This document provides an overview of magnetism and magnetic fields. It begins with an introductory activity on magnetism facts. The document then outlines topics to be covered, including magnetic fields, forces on moving charges and currents, and properties of electromagnets and ferromagnets. Examples are provided to demonstrate how to calculate magnetic field strength and forces. The key points are that magnets produce magnetic fields with north and south poles; magnetic fields exert forces on moving charges; and currents generate magnetic fields according to Ampere's law.

1. Chapter 22 MAGNETISM

2. ACTIVITY!
This activity is called “Fact or Bluff”.

3. ACTIVITY!
“Magnets are surrounded by an
invisible magnetic field.”
Fact or Bluff
???

4. ACTIVITY!
“Magnets generate a contact
force.”
Fact or Bluff
???

5. ACTIVITY!
“Iron, nickel, cobalt and
gadolinium are magnetic
metals.”
Fact or Bluff
???

6. ACTIVITY!
“Earth has a magnetic core
contains iron.”
Fact or Bluff
???

7. TOPIC OUTLINE
The following topics will be covered by this module:
✓ Magnets
✓ Magnetic Fields and Magnetic Lines
✓ Force on a Moving Charge in a Magnetic Field
✓ The Hall effect
✓ Magnetic Force on a Current-carrying conductor
✓ Magnetic Fields produced by Currents: Ampere’s Law
✓ Magnetic Force between Two Parallel Conductors

8. OBJECTIVES
At the end of the lesson, students must be able to:
1. describe the interaction between poles of magnets
2. differentiate electric interactions from magnetic interactions
3. illustrate the magnetic field pattern around a bar magnet and between
the poles of two bar magnets
4. describe the motion of a charged particle in a magnetic field in terms of
its speed, and
5. evaluate the magnetic force on an arbitrary wire segment placed in a
uniform magnetic field

9. NORTHERN & SOUTHERN LIGHT
The magnificent spectacle of the Aurora Borealis, or northern lights, glows in the northern sky above Bear Lake near
Eielson Air Force Base, Alaska. Shaped by the Earth’s magnetic field, this light is produced by radiation spewed from
solar storms. (credit: Senior Airman Joshua Strang, via Flickr)

11. Shanghai Maglev Line
This is the 1st commercial maglev line in the world, which is developed by Sino-
German cooperation.

12. Instrument for magnetic resonance imaging (MRI). The device uses a superconducting
cylindrical coil for the main magnetic field. The patient goes into this “tunnel” on the
gurney. (credit: Bill McChesney, Flickr)

14. MAGNET
A magnet is any object that produces its own magnetic field. Magnets have two poles,
a north pole and a south pole. The magnetic field is represented by field lines that start
at a magnet’s North Pole and end at the South Pole.

15. THE EARTH AS A MAGNET
One end of a bar magnet is suspended from a thread that points toward north. The
magnet’s two poles are labeled N and S for north-seeking and south-seeking poles,
respectively.

16. FIGURE 22.5
Unlike poles attract, whereas like poles repel.

17. Repelling force
between the two
magnets.
Attractive force
between the two
magnets.

20. CURRENT: THE SOURCE OF ALL MAGNETISM
(a) In the planetary model of the atom, an electron orbits a nucleus, forming a closed-current loop and producing a
magnetic field with a north pole and a south pole.
(b) Electrons have spin and can be crudely pictured as rotating charge, forming a current that produces a magnetic field
with a north pole and a south pole. Neither the planetary model nor the image of a spinning electron is completely
consistent with modern physics. However, they do provide a useful way of understanding phenomena.

21. FERROMAGNETS AND ELECTROMAGNETS
There are two type of magnets—
• ferromagnets that can sustain a permanent
magnetic field, and
• electromagnets produced by the flow of
current. These magnets can be found in all
types of electronic devices.

25. (a) An unmagnetized piece of iron (or other ferromagnetic material) has randomly oriented domains.
(b) When magnetized by an external field, the domains show greater alignment, and some grow at the
expense of others. Individual atoms are aligned within domains; each atom acts like a tiny bar
magnet.

