Glossary
B-field: another term for magnetic field
Ampere’s law: the physical law that states that the magnetic field around an electric current is proportional to the current; each segment of current
produces a magnetic field like that of a long straight wire, and the total field of any shape current is the vector sum of the fields due to each
segment
Biot-Savart law: a physical law that describes the magnetic field generated by an electric current in terms of a specific equation
Curie temperature: the temperature above which a ferromagnetic material cannot be magnetized
direction of magnetic field lines: the direction that the north end of a compass needle points
domains: regions within a material that behave like small bar magnets
electromagnet: an object that is temporarily magnetic when an electrical current is passed through it
electromagnetism: the use of electrical currents to induce magnetism
ferromagnetic: materials, such as iron, cobalt, nickel, and gadolinium, that exhibit strong magnetic effects
gauss: G, the unit of the magnetic field strength; 1 G = 10–4 T
Hall effect: the creation of voltage across a current-carrying conductor by a magnetic field
Hall emf: the electromotive force created by a current-carrying conductor by a magnetic field, ε = Blv
Lorentz force: the force on a charge moving in a magnetic field
Maxwell’s equations: a set of four equations that describe electromagnetic phenomena
magnetic field lines: the pictorial representation of the strength and the direction of a magnetic field
CHAPTER 22 | MAGNETISM 801
magnetic field strength (magnitude) produced by a long straight current-carrying wire: defined as B = µ 0 I
2 πr , where I is the current, r is
the shortest distance to the wire, and µ 0 is the permeability of free space
magnetic field strength at the center of a circular loop: defined as B = µ 0 I
2 R where R is the radius of the loop
magnetic field strength inside a solenoid: defined as B = µ 0 nI where n is the number of loops per unit length of the solenoid ( n = N / l , with N being the number of loops and l the length)
magnetic field: the representation of magnetic forces
magnetic force: the force on a charge produced by its motion through a magnetic field; the Lorentz force
magnetic monopoles: an isolated magnetic pole; a south pole without a north pole, or vice versa (no magnetic monopole has ever been
observed)
magnetic resonance imaging (MRI): a medical imaging technique that uses magnetic fields create detailed images of internal tissues and organs
magnetized: to be turned into a magnet; to be induced to be magnetic
magnetocardiogram (MCG): a recording of the heart’s magnetic field as it beats
magnetoencephalogram (MEG): a measurement of the brain’s magnetic field
meter: common application of magnetic torque on a current-carrying loop that is very similar in construction to a motor; by design, the torque is
proportional to I and not θ , so the needle deflection is proportional to the current
motor: loop of wire in a magnetic field; when current is passed through the loops, the magnetic field exerts torque on the loops, which rotates a
shaft; electrical energy is converted to mechanical work in the process
north magnetic pole: the end or the side of a magnet that is attracted toward Earth’s geographic north pole
nuclear magnetic resonance (NMR): a phenomenon in which an externally applied magnetic field interacts with the nuclei of certain atoms
permeability of free space: the measure of the ability of a material, in this case free space, to support a magnetic field; the constant
µ 0 = 4π×10−7 T ⋅ m/A
right hand rule 1 (RHR-1): the rule to determine the direction of the magnetic force on a positive moving charge: when the thumb of the right hand
points in the direction of the charge’s velocity v and the fingers point in the direction of the magnetic field B , then the force on the charge is
perpendicular and away from the palm; the force on a negative charge is perpendicular and into the palm
right hand rule 2 (RHR-2): a rule to determine the direction of the magnetic field induced by a current-carrying wire: Point the thumb of the right
hand in the direction of current, and the fingers curl in the direction of the magnetic field loops
solenoid: a thin wire wound into a coil that produces a magnetic field when an electric current is passed through it
south magnetic pole: the end or the side of a magnet that is attracted toward Earth’s geographic south pole
tesla: T, the SI unit of the magnetic field strength; 1 T = 1 N
A ⋅ m
Section Summary
• Magnetism is a subject that includes the properties of magnets, the effect of the magnetic force on moving charges and currents, and the
creation of magnetic fields by currents.
• There are two types of magnetic poles, called the north magnetic pole and south magnetic pole.
