Grade 11

Exam Preparation

Electricity &
Magnetism III
Exercises

“The will to succeed

is important, but
what’s more important
is the will and
commitment to prepare.”

TouchTutor® Series
Physical Sciences
Section A (Multiple Choice Questions)
1) In the diagram, a bar magnet is moving relative to a coil. The current
induced in the coil is in the direction indicated. The magnet …
A. is stationary
B. is approaching the coil with a north pole
C. induces an electric field around the coil
D. is approaching the coil with a south pole

2) A bar magnet is moved towards or away from a solenoid. Which ONE of the following factors / actions will
increase the deviation on the galvanometer?
A. use a solenoid with a smaller diameter
B. use a solenoid with fewer turns
C. use a weaker magnet
D. move the magnet faster towards and away from the solenoid.

3) A conducting wire, XY, moves between two magnets. Which ONE of the following
actions can lead to an increased induced current in wire XY? Move the wire …
A. quickly and parallel to the magnetic field
B. slowly and parallel to the magnetic field
 C. quickly and perpendicular to the magnetic field
D. slowly and perpendicular to the magnetic field

4) The mutual induction of electric and magnetic fields can produce

A. Light
B. Energy
C. Both light and energy
D. Neither light nore energy

Section B (Structured Questions)

Question 1
1) State Faraday’s Law of Electromagnetic Induction, and express it in symbols.
2) Explain the meaning of the following terms, and express as formula where relevant: electromagnetic induction,
magnetic flux, magnetic flux density, tesla, weber.
3) What is Lenz’ law?
 4) Consider a flat square coil with 45 turns. The coil is 70 cm long on each side, and
has a magnetic field of 1,5 T passing through it. The plane of the coil is
perpendicular to the magnetic field (the field points out of the page). Use Faraday’s
Law to calculate the induced emf, if the magnetic field increases uniformly from 1,5
to 2,5 T in 7 s. Determine the direction of the induced current.

5) A circular coil, with radius 4,5×10-2 m, has 150 turns. Its central axis is at an angle of 30° to the magnetic field
which changes uniformly from 0,2 to 22 T in 10 s. Find the induced emf.

Question 2
1) A single circular loop of wire, 12 cm in diameter, is placed in a 0,6 T magnetic field. It is removed from the
magnetic field in 0,04 s. Calculate …
i. the flux which is linked to this coil.
ii. the average induced emf.
How does the emf change (write only increases, decreases or remains the same) if
 iii. the magnetic field strength changes to 0,5 T?
iv. the coil is removed from the field in 0,02 s?

2) A bar magnet is being pushed into a coil. The current induced in the coil is in the direction indicated.
i. Write down the polarity (north pole or south pole) of the end of the coil
facing the bar magnet, as the bar magnet approaches the coil.
ii. Which end of the bar magnet is approaching the coil? Write down only
NORTH POLE or SOUTH POLE
iii. Write down what will be observed on the galvanometer if the bar
magnet is held stationary inside the coil. Give a reason for the answer.

Faraday's law of electromagnetic induction plays a very important role in the generation of electricity.
iv. Write down Faraday's law of electromagnetic induction in words.
A coil of 100 turns, each of area 4,8 x 10-4 m2, is made from insulated copper wire. The coil is placed in a uniform
magnetic field of 4 x 10-4 T in such a way that the angle between the magnetic field and the normal to the plane of
the coil is 30°. The coil is then rotated so that the angle changes to 70° in a time interval of 0,2 s. Calculate the …
v. magnitude of the emf induced in the coil
vi. current induced in the coil if it has an effective resistance of 2 ohm.
3) A solenoid with 450 turns has cross-sectional area of 176 cm2. It is positioned perpendicular to a uniform
magnetic field of 0,72 T.
i. Calculate the flux through the solenoid.
ii. Calculate the induced emf if the solenoid is pulled out of the magnetic field in 0,22 s.
 Grade 11
Exam Preparation

Electricity &
Magnetism III
Memorandum

“The will to succeed

is important, but
what’s more important
is the will and
commitment to prepare.”

TouchTutor® Series
Physical Sciences
Section A (Multiple Choice Questions)
1) B
2) D
3) D
4) A

Section B (Structured Questions)

Question 1
1) The magnitude of the induced emf across the ends of a conductor is directly proportional to the rate of change in
the magnetic flux linkage with the conductor - or - The induced emf (𝜀) in a circuit loop is proportional to
the rate of change of the magnetic flux (𝜙) through the area (A) of the loop. As formula: 𝜀 = −𝑁 ∆𝜙/∆𝑡

2) (i) Electromagnetic induction: a current – a flow of charge – induces a magnetic field, and a changing magnetic
field induces an electric current.
(ii) the flow of magnetism, or of magnetic energy. It is designated by the symbol phi (ϕ) and is measured in weber
(Wb).
 (iii) magnetic flux density is the strength of the magnetic field – the amount of flux passing through a unit area, that
is at right angles to the magnetic flux at that point. symbol B, measured in tesla (T). 1 tesla = 1 weber of
magnetic flux per square metre (1 T = 1 Wb· m-2)
(iv) tesla is the SI unit of magnetic flux density.

3) The induced current (or the induced emf) always opposes the change in magnetic flux, through the creation of its
own magnetic field.
∆𝜙
4) Faraday’s law: 𝜀 = −𝑁 , with 𝜙 = 𝐵𝐴𝑐𝑜𝑠(𝜃), where N = number of loops in the coil, 𝜀 = emf, B =
∆𝑡
strength of the magnetic field, A the area of the coil, and θ the angle between the magnetic field and the normal to
the coil.
Area A = 0,7 × 0,7 = 0,49 m2, and N = 45 turns.
ΔB = Bf – Bi = 2,5 – 1,5 = 1,0 T, and since θ = 0°, cos(θ) = 1.
The minus sign may be ignored since we are asked to calculate the magnitude of the induced emf.
∆𝜙 𝐵𝑓 𝐴−𝐵𝑖 𝐴
Then 𝜀 = −𝑁 = −𝑁 = (45)(0,49)(2,5 – 1,5) / 10s = 3,15 V.
∆𝑡 ∆𝑡
The induced current is anti-clockwise as viewed from the direction of the magnetic field.