26. This OpenStax ancillary resource is © Rice University under a CC-BY 4.0 International license; it may be reproduced or modified but
must be attributed to OpenStax, Rice University and any changes must be noted. Any images credited to other sources are similarly
available for reproduction, but must be attributed to their sources.
COMBINATION OF ELECTROMAGNET AND FERROMAGNET
Combining a ferromagnet
with an electromagnet can
produce particularly
strong magnetic effects.

27. MAGNETIC FIELDS AND MAGNETIC LINES
The direction of magnetic field lines is defined to be the direction in which the north
end of a compass needle points. The magnetic field is traditionally called the B-field.
https://phet.colorado.edu/sims/cheerpj/faraday/latest/faraday.html?simu
lation=magnets-and-electromagnets

29. FORCE ON A MOVING CHARGE
How does magnet attracts one another?
The answer relies on the fact that all magnetism relies on current,
the flow of charge. Magnetic fields exert forces on moving charges,
and so they exert forces on other magnets, all of which have moving
charges.

30. RIGHT HAND RULE -1

31. RIGHT HAND RULE -1

32. RIGHT HAND RULE -1

33. QUICK NOTE ON MAGNETIC FIELDS
Magnetic Fields 𝑩 𝒕𝒆𝒔𝒍𝒂 (𝑻)
Like the electric field, the magnetic field is a 𝑽𝒆𝒄𝒕𝒐𝒓,
having both direction and magnitude
𝟏 𝒕𝒆𝒔𝒍𝒂 = 𝟏 𝑻 = 𝟏
𝑵
𝑨 ∙ 𝒎
There is another unit that is also used and that is the 𝒈𝒂𝒖𝒔𝒔
1 𝑔𝑎𝑢𝑠𝑠 = 10−4 𝑇

34. CALCULATE THE STRENGTH OF MAGNETIC FIELD (𝐵)
Strength of Magnetic Field 𝑩 𝒕𝒆𝒔𝒍𝒂 (𝑻)
Distance 𝑹 𝒎𝒆𝒕𝒆𝒓 (𝒎)
𝑩 =
𝝁𝟎𝑰
𝟐𝝅𝑹
𝑰 ↑ 𝑩 ↑ *** Note: Anytime you increase the electric
current in the wire – strength of the magnetic
field will increase and as move away from the
wire the strength of magnetic field will
decrease.
𝑹 ↑ 𝑩 ↓

35. Example 1. A vertical wire carries of 45 𝐴 due south. Calculate the
magnitude and the direction of the magnetic field 2.0 𝑐𝑚 to the right of
the wire.
𝐵 =
𝜇0𝐼
2𝜋𝑅
=
4𝜋𝑥10−7(45 𝐴)
2𝜋 (0.02 𝑚)
= 4.5𝑥10−4 𝑇
→ strength of magnetic field 2 𝑐𝑚 away from the wire

36. Example 2: A wire carries of 10 𝐴. At what distance from the wire will a
magnetic field of 8.0𝑥10−4 𝑇 be produced?
𝑅 =
𝜇0𝐼
2𝜋𝐵
=
4𝜋𝑥10−7
(10 𝐴)
2𝜋 (8.0𝑥10−4 𝑇)
𝑅 = 2.5𝑥10−3 𝑚 𝑜𝑟 2.5 𝑚𝑚

37. MAGNETIC FORCES
Magnetic Fields 𝑩 𝒕𝒆𝒔𝒍𝒂 (𝑻)
Magnetic Forces 𝑭 𝑵𝒆𝒘𝒕𝒐𝒏 (𝑵)
Charge 𝑞
Speed 𝑣
𝑭 = 𝒒𝒗𝑩 𝒔𝒊𝒏 𝜽, where
𝜽 is the angle between
the directions of 𝒗 and
𝑩.