• North magnetic poles are those that are attracted toward the Earth’s geographic north pole.
• Like poles repel and unlike poles attract.
• Magnetic poles always occur in pairs of north and south—it is not possible to isolate north and south poles.
22.2 Ferromagnets and Electromagnets
• Magnetic poles always occur in pairs of north and south—it is not possible to isolate north and south poles.
• All magnetism is created by electric current.
• Ferromagnetic materials, such as iron, are those that exhibit strong magnetic effects.
• The atoms in ferromagnetic materials act like small magnets (due to currents within the atoms) and can be aligned, usually in millimeter-sized
regions called domains.
• Domains can grow and align on a larger scale, producing permanent magnets. Such a material is magnetized, or induced to be magnetic.
• Above a material’s Curie temperature, thermal agitation destroys the alignment of atoms, and ferromagnetism disappears.
• Electromagnets employ electric currents to make magnetic fields, often aided by induced fields in ferromagnetic materials.
802 CHAPTER 22 | MAGNETISM
22.3 Magnetic Fields and Magnetic Field Lines
• Magnetic fields can be pictorially represented by magnetic field lines, the properties of which are as follows:
1. The field is tangent to the magnetic field line.
2. Field strength is proportional to the line density.
3. Field lines cannot cross.
4. Field lines are continuous loops.
22.4 Magnetic Field Strength: Force on a Moving Charge in a Magnetic Field
• Magnetic fields exert a force on a moving charge q, the magnitude of which is
F = qvB sin θ,
where θ is the angle between the directions of v and B .
• The SI unit for magnetic field strength B is the tesla (T), which is related to other units by
1 T = 1 N
C ⋅ m/s = 1 N
A ⋅ m.
• The direction of the force on a moving charge is given by right hand rule 1 (RHR-1): Point the thumb of the right hand in the direction of v , the
fingers in the direction of B , and a perpendicular to the palm points in the direction of F .
• The force is perpendicular to the plane formed by v and B . Since the force is zero if v is parallel to B , charged particles often follow
magnetic field lines rather than cross them.
22.5 Force on a Moving Charge in a Magnetic Field: Examples and Applications
• Magnetic force can supply centripetal force and cause a charged particle to move in a circular path of radius
r = mv
qB,
where v is the component of the velocity perpendicular to B for a charged particle with mass m and charge q .
• The Hall effect is the creation of voltage ε , known as the Hall emf, across a current-carrying conductor by a magnetic field.
• The Hall emf is given by
ε = Blv ( B, v, and l, mutually perpendicular)
for a conductor of width l through which charges move at a speed v .
22.7 Magnetic Force on a Current-Carrying Conductor
• The magnetic force on current-carrying conductors is given by F = IlB sin θ,
where I is the current, l is the length of a straight conductor in a uniform magnetic field B , and θ is the angle between I and B . The force follows RHR-1 with the thumb in the direction of I .
22.8 Torque on a Current Loop: Motors and Meters
• The torque τ on a current-carrying loop of any shape in a uniform magnetic field. is
τ = NIAB sin θ,
where N is the number of turns, I is the current, A is the area of the loop, B is the magnetic field strength, and θ is the angle between the perpendicular to the loop and the magnetic field.
22.9 Magnetic Fields Produced by Currents: Ampere’s Law
• The strength of the magnetic field created by current in a long straight wire is given by
B = µ 0 I
2 πr (long straight wire) ,
where I is the current, r is the shortest distance to the wire, and the constant µ 0 = 4π × 10−7 T ⋅ m/A is the permeability of free space.
• The direction of the magnetic field created by a long straight wire is given by right hand rule 2 (RHR-2): Point the thumb of the right hand in the
direction of current, and the fingers curl in the direction of the magnetic field loops created by it.
• The magnetic field created by current following any path is the sum (or integral) of the fields due to segments along the path (magnitude and
direction as for a straight wire), resulting in a general relationship between current and field known as Ampere’s law.
• The magnetic field strength at the center of a circular loop is given by
B = µ 0 I
2 R (at center of loop) ,
where R is the radius of the loop. This equation becomes B = µ 0 nI / (2 R) for a flat coil of N loops. RHR-2 gives the direction of the field about the loop. A long coil is called a solenoid.