5) Apply Faraday’s law.

 Δ𝜙 = BfAcos(θ) – BiAcos(θ) = 22 × 4,5×10-2 × cos(30°) – 0,2 × 4,5×10-2 × cos(30°) = 0,85 Wb
ε = N·Δ𝜙 / Δt = 150 × 0,85 / 10 = 12,75 V.
The induced current is anti-clockwise as viewed from the direction of the magnetic field.

Question 2
1) (i) Area A = πr2 2 cos(0°) = 6,79×10-3 Wb
∆𝜙
(ii) 𝜀 = −𝑁 = (-1)(0 – 6,79×10-3)/0,04 = 0,17 V
∆𝑡
(iii) decreases – if numerator decreases, the fraction value decreases
(iv) increases

2) (i) north pole

(ii) north pole
(iii) There will be no reading / no deflection. EM induction only takes place in the context of a changing magnetic
field, so the coil or magnet must move.
(iv) The magnitude of the induced emf (in a conductor) is equal to the rate of change of magnetic flux linkage.
∆𝜙 (𝜙70 −𝜙30 ) 𝐵𝑓 𝐴𝑐𝑜𝑠(70)−𝐵𝑖 𝐴𝑐𝑜𝑠(30)
(v) 𝜀 = −𝑁 = −𝑁 −𝑁
∆𝑡 ∆𝑡 ∆𝑡
 = -100[(4×10 - 4)(4,8×10 - 4)cos(70°) - (4×10 - 4)(4,8×10 - 4)cos(30°)]/0,2 = 5,03×10-5 V.
(vi) ε = IR, thus I = ε /R = 5,03×10-5 / 2 = 2,52×10-5 A.

3) (i) 𝜙 = BA cos(θ) = 0,72 × 0,0176 × cos(0°) = 0,013 Wb

∆𝜙
(ii) 𝜀 = −𝑁 = - 450(0 – 0,013) / 0,22 = 26,59 V.
∆𝑡
 TouchTutor Series
Physical Sciences
Grade 11

Exam Preparation

ELECTRICITY & MAGNETISM III

ELECTROMAGNETISM

© GMMDC, Nelson Mandela University

Exam Guidelines: Electricity & Magnetism

ELECTRICITY & MAGNETISM is examined in Paper 1 (3 hr)

Exam Weighting
• 50 marks out of 150 – 33%

Examinable Materials
• Electrostatics (Electricity & Magnetism I)
• Coulomb’s law, electric fields
• Electric Circuits (Electricity & Magnetism II)
• Ohm’s law, power & energy
• Electromagnetism (Electricity & Magnetism III)
• Magnetic fields associated with current-carrying
conductors, Faraday’s law of electromagnetic induction
TouchTutor® Resources
For more detailed treatment of the topics explored here, please
consult the following videos / documents in the TouchTutor®
Physical Sciences Grade 11 package.
on Electromagnetism
• Induced Magnetic Fields
• Electromagnetic Induction
 Current Induced Magnetic Field
A battery is connected to a conductor …
• as current flows, a magnetic field is
created around the conductor.
• when the current stops, there is no
magnetic field
• when current flows in the opp. dir., the
magnetic field also changes direction
As the animation shows, a magnetic field
from PhET simulation
Do note: is created by a flowing current.
the magnetic field produced by an electric current is always at
right angles (perpendicular) to the direction of the current flow.

The magnetic field is always perpendicular to current flow …

• this implies that the shape and direction of the magnetic field
depends on the shape of the conductor, and the direction of
current flow.
Around a Straight Current-Carrying Conductor
Consider first a straight current-carrying conductor …
This magnetic field can be represented
by a series of ever-larger concentric
circles, with the conductor at the centre.
From above …
A note on conventions …
• current flowing upward, out of the screen,
- indicated (as here) with a circled dot ⊙ ⊙
⊗
• current flowing downward, into the screen,
- represented with a ⊗
Note: the magnetic field lines
were all drawn with arrows i.e. magnetic fields have
direction.
The direction of the field may be determined using
the RIGHT HAND RULE (RHR)
Right Hand Rule
the RIGHT HAND RULE (RHR) …
– with thumb in the direction of current flow,
the curl of the fingers on the right hand
will show the direction of the field.
Please note that you must, absolutely must,
use the right hand to determine the field
direction.
A further point: the field is …
strongest close to the wire,
and weakens as the distance from the
wire increases.
This is reflected in the density of the field
lines – close together near the wire,
then further apart.
Use Your Right Hand …
Use the RHR to determine the direction of the magnetic field
around the following. State
whether current flows into / out
of the screen, clockwise or anti-  ⊙
clockwise.
Consider a current-carrying
into / clockwise out / anti-clockwise
conductor – not straight, but
bent into a LOOP. What will the magnetic field look like around
such a loop?
Imagine a sheet of
A B paper as shown.
side view Now determine
of paper the field at A and
B, where the loop crosses
the plane. Use the RHR.
 Current-Carrying Loop
The current emerges upward from sheet at point A, and enters the
sheet downward at B. Use the RHR to draw the magnetic field
around points A & B.
Around A, the field lines
rotate anti-clockwise,
thus the magnetic field
looks as follows … A⊙ ⊗B

Around B, the field lines

rotate clockwise, and thus
the field looks as follows …
Do note …
• the field lines are much more compressed inside the loop –
the field is stronger there than on the outside …
• the field lines move in the same direction inside the loop –
strengthening each other, not opposing each other.
 360°