39. CALCULATE THE STRENGTH OF THE MAGNETIC FORCE
Magnetic Fields 𝑩 𝒕𝒆𝒔𝒍𝒂 (𝑻)
Magnetic Forces 𝑭 𝑵𝒆𝒘𝒕𝒐𝒏 (𝑵)
Charge 𝑞
Speed 𝑣
𝑭 = 𝒒𝒗𝑩 𝒔𝒊𝒏 𝜽, where 𝜽 is the angle between the directions of 𝒗 and 𝑩.
𝑰 ↑ 𝑭 ↑ *** Note: the strength of magnetic force is
proportional to the current
𝑩 ↑ 𝑭 ↑ *** Note: Magnetic force is proportional to
the strength of magnetic field
𝒍 ↑ 𝑭 ↑ *** Note: length is proportional to the
magnetic force depends to angle

40. 𝑰 ⊥ 𝑩 𝑰 is at angle to 𝑩 𝑰 is parallel to 𝑩
***when they are
perpendicular 𝐬𝐢𝐧 𝟗𝟎𝟎
= 𝟏
***So the maximum force
occurs when 𝑰 ⊥ 𝑩
𝜃 →angle between 𝑰 𝑎𝑛𝑑 𝑩
***So we can use the
equation:
𝑭 = 𝒒𝒗𝑩 𝒔𝒊𝒏 𝜽
***when parallel the
𝜃 = 00
→ sin 𝜃 = 0
***So the magnetic field
exerts NO magnetic
force
NO FORCE acting on the current if it is parallel to Magnetic Field 𝐵 , they to be perpendicular
or at the angle with respect to each other.
Example:

41. WHAT ABOUT THE DIRECTION?

42. FORCE ON A MOVING CHARGE IN A MAGNETIC FIELD
What will happen if the force and velocity are ⊥ to each other and the
magnetic field is stationary? What will happen to the direction of a particle?

43. FORCE ON A MOVING CHARGE IN A MAGNETIC FIELD
If the magnetic field is stationary, but charge particle move through it, they experience a
force due to the field which causes them to execute circular motion.

44. If the 𝑭 and 𝒗 are ⊥to each other the particle or object will turn
If the 𝑭 and 𝒗 are parallel to each other, the particle will speed up.
If the 𝑭 and 𝒗 are in the opposite direction the particle or the object will
slows down
***REMEMBER

45. CENTRIPETAL FORCE 𝑭𝒄
Magnetic force 𝑭 supplies the centripetal force 𝑭𝒄, we
have 𝒒𝒗𝑩 =
𝒎𝒗𝟐
𝒓
.
Solving for 𝑟 yields 𝒓 =
𝒎𝒗
𝒒𝑩
.

47. THE HALL EFFECT
Charge creates a voltage ε, known as the Hall emf, across the conductor. The creation of a
voltage across a current-carrying conductor by a magnetic field is known as the Hall Effect.

48. THE HALL EFFECT
Solving the magnitude of Hall
emf yields
𝜺 = 𝑩𝒍𝒗
Magnetic Field 𝑩
Speed 𝒗
With of
conductor
𝒍

50. MAGNETIC FORCE ON A CURRENT-CARRYING CONDUCTOR
Charges ordinarily cannot escape a conductor, the magnetic force on
charges moving in a conductor is transmitted to the conductor itself.

51. MAGNETIC FORCE ON A CURRENT-CARRYING CONDUCTOR
The force on an individual charge moving at the drift velocity 𝒗𝒅 is
given by
𝑭 = 𝒒𝒗𝒅𝑩 𝒔𝒊𝒏𝜽.
Taking 𝐁 to be uniform over a length of wire l and zero elsewhere, the
total magnetic force on the wire is then
𝑭 = (𝒒𝒗𝒅𝑩 𝒔𝒊𝒏𝜽)(𝑵),
Where 𝐍 is the number of charge carriers in the section of wire of
length 𝓵. Now,
𝐍 = 𝐧𝐕
Where 𝐧 is the number of charge carriers per unit volume and 𝐕 is the
volume of wire in the field.