• The magnetic field strength inside a solenoid is
B = µ 0 nI (inside a solenoid) ,
where n is the number of loops per unit length of the solenoid. The field inside is very uniform in magnitude and direction.
22.10 Magnetic Force between Two Parallel Conductors
CHAPTER 22 | MAGNETISM 803
• The force between two parallel currents I 1 and I 2 , separated by a distance r , has a magnitude per unit length given by
Fl = µ 0 I 1 I 2
2 πr .
• The force is attractive if the currents are in the same direction, repulsive if they are in opposite directions.
22.11 More Applications of Magnetism
• Crossed (perpendicular) electric and magnetic fields act as a velocity filter, giving equal and opposite forces on any charge with velocity
perpendicular to the fields and of magnitude
v = EB.
Conceptual Questions
1. Volcanic and other such activity at the mid-Atlantic ridge extrudes material to fill the gap between separating tectonic plates associated with
continental drift. The magnetization of rocks is found to reverse in a coordinated manner with distance from the ridge. What does this imply about the
Earth’s magnetic field and how could the knowledge of the spreading rate be used to give its historical record?
22.3 Magnetic Fields and Magnetic Field Lines
2. Explain why the magnetic field would not be unique (that is, not have a single value) at a point in space where magnetic field lines might cross.
(Consider the direction of the field at such a point.)
3. List the ways in which magnetic field lines and electric field lines are similar. For example, the field direction is tangent to the line at any point in
space. Also list the ways in which they differ. For example, electric force is parallel to electric field lines, whereas magnetic force on moving charges
is perpendicular to magnetic field lines.
4. Noting that the magnetic field lines of a bar magnet resemble the electric field lines of a pair of equal and opposite charges, do you expect the
magnetic field to rapidly decrease in strength with distance from the magnet? Is this consistent with your experience with magnets?
5. Is the Earth’s magnetic field parallel to the ground at all locations? If not, where is it parallel to the surface? Is its strength the same at all locations?
If not, where is it greatest?
22.4 Magnetic Field Strength: Force on a Moving Charge in a Magnetic Field
6. If a charged particle moves in a straight line through some region of space, can you say that the magnetic field in that region is necessarily zero?
22.5 Force on a Moving Charge in a Magnetic Field: Examples and Applications
7. How can the motion of a charged particle be used to distinguish between a magnetic and an electric field?
8. High-velocity charged particles can damage biological cells and are a component of radiation exposure in a variety of locations ranging from
research facilities to natural background. Describe how you could use a magnetic field to shield yourself.
9. If a cosmic ray proton approaches the Earth from outer space along a line toward the center of the Earth that lies in the plane of the equator, in
what direction will it be deflected by the Earth’s magnetic field? What about an electron? A neutron?
10. What are the signs of the charges on the particles in Figure 22.46?
Figure 22.46
11. Which of the particles in Figure 22.47 has the greatest velocity, assuming they have identical charges and masses?
Figure 22.47
12. Which of the particles in Figure 22.47 has the greatest mass, assuming all have identical charges and velocities?
804 CHAPTER 22 | MAGNETISM
13. While operating, a high-precision TV monitor is placed on its side during maintenance. The image on the monitor changes color and blurs slightly.
Discuss the possible relation of these effects to the Earth’s magnetic field.
14. Discuss how the Hall effect could be used to obtain information on free charge density in a conductor. (Hint: Consider how drift velocity and
current are related.)
22.7 Magnetic Force on a Current-Carrying Conductor
15. Draw a sketch of the situation in Figure 22.30 showing the direction of electrons carrying the current, and use RHR-1 to verify the direction of the force on the wire.
16. Verify that the direction of the force in an MHD drive, such as that in Figure 22.32, does not depend on the sign of the charges carrying the current across the fluid.
17. Why would a magnetohydrodynamic drive work better in ocean water than in fresh water? Also, why would superconducting magnets be
desirable?
18. Which is more likely to interfere with compass readings, AC current in your refrigerator or DC current when you start your car? Explain.