⊗⊙
Of course the magnetic field lines aren’t solely on
the horizontal, but around the 360° of the loop …
When the current moves anti-clockwise around ⊗⊙ ⊙⊗
the loop, the magnetic field lines have the

⊙⊗
direction as shown (do they point in the same
direction inside the loop?)
Use the RHR to determine the direction of the magnetic field
inside the loop … when you curl your fingers in the direction of
current flow in the loop, the thumb points in the direction of the
magnetic field.
Given current flow through this
series of loops (a coil), in which
direction will the mag. field be
inside the loops / coil?
 Magnetic Field around a Solenoid
There is a last magnetic field to consider – one in or around a
solenoid (a cylindrical coil of wire) …
in essence, what we had in the last example ..

the magnetic field round

I a solenoid is the same
I
as for a loop, except
extended through the
length of the solenoid
with its many turns.
Now …
apply the RHR to find
Does this magnetic field the m-field direction …
remind you of something?
 Bar Magnet
The m-field around a
solenoid is identical to
I that around a bar
I magnet with its north
and south poles …
• outside the magnet,
S N the field lines run
N→S

• inside the solenoid /

the bar magnet, the
lines run S → N
The magnetic field around a solenoid may be strengthened by
(i) a larger / stronger current flow
(ii) a greater number of turns / coils in the solenoid
(iii) introducing an iron core into the solenoid.
 Electromagnets
The fact that magnetic fields are created by an electric current is
utilised extensively in industrial and other applications.
One example of such use is pictured here – a
scrapyard crane. By switching the current on
or off, huge loads of metal can quickly and
safely be moved from one location to another.
Should you drop a whole lot of pins, this is
also the easiest way to pick them up. Make
a small electromagnet as in this diagram, and
see the pins
‘attaching’ them-
selves to the nail …
Electric bells, security doors, and
loudspeakers are other examples of ‘electromechanical’
devices.
 Electromagnetic Induction
A current (a flow of charge) induces a magnetic field. Similarly, a
changing magnetic field induces an electric current – in what is
called, ELECTROMAGNETIC INDUCTION. Note the following …
• a stationary magnet has no
effect – no current …
• a moving magnet, i.e. a
changing magnetic field,
induces a current
• slow change ≈ low current
• rapid (fast) change ≈ large
current
• polarity of magnet – just
PhET simulation changes current direction
Before studying the induced current direction, & the strength of the
induced emf, we need to consider some new concepts.
Magnetic Flux & Flux Density
What is MAGNETIC FLUX? And MAGNETIC FLUX DENSITY?
First, the term magnetic: an adjective derived from magnetism,
meaning the attractive or repulsive force between certain objects
due to the magnetic field surrounding them. And in English, the
word flux implies a flow of something.
MAGNETIC FLUX is thus about the flow of magnetism, or of magnetic
energy. It is designated by the symbol phi (ϕ) and is
measured in weber (Wb).
Y The amount of magnetic flux
X varies from place to place within a
magnetic field – much as there
are more m-field lines passing
through area X than through an
identically sized area Y.
This difference is suggested in the concept of FLUX DENSITY.
 Magnetic Flux Density
The MAGNETIC FLUX DENSITY at a point in a magnetic field is the
amount of flux passing through a unit area
that is at right angles to the magnetic flux at that point.
high flux density
low flux density
Note: Area at right angles (perpendicular) to flux lines. same sized area: fewer flux lines
Flux density: symbol B, measured in tesla (T). 1 tesla = 1 weber
of magnetic flux per square metre (1 T = 1 Wb·m-2)
It is a measure of magnetic field strength at a point in a magnetic
field (always measured at right angles to the magnetic field lines.
Based on the above, magnetic flux (ϕ) may then be defined as the
product of the magnetic flux density (B), and ….
… the size of the area (A) thru which flux passes.
in symbol form: 𝜙 = 𝐵𝐴
Circuit Loop Orientation
Exploring EM induction in 1831, Faraday noticed that a current
was induced in a circuit loop when within a changing magnetic
field, and that the strength of the induced current depended on ..
• the strength of the magnetic field / how fast it was changing,
• & the area and orientation of the loop
circuit loop

maximum induced current

zero induced current

no mag. flux flowing through circuit
magnetic flux flowing through
loop since parallel to magnetic field
circuit loop at right angles
The formula for magnetic flux 𝜙 = 𝐵𝐴 is then adapted to take
account of the loop orientation …
Flux Linkage
To account for the loop orientation, multiply the loop area (A) by
A
cos(θ), where θ is the angle between the m-field
size of loop direction & the normal to the area. Then …
area ⊥ to
m-field B
θ 𝜙 = 𝐵𝐴𝑐𝑜𝑠(𝜃)
if θ = 0° (loop ⊥ field), cos(θ) = 1 (max. current)
normal
if θ = 90° (loop ∥ field), cos(θ) = 0 (zero current)
magnetic flux / field lines

Suppose more than one loop is used, i.e. a coil of, say, 1000 loops
(a solenoid). In this case …
• the total magnetic flux flowing through the coil is
equal Nϕ, where N = number of loops in the coil or
solenoid.
• Scientists refer to Nϕ as the FLUX LINKAGE for the
coil at that point (you don’t have to remember the word)
Faraday’s Law
Faraday’s law relates the emf induced in a coil (or solenoid) to
the rate of change of flux. Accordingly …
where 𝜀 = induced emf across the coil, N =
∆𝜙 number of loops in the coil, ϕ = the magnetic
𝜀 = −𝑁
∆𝑡 flux, and ∆ϕ ∆𝑡 = rate of change of flux.

