The Biot-Savart force law predicts the force on a charge moving perpendicular to a field.
1.21
The left-hand rule uses the thumb to predict the direction of a charge moving in a magnetic field.
1.22
If the velocity of a charge is parallel to the magnetic field, the force will be
1.23
The force on a straight current-carrying wire in a magnetic field is proportional to the current in the wire, the strength of the field, and the of the wire.
7
.
poles.
on a positive .
✍
1.24
Choose the correct answer. A magnetic field applies forces on
.
a. static charges
c. water flow
b. moving charges 1.25
Magnetic poles cannot be
.
a. isolated
c. relocated
b. canceled
✍ 1.26
Complete this activity. The formulas F = qvB and F = BIL both deal with moving charges in a wire. Start with F = qvB and derive F = BIL. [Hint: v = d/t]
Review the material in this section in preparation for the Self Test. This Self Test will check your mastery of this particular section. The items missed on this Self Test will indicate specific areas where restudy is needed for mastery.
8
SELF TEST 1 Answer true or false (each answer, 1 point). 1.01
Man first regarded magnets with mystery, but later used them as navigation tools.
1.02
The earth’s magnetic field extends from the center of the earth to outer space.
1.03
Like magnetic poles attract.
1.04
A bar magnet cut in half will yield two complete bar magnets.
1.05
A current-carrying wire is surrounded by a magnetic field.
1.06
The field around a solenoid is similar to the field around a bar magnet.
1.07
The force between two magnetic poles varies directly with the distance of separation.
1.08
A charged particle moving parallel to a magnetic field line will experience no force.
1.09
The left-hand rule predicts the direction of force on a positively charged object moving in a magnetic field.
1.010
The Biot-Savart force law does not apply if the velocity is parallel to the field direction.
Choose the correct answer (each answer, 2 points). 1.011
A positive charge q moves with velocity v in the z direction through a magnetic field whose vector is in the x direction. y -z B
-x
x
z v -y The force FM will be in the
1.012
1.013
.
a. positive-y direction
c. positive-z direction
b. negative-z direction
d. positive-x direction
If the charge is negative and it moves in the negative-z direction, the force on the charge will be . a. reversed
c. zero
b. unchanged
d. increased
In the formula FM = K M1M2 r2 r is the distance
.
a. from the north pole
c. from M1 to the nearest magnetic body
b. between poles M1 and M2
d. between the magnetic lines of force
9
1.014
1.015
A solenoid field is
.
a. never zero
c. increased with an increased current flow
b. located outside the coil only
d. entirely within the coil .
A bar magnet’s field is maintained by a. microscope currents
c. a difference in temperature between north and south poles
b. orientation with the earth’s field
d. the lines of force
Complete these sketches (each answer, 5 points). 1.016
Sketch the magnetic field lines for the two magnets.
S
1.017
N
S
N
Sketch the magnetic field lines around the two magnets.
N
S
S
N
Score Adult check
24 30
______________________ Initial
10
Date
SCIENCE 1208 MAGNETISM
CONTENTS I. FIELDS AND FORCES. . . . . . . . . . . . . . . . . . .
2
FIELDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . FORCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 5
II. ELECTROMAGNETISM . . . . . . . . . . . . . . . . .
11
THE ELECTROMAGNETIC FIELD . . . . . . . . . . . . . . . . . . . . CURRENTS AND MAGNETISM . . . . . . . . . . . . . . . . . . . . . . ELECTROMAGNETIC INDUCTION . . . . . . . . . . . . . . . . . . . .
11 12 15
III. ELECTRON BEAMS . . . . . . . . . . . . . . . . . . . . .
21
MAGNETIC DEFLECTION . . . . . . . . . . . . . . . . . . . . . . . . . . THE CATHODE-RAY TUBE . . . . . . . . . . . . . . . . . . . . . . . . .
21 22
GLOSSARY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
Author:
James T. Coleman, Ph.D.
Editor:
Alan Christopherson, M.S.
Illustrations:
Alpha Omega Graphics
804 N. 2nd Ave. E., Rock Rapids, IA 51246-1759 © MM by Alpha Omega Publications, Inc. All rights reserved. LIFEPAC is a registered trademark of Alpha Omega Publications, Inc.