22.8 Torque on a Current Loop: Motors and Meters
19. Draw a diagram and use RHR-1 to show that the forces on the top and bottom segments of the motor’s current loop in Figure 22.34 are vertical and produce no torque about the axis of rotation.
22.9 Magnetic Fields Produced by Currents: Ampere’s Law
20. Make a drawing and use RHR-2 to find the direction of the magnetic field of a current loop in a motor (such as in Figure 22.34). Then show that the direction of the torque on the loop is the same as produced by like poles repelling and unlike poles attracting.
22.10 Magnetic Force between Two Parallel Conductors
21. Is the force attractive or repulsive between the hot and neutral lines hung from power poles? Why?
22. If you have three parallel wires in the same plane, as in Figure 22.48, with currents in the outer two running in opposite directions, is it possible for the middle wire to be repelled by both? Attracted by both? Explain.
Figure 22.48 Three parallel coplanar wires with currents in the outer two in opposite directions.
23. Suppose two long straight wires run perpendicular to one another without touching. Does one exert a net force on the other? If so, what is its
direction? Does one exert a net torque on the other? If so, what is its direction? Justify your responses by using the right hand rules.
24. Use the right hand rules to show that the force between the two loops in Figure 22.49 is attractive if the currents are in the same direction and repulsive if they are in opposite directions. Is this consistent with like poles of the loops repelling and unlike poles of the loops attracting? Draw
sketches to justify your answers.
CHAPTER 22 | MAGNETISM 805
Figure 22.49 Two loops of wire carrying currents can exert forces and torques on one another.
25. If one of the loops in Figure 22.49 is tilted slightly relative to the other and their currents are in the same direction, what are the directions of the torques they exert on each other? Does this imply that the poles of the bar magnet-like fields they create will line up with each other if the loops are
allowed to rotate?
26. Electric field lines can be shielded by the Faraday cage effect. Can we have magnetic shielding? Can we have gravitational shielding?
22.11 More Applications of Magnetism
27. Measurements of the weak and fluctuating magnetic fields associated with brain activity are called magnetoencephalograms (MEGs). Do the
brain’s magnetic fields imply coordinated or uncoordinated nerve impulses? Explain.
28. Discuss the possibility that a Hall voltage would be generated on the moving heart of a patient during MRI imaging. Also discuss the same effect
on the wires of a pacemaker. (The fact that patients with pacemakers are not given MRIs is significant.)
29. A patient in an MRI unit turns his head quickly to one side and experiences momentary dizziness and a strange taste in his mouth. Discuss the
possible causes.
30. You are told that in a certain region there is either a uniform electric or magnetic field. What measurement or observation could you make to
determine the type? (Ignore the Earth’s magnetic field.)
31. An example of magnetohydrodynamics (MHD) comes from the flow of a river (salty water). This fluid interacts with the Earth’s magnetic field to
produce a potential difference between the two river banks. How would you go about calculating the potential difference?
32. Draw gravitational field lines between 2 masses, electric field lines between a positive and a negative charge, electric field lines between 2
positive charges and magnetic field lines around a magnet. Qualitatively describe the differences between the fields and the entities responsible for
the field lines.
806 CHAPTER 22 | MAGNETISM
Problems & Exercises
10. An electron moving at 4.00×103 m/s in a 1.25-T magnetic field
experiences a magnetic force of 1.40×10−16 N . What angle does the
22.4 Magnetic Field Strength: Force on a Moving
velocity of the electron make with the magnetic field? There are two
answers.
1. What is the direction of the magnetic force on a positive charge that
11. (a) A physicist performing a sensitive measurement wants to limit the
moves as shown in each of the six cases shown below?
magnetic force on a moving charge in her equipment to less than
1.00×10−12 N . What is the greatest the charge can be if it moves at a
maximum speed of 30.0 m/s in the Earth’s field? (b) Discuss whether it
would be difficult to limit the charge to less than the value found in (a) by
comparing it with typical static electricity and noting that static is often
absent.
Figure 22.50
22.5 Force on a Moving Charge in a Magnetic Field:
2. Repeat Exercise 22.1 for a negative charge.
3. What is the direction of the velocity of a negative charge that
experiences the magnetic force shown in each of the three cases in
If you need additional support for these problems, see More