In words: the induced emf (𝜀) in a circuit loop is proportional to the rate of
change of the magnetic flux (𝜙) through the area (A) of the loop.

• phi (ϕ) in Faraday’s law may be replaced by B·Acos(θ) ….

• where B is magnetic flux density (the strength of the magnetic
field), &
• A the area enclosed by the loop (coil).

What about the minus sign?

It may be ignored in calculations, however ...
Lenz’s Law
The (–) sign points to a very important aspect of EM induction ..
The induced current (or the induced emf) ALWAYS,
ALWAYS, OPPOSES the change in magnetic flux

How does it do this? By creating its own magnetic field. This is

known as LENZ’S LAW (you don’t have to remember the name).
When a magnet is moved towards a coil, a current is induced in
the coil (Faraday’s Law). This induced current opposes the
magnet’s motion by creating its own magnetic field (Lenz’s law).
Direction of Induced Current

In what direction does the current induced in the coil flow?

If the magnetic field created by this induced current opposes the
incoming magnet, the right hand side of the coil’s field must be a
north pole (N), since N and N repel each other.
This implies that the magnetic field must flow as shown now …
And now use the RHR for solenoids to determine the direction in
which the current induced in the coil will flow ….
With thumb towards N, the curl of the fingers will give the
direction of the induced current flow …
 Opposite Direction

S
What is the direction of the induced current when the magnet is
moved away from the coil?
Think it through. Answer it for yourself first ….
The coil’s induced magnetic field will resist the change through a
magnetic field with a south pole (S) on the right (as shown) since S
and N attract.
Use the RHR to determine the direction of current flow in the coil:
with thumb towards the left, and the curl of the fingers over the
coil.
Current will move as shown …
Exercises – Understanding: The End

Having studied this section on Electromagnetism, work through

as many of the associated exercises as possible.
Remember, practice (and more practice) makes perfect.
Where you are uncertain about something, consult with your
teacher, or your classmates. Always try to clarify difficulties as
soon as possible.
And remember too: is
key – the right answer will then take care of itself.
 CHAPTER 10

Electromagnetism

10.1 Introduction 346

10.2 Magnetic field associated with a current 346
10.3 Faraday’s law of electromagnetic induction 357
10.4 Chapter summary 369
 10 Electromagnetism

10.1 Introduction ESBPR

Electromagnetism describes the interaction between charges, currents and the electric
and magnetic fields to which they give rise. An electric current creates a magnetic
field and a changing magnetic field will create a flow of charge. This relationship
between electricity and magnetism has been studied extensively. This has resulted
in the invention of many devices which are useful to humans, for example cellular
telephones, microwave ovens, radios, televisions and many more.

10.2 Magnetic field associated with a current ESBPS

If you hold a compass near a wire through which current is flowing, the needle on the
compass will be deflected.

Since compasses work by pointing along magnetic field lines, this means that there
must be a magnetic field near the wire through which the current is flowing.

The magnetic field produced by an electric current is always oriented perpendicular to

the direction of the current flow. Below is a sketch of what the magnetic field around
a wire looks like when the wire has a current flowing in it. We use B  to denote a
magnetic field and arrows on field lines to show the direction of the magnetic field.
Note that if there is no current there will be no magnetic field.

The direction of the current in the conductor (wire) is shown by the central arrow. The
circles are field lines and they also have a direction indicated by the arrows on the
lines. Similar to the situation with electric field lines, the greater the number of lines
(or the closer they are together) in an area the stronger the magnetic field.

346 10.1. Introduction

Important: all of our discussion regarding field directions assumes that we are dealing FACT
with conventional current. The Danish physicist,
Hans Christian Oersted,
was lecturing one day in
1820 on the possibility of
electricity and magnetism
To help you visualise this situation, being related to one
stand a pen or pencil straight up on a another, and in the
desk. The circles are centred around process demonstrated it
conclusively with an
the pencil or pen and would be drawn experiment in front of his
parallel to the surface of the desk. The whole class. By passing
tip of the pen or pencil would point in an electric current
the direction of the current flow. through a metal wire
suspended above a
magnetic compass,
Oersted was able to
produce a definite motion
You can look at the pencil or pen from of the compass needle in
above and the pencil or pen will be a response to the current.
dot in the centre of the circles. The What began as a guess at
the start of the class
direction of the magnetic field lines is session was confirmed as
counter-clockwise for this situation. fact at the end. Needless
To make it easier to see what is hap- to say, Oersted had to
pening we are only going to draw one revise his lecture notes for
future classes. His
set of circular fields lines but note that discovery paved the way
this is just for the illustration. for a whole new branch
of science -
If you put a piece of paper behind the electromagnetism.
pencil and look at it from the side, then
× you would be seeing the circular field
× lines side on and it is hard to know that
× they are circular. They go through the
× paper. Remember that field lines have
× a direction, so when you are looking
× at the piece of paper from the side it
means that the circles go into the paper
on one side of the pencil and come out
of the paper on the other side.

When we are drawing directions of

magnetic fields and currents, we use
the symbols  and ⊗. The symbol  +
represents an arrow that is coming out +
+
of the page and the symbol ⊗ repre- +
+
sents an arrow that is going into the
+
+
page. +
+
It is easy to remember the meanings of +
+
the symbols if you think of an arrow +
with a sharp tip at the head and a tail
with feathers in the shape of a cross.

We will now look at three examples of current carrying wires. For each example
we will determine the magnetic field and draw the magnetic field lines around the
conductor.

Chapter 10. Electromagnetism 347

 Magnetic field around a straight wire ESBPT

The direction of the magnetic field around the current carrying conductor is shown in
Figure 10.1.

 ⊗

(a) (b)
Figure 10.1:
Magnetic field around a conductor when you look at the conductor from one end. (a) Current
flows out of the page and the magnetic field is counter-clockwise. (b) Current flows into the
page and the magnetic field is clockwise.