All trademarks and/or service marks referenced in this material are the property of their respective owners. Alpha Omega Publications, Inc. makes no claim of ownership to any trademarks and/or service marks other than their own and their affiliates’, and makes no claim of affiliation to any companies whose trademarks may be listed in this material, other than their own.
MAGNETISM Science LIFEPAC® 1207 dealt with the nature of electric current and was the second unit on electrophysics: the relation of the electrical nature of matter to physical systems. Science LIFEPAC 1208 will deal with the force laws for natural and man-made magnets, and with the subject of electromagnetism. The flow of the electrical charge is a current; when the current flows, a magnetic field is created. You will see that understanding of electromagnetism is being used daily, often without our knowledge. Electromagnetism generates the power that comes to our homes, and electromagnetic transformers send it from the generators over long distances to our homes. The laws of electromagnetic induction are so regular that an entire power distribution system may be designed for a city, including generators
and transformers; and its performance would be predictable before a single wire is connected. Such is the regularity of these electromagnetic laws. This LIFEPAC will introduce you to the electromagnetic world that the Lord has provided. God has power-generating stations around the earth in the upper regions of the ionosphere, about 100 kilometers above the earth’s surface. Above the equator the equatorial electrojet uses the tidal motion of the atmosphere to generate a 100,000 ampere current in that region. This electrojet is part of His invisible creation. Colossians 1:16 credits God with all Creation, which certainly includes electricity. We cannot see the flow of electrons, but we can the flow’s effect, including magnetism and electromagnetism.
OBJECTIVES Read these objectives. The objectives tell you what you will be able to do when you have successfully completed this LIFEPAC. When you have finished this LIFEPAC, you should be able to: 1.
Sketch various magnetic fields.
2.
Write the force law for magnetic pole interactions.
3.
Describe forces on charges in magnetic fields.
4.
Explain how electric and magnetic field effects interact.
5.
Describe the application of electromagnetic induction.
6.
Interpret electric and magnetic deflection of electron beams.
7.
Explain the operating principles of a cathode ray tube (CRT).
Survey the LIFEPAC. Ask yourself some questions about this study. Write your questions here.
1
I. FIELDS AND FORCES Magnetic fields are around us everywhere. The earth’s magnetic field is with us wherever we go, as is the gravitational field. We are more aware of the force of gravity, without which we could not walk across the street. The forces due to a magnetic field are more subtle, and we are exposed to these every day. When we walk under electrical power lines, we are exposed to both alternating magnetic
fields and the earth’s magnetic field. The effects of these fields on the body are not well understood, but their effects on electrical conductors and on currents of electrical charge are well known. This section will introduce the laws for forces between magnetic poles (magnets), and the forces on moving electrical charges in magnetic fields.
SECTION OBJECTIVES Review these objectives. When you have completed this section, you should be able to: 1.
Sketch various magnetic fields.
2.
Write the force law for magnetic pole interactions.
3.
Describe forces on charges in magnetic fields.
VOCABULARY Study these words to enhance your learning success in this section. aurora borealis
ionosphere
magnetic pole
electrojet
left hand rule
solenoid
field line
magnetic field
FIELDS The region around a magnetic pole (magnet) in which a bit of iron experiences a force is called a magnetic field. It is the magnet’s “sphere of influence.” The magnetic field has direction, as defined by the force on a test north pole at any point in the field. The path followed by the test north pole describes a magnetic line of force, or a magnetic field line. Magnetic fields, such as the earth’s magnetic field, occur in nature and around such man-made objects as the bar magnet and the solenoid.
N. Magnetic Pole
S. Geographic Pole
Natural fields. Magnets have been known to man since the dawn of history. They were probably first regarded with an air of mystery; later they were used as navigational tools. The earth’s magnetic field is used as a direction-finding aid. Suspended magnetic needles, acting as compasses, follow the direction of the earth’s field lines.