52. MAGNETIC FORCE ON A CURRENT-CARRYING CONDUCTOR
Noting that 𝑽 = 𝑨𝒍, where 𝐀 is the cross-sectional area of the
wire, then the force on the wire:
𝑭 = (𝒒𝒗𝒅𝑩 𝒔𝒊𝒏𝜽)(𝒏𝑨𝓵).
(Note:𝐼 = 𝑛𝑞𝐴𝑣𝑑)
Gathering terms, 𝑭 = (𝒏𝒒𝑨𝒗𝒅)𝓵𝑩 𝒔𝒊𝒏𝜽) → 𝑭 = 𝑰𝒍𝑩 𝒔𝒊𝒏𝜽

53. Example 3: A 2.5 𝑚 long wire carries a current of 5.0 A in the presence
of a magnetic field with a strength of 2.0 𝑥 10−3 𝑇. Calculate the
magnitude force on the wire.
𝐹 = 𝐼ℓ𝐵 sin 𝜃
𝐹 = 5.0 2.5 𝑚 2.0 𝑥 10−3
𝑇 (sin 300
)
𝐹 = 0.02 𝑁

54. MAGNETIC FIELDS PRODUCED BY CURRENTS:
AMPERE’S LAW
The right hand rule 2 (RHR-2) emerges from this exploration and is
valid for any current segment—point the thumb in the direction of the
current, and the fingers curl in the direction of the magnetic field
loops created by it

55. MAGNETIC FIELDS PRODUCED BY CURRENTS:
AMPERE’S LAW
The magnetic field strength (magnitude) produced by a long
straight current-carrying wire :
𝑩 =
𝝁𝟎𝑰
𝟐𝝅𝒓
(long straight wire),
where 𝑰 is the current, 𝒓 is the shortest distance to the wire,
and the constant
𝝁𝟎 = 𝟒𝝅 × 𝟏𝟎−𝟕
𝑻. 𝒎/𝑨

56. MAGNETIC FIELD: CURRENT-CARRYING CIRCULAR LOOP

57. MAGNETIC FIELD PRODUCED BY A CURRENT-CARRYING SOLENOID

58. MAGNETIC FIELD PRODUCED BY A CURRENT-CARRYING SOLENOID
To get a larger field is to have 𝑵 loops; then, the field is
𝑩 =
𝝁𝟎𝑰
𝟐𝑹
.
The magnetic field strength inside a solenoid is
𝑩 = 𝝁𝟎𝒏𝒍
where 𝒏 (no. of turns per meter) is
𝒏 =
𝑵
𝒍
with 𝑵 being the number of loops and 𝒍 the length).

59. 𝐼 ↑ 𝐵 ↑
𝑛 ↑ 𝐵 ↑
ℓ ↓ 𝐵 ↑
MAGNETIC FIELD PRODUCED BY A CURRENT-CARRYING SOLENOID
The magnetic field is directly related to current and no. of
turns/meter (or loops/meter), while it is inversely related to
length.

60. Example 4: A solenoid has a length of 15 𝑐𝑚 and a total of 800 turns
of wire. Calculate the strength of the magnetic field at its center if the
solenoid carries a current of 5.0 𝐴.
𝑛 =
𝑁
ℓ
=
800
0.15 𝑚
= 5, 333 𝑙𝑜𝑜𝑝𝑠/𝑚
To calculate the strength of magnetic field:
𝐵 = 𝜇0𝑛𝐼
𝐵 = 4𝜋 𝑥10−7(5, 333)(5.0)
𝐵 = 0.0335 𝑇

61. MAGNETIC FORCE BETWEEN TWO PARALLEL
CONDUCTORS
(a) The magnetic field produced by a long straight conductor is perpendicular to a parallel conductor, as indicated by
RHR-2.
(b) A view from above of the two wires shown in (a), with one magnetic field line shown for each wire. RHR-1 shows
that the force between the parallel conductors is attractive when the currents are in the same direction. A similar
analysis shows that the force is repulsive between currents in opposite directions.

62. MAGNETIC FORCE BETWEEN TWO PARALLEL
CONDUCTORS
The field due to 𝑰𝟏 at a distance r
𝑩 𝟏 =
𝝁𝟎𝑰𝟏
(𝟐𝝅𝒓)
.
The force between two parallel
currents
𝑭
𝒍
=
𝝁𝟎𝑰𝟏𝑰𝟐
𝟐𝝅𝒓
.