   ⊗ ⊗ ⊗
current flow

current flow
⊗ ⊗ ⊗   

Figure 10.2:
Magnetic fields around a conductor looking down on the conductor. (a) Current flows clock-
wise. (b) current flows counter-clockwise.

Activity: Direction of a magnetic field

Using the directions given in Figure 10.1 and Figure 10.2 try to find a rule that easily
tells you the direction of the magnetic field.

Hint: Use your fingers. Hold the wire in your hands and try to find a link between the
direction of your thumb and the direction in which your fingers curl.

The magnetic field

around a current carry-
ing conductor.

348 10.2. Magnetic field associated with a current

There is a simple method of finding the relationship between the direction of the
current flowing in a conductor and the direction of the magnetic field around the same
conductor. The method is called the Right Hand Rule. Simply stated, the Right Hand
Rule says that the magnetic field lines produced by a current-carrying wire will be
oriented in the same direction as the curled fingers of a person’s right hand (in the
“hitchhiking” position), with the thumb pointing in the direction of the current flow.

IMPORTANT!

Your right hand and left hand are unique in the sense that you cannot rotate one of
them to be in the same position as the other. This means that the right hand part of the
rule is essential. You will always get the wrong answer if you use the wrong hand.

Activity: The Right Hand Rule

Use the Right Hand Rule to draw in the directions of the magnetic fields for the follow-
ing conductors with the currents flowing in the directions shown by the arrows. The
first problem has been completed for you.

⊗ ⊗ ⊗

1.    2. 3. 4.

5. 6. 7. 8.

9. 10. 11. 12.

Chapter 10. Electromagnetism 349

 Activity: Magnetic field around a current carrying conductor

Apparatus:

1. one 9 V battery with holder

2. two hookup wires with alligator clips

3. compass

4. stop watch

Method:

1. Connect your wires to the battery leaving one end of each wire unconnected so
that the circuit is not closed.

2. Be sure to limit the current flow to 10 seconds at a time (Why you might ask, the
wire has very little resistance on its own so the battery will go flat very quickly).
This is to preserve battery life as well as to prevent overheating of the wires and
battery contacts.

3. Place the compass close to the wire.

4. Close the circuit and observe what happens to the compass.

5. Reverse the polarity of the battery and close the circuit. Observe what happens
to the compass.

Conclusions:

Use your observations to answer the following questions:

1. Does a current flowing in a wire generate a magnetic field?

2. Is the magnetic field present when the current is not flowing?

3. Does the direction of the magnetic field produced by a current in a wire depend
on the direction of the current flow?

4. How does the direction of the current affect the magnetic field?

Magnetic field around a current carrying loop ESBPV

So far we have only looked at straight wires carrying a current and the magnetic fields
around them. We are going to study the magnetic field set up by circular loops of wire
carrying a current because the field has very useful properties, for example you will
see that we can set up a uniform magnetic field.

350 10.2. Magnetic field associated with a current

Activity: Magnetic field around a loop of conductor

Imagine two loops made from wire which carry currents (in opposite directions) and
are parallel to the page of your book. By using the Right Hand Rule, draw what you
think the magnetic field would look like at different points around each of the two
loops. Loop 1 has the current flowing in a counter-clockwise direction, while loop 2
has the current flowing in a clockwise direction.

direction of current direction of current

loop 1 loop 2

direction of current direction of current

If you make a loop of current carrying conductor, then the direction of the magnetic
field is obtained by applying the Right Hand Rule to different points in the loop.

⊗ ⊗
⊗  
 The directions of the magnetic
⊗

⊗ field around a loop of current
 ⊗ carrying conductor with the
⊗ current flowing in a counter-

 ⊗ clockwise direction is shown.
⊗  
⊗ ⊗
6
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6 -7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6

Notice that there is a variation on the Right Hand Rule. If you make the fingers of your
right hand follow the direction of the current in the loop, your thumb will point in the
direction where the field lines emerge. This is similar to the north pole (where the
field lines emerge from a bar magnet) and shows you which side of the loop would
attract a bar magnet’s north pole.

Chapter 10. Electromagnetism 351

 Magnetic field around a solenoid ESBPW

If we now add another loop with the current in the same direction, then the magnetic
field around each loop can be added together to create a stronger magnetic field. A
coil of many such loops is called a solenoid. A solenoid is a cylindrical coil of wire
acting as a magnet when an electric current flows through the wire. The magnetic
field pattern around a solenoid is similar to the magnetic field pattern around the bar
magnet that you studied in Grade 10, which had a definite north and south pole as
shown in Figure 10.3.

current flow

Figure 10.3:
Magnetic field around a solenoid.
8
7
6
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8 -7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6

Real-world applications ESBPX

Electromagnets

An electromagnet is a piece of wire intended to generate a magnetic field with the

passage of electric current through it. Though all current-carrying conductors produce
magnetic fields, an electromagnet is usually constructed in such a way as to maximise
the strength of the magnetic field it produces for a special purpose. Electromagnets are
commonly used in research, industry, medical, and consumer products. An example

352 10.2. Magnetic field associated with a current

of a commonly used electromagnet is in security doors, e.g. on shop doors which
open automatically.

As an electrically-controllable magnet, electromagnets form part of a wide variety of

“electromechanical” devices: machines that produce a mechanical force or motion
through electrical power. Perhaps the most obvious example of such a machine is the
electric motor which will be described in detail in Grade 12. Other examples of the
use of electromagnets are electric bells, relays, loudspeakers and scrapyard cranes.

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General experiment: Electromagnets

Aim:

A magnetic field is created when an electric current flows through a wire. A single
wire does not produce a strong magnetic field, but a wire coiled around an iron core
does. We will investigate this behaviour.