N. Geographic Pole
S. Magnetic Pole
The magnetic field of the earth extends from the center of the earth, up through the oceans, and
2
into outer space. It influences the outer atmosphere in particular (the ionosphere) and has a strong influence on the flow of currents in that region. At great distances from the earth, the earth’s magnetic field controls the flow of electrical currents that come from the surface of the sun. The current systems closer to the earth are called electrojets. One exists in the region near the North Pole and is called the auroral electrojet, which helps to produce the northern lights of high latitudes. Another high current system is near the equator and is called the equatorial electrojet. Both current systems are controlled and, to a degree, are generated by the earth’s magnetic field. An estimated 1 million amperes of current flow every night in the auroral electrojet. The Inuit depend upon the northern lights to enable them to see at night. The northern lights (aurora borealis) are a marvelous display of multicolored and beautifully formed sheets of light in the sky. Currents from outer space funnel down the earth’s magnetic field lines to form these beautiful displays. Thus the natural magnetic field of the earth has a profound influence on nature and the outer atmosphere. You will study this field and will discover some of its properties and attributes.
toward the earth’s north pole. The poles behave somewhat like electric charges: Like poles repel and unlike poles attract. The form of the magnetic field around a bar magnet will be found by experiments you will perform. The direction of the field lines can be traced and will generally be considered to “flow” from the north pole outside the magnet to the south pole. In other words, the presence of a magnetic field is sensed by a test north pole. The similarity to the case of two opposite electric charges ends at this point, because when a bar magnet is cut in half, two new smaller magnets are formed, each complete with a north pole and a south pole. A magnetic field is formed when a current flows in a wire. A compass brought near a current-carrying wire will align itself as shown in Figure 1.
Man-made fields. A simple example of a man-made magnetic field is the bar magnet. The magnet has two poles. The pole that points toward the earth’s north pole is termed the north-seeking pole, or simply the north pole, of the magnet. If the magnet is floated in water on a piece of cork, it will again align itself with the earth’s field, with its north pole pointing
The magnetic field B will form as indicated by the compass needle’s direction. The needle aligns with the magnetic field. When the wire is wound into a coil, the fields around the wires add to form a solenoid. A solenoid is a coil of wire designed to produce a magnetic field by means of a current passed through its windings. The field around the solenoid will be similar to the one around a bar magnet, with north and south poles as shown. This field is termed an electromagnet. Increasing the electric current will produce a stronger magnetic field.
A
I B compass
FIGURE 1
S I
e–
B
B a. Bar Magnet Field
b. Bar Magnet Cut in Half
N
BAR MAGNET FIELDS
3
✍
Choose the correct answer.
1.1
.
The earth’s magnetic field extends
1.2
a.
from the earth’s surface to the upper atmosphere
b.
from the center of the earth to the sun
c.
from the earth’s core to outer space
The earth’s magnetic field captures the flow of current from
1.3
a.
the moon
c. the sun
b.
Saturn
d. the center of the earth
High natural currents flow above the earth’s atmosphere in
1.4
a.
the aurora
c. outer space
b.
upper clouds
d. the asthenosphere
Two north poles will
1.5
.
.
a.
attract each other
c. experience neither attraction nor repulsion
b.
repel each other
d. cancel each other .
A north compass needle points to the
1.6
.
a.
north magnetic pole
c. north geographic pole
b.
south magnetic pole
d. south geographic pole
The field around a solenoid is a.
similar to a bar magnet
b.
unipolar
. c. nonsymmetical
Try this activity to investigate the nature of magnetic fields.
These supplies are needed: 2 bar magnets 3 sheets of stiff cardboard iron filings
✍
Follow these directions and complete the activities. Place a check in the box after each step is completed.
❏ 1. Place the sheet of stiff cardboard over one of the bar magnets so that the cardboard is level. ❏ 2. Sprinkle the iron filings on the cardboard. ❏ 3. Tap the cardboard to help the filings align with the magnetic field lines. 1.7
Sketch the magnetic field lines or take a Polaroid™ photograph.
1.8
Indicate where the magnetic field lines appear to be concentrated.
❏ ❏ ❏ ❏
4. Place the north pole of one magnet 1 inch from the south pole of the other magnet. 5. Place the second cardboard over the two magnets. 6. Sprinkle iron filings on the cardboard. 7. Tap the cardboard.
1.9
Sketch the field lines or take a Polaroid™ photograph.
1.10
Indicate where the magnetic field lines appear to be concentrated.
4
❏ ❏ ❏ ❏
8. Place the north pole of one magnet 2 inches away from the north pole of the second magnet. 9. Place the third cardboard over the two magnets. 10. Sprinkle iron filings on the cardboard. 11. Tap the cardboard.