63. Example 5: What is the magnitude and direction of the force
between two parallel wires that are 30 𝑚 long and 2 𝑐𝑚 apart, each
carrying a current of 50 𝐴 in the same direction?
The magnitude force between two wires is F = 0.75 𝑁.
The force between the two wires are directed to each other – there’s a force of
attraction present between the wires.
𝐹 =
𝜇0𝐼1𝐼2
2𝜋𝑅
𝐹 =
(4𝑥10−7
)(50 𝐴)2
(30 𝑚)
2𝜋(0.02 𝑚)
= 0.75 𝑁

64. SUMMARY
Magnet
• 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.
Ferromagnets and Electromagnets
• Magnetic poles always occur in pairs of north and south—it is not possible to
isolate north and south poles.
• Ferromagnetic materials, such as iron, are those that exhibit strong magnetic
effects.
• Electromagnets employ electric currents to make magnetic fields, often aided
by induced fields in ferromagnetic materials

65. SUMMARY
Magnetic Fields and Magnetic Field Lines
• Magnetic fields can be pictorially represented by magnetic field lines,
the properties of which are as follows:
• The field is tangent to the magnetic field line.
• Field strength is proportional to the line density.
• Field lines cannot cross.
• Field lines are continuous loops.
Magnetic Fields 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 𝒔𝒊𝒏𝜽, where 𝜽 is the angle between the directors of 𝒗 and 𝑩
• The SI unit for magnetic field strength 𝑩 is the tesla (𝑻), which is related to other
units by
𝟏𝑻 =
𝟏𝑵
𝑪 ∙ Τ
𝒎 𝒔
=
𝟏𝑵
𝑨 ∙ 𝒎

66. SUMMARY
Magnetic Fields Strength: Force on a Moving Charge in a Magnetic Field
• Magnetic force can supply force and cause a charged particle to move in a circular
path of radius 𝒓 =
𝒎𝒗
𝒒𝑩
,
The Hall Effect
• The Hall 𝒆𝒎𝒇 is given by 𝜺 = 𝑩𝒍𝒗 (𝑩, 𝒗, 𝒍, 𝒎𝒖𝒕𝒖𝒂𝒍𝒍𝒚 𝒑𝒆𝒓𝒑𝒆𝒏𝒅𝒊𝒄𝒖𝒍𝒂𝒓)
Magnetic Force on a Current-Carrying Capacitor
• The magnetic force on current-carrying conductors is given by 𝑭 = 𝒏𝑩𝒔𝒊𝒏𝜽,

67. SUMMARY
Magnetic Fields Produced by Currents: Ampere’ Law
• The strength of the magnetic field created by current in along straight wire is given by
𝑩 = 𝝁𝟎𝑰 𝟐𝝅𝒓 (long straight wire)
• The magnetic field strength at the center of a circular loop is given by
𝑩 =
𝝁𝟎𝑰
𝟐𝑹
(𝑎𝑡 𝑡ℎ𝑒 𝑐𝑒𝑛𝑡𝑒𝑟 𝑜𝑓 𝑙𝑜𝑜𝑝),
This equation becomes 𝑩 = 𝝁𝟎𝒏𝑰(𝟐𝑹)
• The magnetic field strength inside a solenoid is
𝑩 = 𝝁𝟎𝒏𝑰 (inside a solenoid)

68. SUMMARY
Magnetic Force between Two Parallel Conductors
• The force between two parallel currents I1 and I2, separated
by a distance r, has a magnitude per unit length given by
𝑭
𝒍
=
𝝁𝟎𝑰𝟏𝑰𝟐
𝟐𝝅𝒓
• The force is attractive if the currents are in the same
direction, repulsive if they are in opposite directions.

69. SEATWORK
What is the direction of the velocity of a negative charge that
experiences the magnetic force shown in each of the three cases
in Figure, assuming it moves perpendicular to 𝐵 ?