Apparatus:

1. a battery and holder

2. a length of wire

3. a compass

4. a few nails

Method:

1. If you have not done the previous experiment in this chapter do it now.

2. Bend the wire into a series of coils before attaching it to the battery. Observe
what happens to the deflection of the needle on the compass. Has the deflection
of the compass grown stronger?

3. Repeat the experiment by changing the number and size of the coils in the wire.
Observe what happens to the deflection on the compass.

Chapter 10. Electromagnetism 353

 4. Coil the wire around an iron nail and then attach the coil to the battery. Observe
what happens to the deflection of the compass needle.

Conclusions:

1. Does the number of coils affect the strength of the magnetic field?

2. Does the iron nail increase or decrease the strength of the magnetic field?

Case study: Overhead power lines and the environment

Physical impact:

Power lines are a common sight all

across our country. These lines bring
power from the power stations to our
homes and offices. But these power
lines can have negative impacts on the
environment. One hazard that they
pose is to birds which fly into them.
Conservationist Jessica Shaw has spent
the last few years looking at this threat.
In fact, power lines pose the primary
threat to the blue crane, South Africa’s
national bird, in the Karoo.

“We are lucky in South Africa to have

a wide range of bird species, includ-
ing many large birds like cranes, storks
and bustards. Unfortunately, there are
also a lot of power lines, which can im-
pact on birds in two ways. They can be
electrocuted when they perch on some
types of pylons, and can also be killed
by colliding with the line if they fly into
it, either from the impact with the line
or from hitting the ground afterwards.

These collisions often happen to large birds, which are too heavy to avoid a power line
if they only see it at the last minute. Other reasons that birds might collide include
bad weather, flying in flocks and the lack of experience of younger birds.

Over the past few years we have been researching the serious impact that power line
collisions have on Blue Cranes and Ludwig’s Bustards. These are two of our endemic
species, which means they are only found in southern Africa. They are both big birds
that have long lifespans and breed slowly, so the populations might not recover from
high mortality rates. We have walked and driven under power lines across the Over-
berg and the Karoo to count dead birds. The data show that thousands of these birds

354 10.2. Magnetic field associated with a current

 FACT
are killed by collisions every year, and Ludwig’s Bustard is now listed as an Endan- When lightning strikes a
ship or an aeroplane, it
gered species because of this high level of unnatural mortality. We are also looking
can damage or otherwise
for ways to reduce this problem, and have been working with Eskom to test different change its magnetic
line marking devices. When markers are hung on power lines, birds might be able to compass. There have
see the power line from further away, which will give them enough time to avoid a been recorded instances
collision.” of a lightning strike
changing the polarity of
the compass so the
Impact of fields: needle points south
instead of north.
The fact that a field is created around the power lines means that they can potentially
have an impact at a distance. This has been studied and continues to be a topic of
significant debate. At the time of writing, the World Health Organisation guidelines
for human exposure to electric and magnetic fields indicate that there is no clear link
between exposure to the magnetic and electric fields that the general public encounters
from power lines, because these are extremely low frequency fields.

Power line noise can interfere with radio communications and broadcasting. Essen-
tially, the power lines or associated hardware improperly generate unwanted radio
signals that override or compete with desired radio signals. Power line noise can
impact the quality of radio and television reception. Disruption of radio communica-
tions, such as amateur radio, can also occur. Loss of critical communications, such as
police, fire, military and other similar users of the radio spectrum, can result in even
more serious consequences.

Group discussion:

• Discuss the above information.

• Discuss other ways that power lines affect the environment.

Exercise 10 – 1: Magnetic Fields

1. Give evidence for the existence of a magnetic field near a current carrying wire.

2. Describe how you would use your right hand to determine the direction of a
magnetic field around a current carrying conductor.

3. Use the Right Hand Rule to determine the direction of the magnetic field for the
following situations:

Chapter 10. Electromagnetism 355

 current flow

a)

current flow

b)

4. Use the Right Hand Rule to find the direction of the magnetic fields at each of
the points labelled A - H in the following diagrams.

A E
B F

 ⊗
D H
C G

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356 10.2. Magnetic field associated with a current

10.3 Faraday’s law of electromagnetic induction ESBPY

Current induced by a changing magnetic field ESBPZ

While Oersted’s surprising discovery of electromagnetism paved the way for more
practical applications of electricity, it was Michael Faraday who gave us the key to the
practical generation of electricity: electromagnetic induction.

Faraday discovered that when he moved a magnet near a wire a voltage was generated
across it. If the magnet was held stationary no voltage was generated, the voltage only
existed while the magnet was moving. We call this voltage the induced emf (E).

A circuit loop connected to a sensitive ammeter will register a current if it is set up as

in this figure and the magnet is moved up and down:



Magnetic flux

Before we move onto the definition of Faraday’s law of electromagnetic induction and
examples, we first need to spend some time looking at the magnetic flux. For a loop of
 the magnetic flux (φ) is defined
area A in the presence of a uniform magnetic field, B,
as:
φ = BA cos θ

Chapter 10. Electromagnetism 357

 Where:

θ = the angle between the magnetic field, B, and the normal to the loop of area A
A = the area of the loop
B = the magnetic field

The S.I. unit of magnetic flux is the weber (Wb).

You might ask yourself why the angle θ is included. The flux depends on the magnetic
field that passes through surface. We know that a field parallel to the surface can’t
induce a current because it doesn’t pass through the surface. If the magnetic field is
not perpendicular to the surface then there is a component which is perpendicular and
a component which is parallel to the surface. The parallel component can’t contribute
to the flux, only the vertical component can.

In this diagram we show that a magnetic field at an angle other than perpendicular
can be broken into components. The component perpendicular to the surface has the
magnitude B cos(θ) where θ is the angle between the normal and the magnetic field.