1.11
Sketch the field lines or take a Polaroid™ photograph.
1.12
Indicate the concentration of field lines and where the field lines seem to be opposing rather than adding.
✍
Answer these questions.
1.13
Where are the magnetic field lines concentrated in Activity 1.7?
1.14
Are the magnetic field lines continuous between the poles in Activity 1.9?
1.15
Are the lines of force continuous between the poles in Activity 1.11?
Without the magnet, the filings are without any order. When the magnet is brought near, the filings themselves become little magnets, having magnetism induced into them. The filings have north poles and south poles, similar to the big bar magnet. FORCES Forces are pushes and pulls. Magnets both attract and repel each other through empty space. Magnetism is one of the three forces that operate without an intervening medium, the others being gravity and electrostatics. Magnets also produce currents in conductors and exert forces on current-carrying conductors.
south magnet pairs are formed. Each will be similar to the unbroken magnet. A force of attraction exists between the two magnet halves. The unlike poles (north and south) of the two magnet ends will attract each other. Individual magnetic poles cannot exist. A north pole cannot exist without a corresponding south pole. In other words, a separate north pole cannot be moved completely away from its south pole. The two opposite poles always exist in pairs. The force of attraction between two magnetic poles is expressed in a form similar to Coulomb’s law:
Forces of attraction or repulsion. The laws of attraction and repulsion for magnetic poles are similar to Coulomb’s law for electrical charges. The force will be repulsive if the poles are alike, and will be attractive for dissimilar poles. An example is the splitting of a bar magnet. When a bar magnet is cut in half, two new north-
FM = K M1M2 r2 M1 is the strength of magnetic pole M1, M2 is the strength of magnetic pole M2, r is the separation between M1 and M2, and K is a constant that is dependent upon the units used in the formula (usually the metric system). The sign of the pole is used in the formula, as in Coulomb’s law. Like poles repel and unlike poles attract. The product of M1 and M2 will be negative for attraction and positive for repulsion, similar to Coulomb’s law.
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If the distance between the two poles is cut in half the force FM will be increased four times, the result of the inverse square relationship in the formula. Similarly, if we cause the distance between two magnetic poles to be tripled, the force between them will be reduced to one-ninth of its previous value.
(positive) charge flow. The force, or thrust, is then in the direction of the thumb. (Note: If electron flow is considered instead, v is reversed, q is then negative, which gives the same direction for F.)
F The Biot-Savart force law. Consider an electric charge in motion in a magnetic field. The moving charge will experience a magnetic force FM. The magnitude of the force will depend on the magnitude of the charge, its velocity, and the direction in which the charge moves relative to the field direction. Experiments determine the relationship between these quantities. B B v
q
FM = O v
LEFT HAND RULE
Another way to remember the directions is the motion for turning a right-hand screw. ZERO FORCE CONDITION A charge q moving parallel to the field experiences no force because no field lines are crossed. If the opposite condition is chosen and a charge is moved normal to the field lines, the force on the charge is the maximum force Fmax.
v
screw
B
a.
B
b. v
B FIGURE 2 v
FM = Fmax
In Figure 2a the velocity of the positive conventional charge flow is in the direction of v, and the magnetic field is in the direction B. If we arrange the velocity of vector v (translate it to just meet B) as shown in Figure 2b, then a screw turned the clockwise direction formed by v and B would move into the paper, the force being into the paper in agreement with the left-hand rule. The vectors v and B in the figure define a plane. Vectors in a plane can always be translated in position (but not in direction) so that they will meet at some point in the plane. The direction of the force will then be perpendicular to this x-y plane, as indicated above. If the vectors v and B are not perpendicular to each other but pass through the same point, the rule can still be applied.
q
MAXIMUM FORCE CONDITION The force FM will be perpendicular to both the directions of the velocity v and the field B. The magnitude of the force FM is given by Fmax = qvB The direction of the force can be found by using the left-hand rule. To use the left-hand rule, align the first finger of the left hand with the field and the second finger with the speed of a conventional
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B is the magnetic field, L is the length of wire, and I is the current in wire. The force F will be in a direction found from using the left-hand rule: It results from the flow of electrical charge perpendicular to the magnetic field. The geometry for the force on the wire is given in Figure 4.
v B
a.