B

B

B sin(θ)

B cos(θ)
θ 
B

B

DEFINITION: Faraday’s Law of electromagnetic induction

The emf, E, produced around a loop of conductor is proportional to the rate of change
of the magnetic flux, φ, through the area, A, of the loop. This can be stated mathemat-
ically as:

∆φ
E = −N
∆t
where φ = B · A and B is the strength of the magnetic field. N is the number of circuit
loops. A magnetic field is measured in units of teslas (T). The minus sign indicates
direction and that the induced emf tends to oppose the change in the magnetic flux.
The minus sign can be ignored when calculating magnitudes.

Faraday’s Law relates induced emf to the rate of change of flux, which is the product
of the magnetic field and the cross-sectional area through which the field lines pass.

358 10.3. Faraday’s law of electromagnetic induction

IMPORTANT!

It is not the area of the wire itself but the area that the wire encloses. This means that
if you bend the wire into a circle, the area we would use in a flux calculation is the
surface area of the circle, not the wire.

In this illustration, where the magnet is in the same plane as the circuit loop, there
would be no current even if the magnet were moved closer and further away. This is
because the magnetic field lines do not pass through the enclosed area but are parallel
to it. The magnetic field lines must pass through the area enclosed by the circuit loop
for an emf to be induced.

 

Direction of induced current ESBQ2

The most important thing to remember is that the induced current opposes whatever
change is taking place.

In the first picture (left) the circuit loop has the south pole of a magnet moving closer.
The magnitude of the field from the magnet is getting larger. The response from the
induced emf will be to try to resist the field towards the pole getting stronger. The field
is a vector so the current will flow in a direction so that the fields due to the current
tend to cancel those from the magnet, keeping the resultant field the same.

To resist the change from an approaching south pole from above, the current must
result in field lines that move away from the approaching pole. The induced magnetic
field must therefore have field lines that go down on the inside of the loop. The current
direction indicated by the arrows on the circuit loop will achieve this. Test this by using
the Right Hand Rule. Put your right thumb in the direction of one of the arrows and
notice what the field curls downwards into the area enclosed by the loop.

Chapter 10. Electromagnetism 359

 





A A

In the second diagram the south pole is moving away. This means that the field from
the magnet will be getting weaker. The response from the induced current will be
to set up a magnetic field that adds to the existing one from the magnetic to resist it
decreasing in strength.

Another way to think of the same feature is just using poles. To resist an approaching
south pole the current that is induced creates a field that looks like another south pole
on the side of the approaching south pole. Like poles repel, you can think of the
current setting up a south pole to repel the approaching south pole. In the second
panel, the current sets up a north pole to attract the south pole to stop it moving away.

We can also use the variation of the Right Hand Rule, putting your fingers in the
direction of the current to get your thumb to point in the direction of the field lines (or
the north pole).

We can test all of these on the cases of a north pole moving closer or further away
from the circuit. For the first case of the north pole approaching, the current will resist
the change by setting up a field in the opposite direction to the field from the magnet
that is getting stronger. Use the Right Hand Rule to confirm that the arrows create a
field with field lines that curl upwards in the enclosed area cancelling out those curling
downwards from the north pole of the magnet.

Like poles repel, alternatively test that putting the fingers of your right hand in the
direction of the current leaves your thumb pointing upwards indicating a north pole.

360 10.3. Faraday’s law of electromagnetic induction

 





A A

For the second figure where the north pole is moving away the situation is reversed.

Direction of induced current in a solenoid ESBQ3

The approach for looking at the direction of current in a solenoid is the same the
approach described above. The only difference being that in a solenoid there are
a number of loops of wire so the magnitude of the induced emf will be different.
The flux would be calculated using the surface area of the solenoid multiplied by the
number of loops.

Remember: the directions of currents and associated magnetic fields can all be found
using only the Right Hand Rule. When the fingers of the right hand are pointed in
the direction of the magnetic field, the thumb points in the direction of the current.
When the thumb is pointed in the direction of the magnetic field, the fingers point in
the direction of the current.

The direction of the current will be such as to oppose the change. We would use a
setup as in this sketch to do the test:

coil with N
turns and cross-
sectional area,
A
induced
current  
direction

magnetic field, B
moving to the left.

In the case where a north pole is brought towards the solenoid the current will flow so

Chapter 10. Electromagnetism 361

TIP that a north pole is established at the end of the solenoid closest to the approaching
An easy way to create a magnet to repel it (verify using the Right Hand Rule):
magnetic field of
changing intensity is to
move a permanent
magnet next to a wire or
coil of wire. The
magnetic field must
increase or decrease in  
intensity perpendicular to
the wire (so that the
magnetic field lines “cut
across” the conductor), or
else no voltage will be
induced.
In the case where a north pole is moving away from the solenoid the current will flow
TIP so that a south pole is established at the end of the solenoid closest to the receding
The induced current magnet to attract it:
generates a magnetic
field. The induced
magnetic field is in a
direction that tends to
cancel out the change in
the magnetic field in the
loop of wire. So, you can  
use the Right Hand Rule
to find the direction of the
induced current by
remembering that the
induced magnetic field is
opposite in direction to
the change in the In the case where a south pole is moving away from the solenoid the current will flow
magnetic field. so that a north pole is established at the end of the solenoid closest to the receding
magnet to attract it:

 

In the case where a south pole is brought towards the solenoid the current will flow so
that a south pole is established at the end of the solenoid closest to the approaching
magnet to repel it:

 

362 10.3. Faraday’s law of electromagnetic induction

Induction

Electromagnetic induction is put into practical use in the construction of electrical

generators which use mechanical power to move a magnetic field past coils of wire to
generate voltage. However, this is by no means the only practical use for this principle.