B b.
v 0
F
FM Fmax
I FIGURE 3: NONPERPENDICULAR CASE In Figure 3a velocity v is not perpendicular to the field B. In Figure 3b the vectors can be made to intersect at a point, but the angle θ between them is not 90°. To find the equivalent of mutually perpendicular v and B vectors, multiply by the sine of the angle θ . The force will then be indicated:
B
FM = qvB sin θ FIGURE 4
This more general form of the Biot-Savart force law will apply to all velocity and field directions. If the velocity is in the same direction as the field, then the force FM is zero, since θ would be zero and the sine of θ is zero. The formula Fmax given previously assumes θ is 90°, a condition giving the maximum force. The preceding expression for FM is the more general case. The force on a long, straight, current-carrying wire in a magnetic field B is given by
Apply the left-hand rule to this figure, and the force FM will be in the direction shown. If the magnetic field is not perpendicular to the current in the wire, the force will be given by FM = B L I sin θ where θ is the angle between the vectors I and B, as before.
FM = B I L.
✍
Complete these sentences. .
1.16
The laws of attraction and repulsion for magnetic poles are similar in form to
1.17
The force between two magnetic poles is repulsive if the poles are
1.18
A bar magnet cut in half will form a total of
1.19
The equation that relates two poles to the force between them and their separation is the square law.
1.20
The Biot-Savart force law predicts the force on a charge moving perpendicular to a field.
1.21
The left-hand rule uses the thumb to predict the direction of a charge moving in a magnetic field.
1.22
If the velocity of a charge is parallel to the magnetic field, the force will be
1.23
The force on a straight current-carrying wire in a magnetic field is proportional to the current in the wire, the strength of the field, and the of the wire.
7
.
poles.
on a positive .
✍
1.24
Choose the correct answer. A magnetic field applies forces on
.
a. static charges
c. water flow
b. moving charges 1.25
Magnetic poles cannot be
.
a. isolated
c. relocated
b. canceled
✍ 1.26
Complete this activity. The formulas F = qvB and F = BIL both deal with moving charges in a wire. Start with F = qvB and derive F = BIL. [Hint: v = d/t]
Review the material in this section in preparation for the Self Test. This Self Test will check your mastery of this particular section. The items missed on this Self Test will indicate specific areas where restudy is needed for mastery.
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SELF TEST 1 Answer true or false (each answer, 1 point). 1.01
Man first regarded magnets with mystery, but later used them as navigation tools.
1.02
The earth’s magnetic field extends from the center of the earth to outer space.
1.03
Like magnetic poles attract.
1.04
A bar magnet cut in half will yield two complete bar magnets.
1.05
A current-carrying wire is surrounded by a magnetic field.
1.06
The field around a solenoid is similar to the field around a bar magnet.
1.07
The force between two magnetic poles varies directly with the distance of separation.
1.08
A charged particle moving parallel to a magnetic field line will experience no force.
1.09
The left-hand rule predicts the direction of force on a positively charged object moving in a magnetic field.
1.010
The Biot-Savart force law does not apply if the velocity is parallel to the field direction.
Choose the correct answer (each answer, 2 points). 1.011
A positive charge q moves with velocity v in the z direction through a magnetic field whose vector is in the x direction. y -z B
-x
x
z v -y The force FM will be in the
1.012
1.013
.
a. positive-y direction
c. positive-z direction
b. negative-z direction
d. positive-x direction
If the charge is negative and it moves in the negative-z direction, the force on the charge will be . a. reversed
c. zero
b. unchanged
d. increased
In the formula FM = K M1M2 r2 r is the distance
.
a. from the north pole
c. from M1 to the nearest magnetic body
b. between poles M1 and M2
d. between the magnetic lines of force
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1.014
1.015
A solenoid field is
.
a. never zero
c. increased with an increased current flow
b. located outside the coil only
d. entirely within the coil .
A bar magnet’s field is maintained by a. microscope currents
c. a difference in temperature between north and south poles
b. orientation with the earth’s field
d. the lines of force
Complete these sketches (each answer, 5 points). 1.016
Sketch the magnetic field lines for the two magnets.
S
1.017
N
S
N
Sketch the magnetic field lines around the two magnets.
N
S
S
N
Score Adult check
24 30
______________________ Initial
10
Date