If we recall, the magnetic field produced by a current-carrying wire is always perpen-

dicular to the wire, and that the flux intensity of this magnetic field varies with the
amount of current which passes through it. We can therefore see that a wire is capable
of inducing a voltage along its own length if the current is changing. This effect is
called self-induction. Self-induction is when a changing magnetic field is produced by
changes in current through a wire, inducing a voltage along the length of that same
wire.

If the magnetic flux is enhanced by bending the wire into the shape of a coil, and/or
wrapping that coil around a material of high permeability, this effect of self-induced
voltage will be more intense. A device constructed to take advantage of this effect is
called an inductor.

Remember that the induced current will create a magnetic field that opposes the
change in the magnetic flux. This is known as Lenz’s law.

Worked example 1: Faraday’s law

QUESTION

Consider a flat square coil with 5 turns. The coil is 0,50 m on each side and has a
magnetic field of 0,5 T passing through it. The plane of the coil is perpendicular to
the magnetic field: the field points out of the page. Use Faraday’s Law to calculate
the induced emf, if the magnetic field is increases uniformly from 0,5 T to 1 T in 10 s.
Determine the direction of the induced current.


B

SOLUTION

Step 1: Identify what is required

We are required to use Faraday’s Law to calculate the induced emf.

Step 2: Write Faraday’s Law

Chapter 10. Electromagnetism 363

 ∆φ
E = −N
∆t
We know that the magnetic field is at right angles to the surface and so aligned with
the normal. This means we do not need to worry about the angle that the field makes
with the normal and φ = BA. The starting or initial magnetic field, Bi , is given as is
the final field magnitude, Bf . We want to determine the magnitude of the emf so we
can ignore the minus sign.

The area, A, is the area of square coil.

Step 3: Solve Problem

∆φ
E =N
∆t
φf − φ i
=N
∆t
Bf A − B i A
=N
∆t
A(Bf − Bi )
=N
∆t
(0,50)2 (1 − 0,50)
= (5)
10
(0,50)2 (1 − 0,50)
= (5)
10
= 0,0625 V

The induced current is anti-clockwise as viewed from the direction of the increasing
magnetic field.

Worked example 2: Faraday’s law

QUESTION

Consider a solenoid of 9 turns with unknown radius, r. The solenoid is subjected to

a magnetic field of 0,12 T. The axis of the solenoid is parallel to the magnetic field.
When the field is uniformly switched to 12 T over a period of 2 minutes an emf with a
magnitude of −0,3 V is induced. Determine the radius of the solenoid.


B

SOLUTION

Step 1: Identify what is required

364 10.3. Faraday’s law of electromagnetic induction

We are required to determine the radius of the solenoid. We know that the relationship
between the induced emf and the field is governed by Faraday’s law which includes
the geometry of the solenoid. We can use this relationship to find the radius.

Step 2: Write Faraday’s Law

∆φ
E = −N
∆t
We know that the magnetic field is at right angles to the surface and so aligned with
the normal. This means we do not need to worry about the angle the field makes with
the normal and φ = BA. The starting or initial magnetic field, Bi , is given as is the
final field magnitude, Bf . We can drop the minus sign because we are working with
the magnitude of the emf only.

The area, A, is the surface area of the solenoid which is πr2 .

Step 3: Solve Problem

∆φ
E =N
∆t
φf − φ i
=N
∆t
Bf A − B i A
=N
∆t
A(Bf − Bi )
=N
∆t
2
(πr )(12 − 0,12)
(0,30) = (9)
120
(0,30)(120)
r2 =
(9)π(12 − 0,12)
2
r = 0,107175
r = 0,32 m

The solenoid has a radius of 0,32 m.

Worked example 3: Faraday’s law

QUESTION

Consider a circular coil of 4 turns with radius 3 × 10−2 m. The solenoid is subjected
to a varying magnetic field that changes uniformly from 0,4 T to 3,4 T in an interval of
27 s. The axis of the solenoid makes an angle of 35◦ to the magnetic field. Find the
induced emf.

Chapter 10. Electromagnetism 365

 
B

SOLUTION

Step 1: Identify what is required

We are required to use Faraday’s Law to calculate the induced emf.

Step 2: Write Faraday’s Law

∆φ
E = −N
∆t
We know that the magnetic field is at an angle to the surface normal. This means we
must account for the angle that the field makes with the normal and φ = BA cos(θ).
The starting or initial magnetic field, Bi , is given as is the final field magnitude, Bf .
We want to determine the magnitude of the emf so we can ignore the minus sign.

The area, A, will be πr2 .

Step 3: Solve Problem

∆φ
E =N
∆t
φf − φ i
=N
∆t
Bf A cos(θ) − Bi A cos(θ)
=N
∆t
A cos(θ)(Bf − Bi )
=N
∆t
(π(0,03)2 cos(35))(3,4 − 0,4)
= (4)
27
−3
= 1,03 × 10 V

The induced current is anti-clockwise as viewed from the direction of the increasing
magnetic field.

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366 10.3. Faraday’s law of electromagnetic induction

Real-life applications

The following devices use Faraday’s Law in their operation.

• induction stoves

• tape players

• metal detectors

• transformers

Project: Real-life applications of Faraday’s Law

Choose one of the following devices and do some research on the internet, or in
a library, how your device works. You will need to refer to Faraday’s Law in your
explanation.

• induction stoves

• tape players

• metal detectors

• transformers

Exercise 10 – 2: Faraday’s Law

1. State Faraday’s Law of electromagnetic induction in words and write down a

mathematical relationship.

2. Describe what happens when a bar magnet is pushed into or pulled out of a
solenoid connected to an ammeter. Draw pictures to support your description.

3. Explain how it is possible for the magnetic flux to be zero when the magnetic
field is not zero.

4. Use the Right Hand Rule to determine the direction of the induced current in the
solenoid below.

Chapter 10. Electromagnetism 367

 coil with N
turns and cross-
sectional area,
A

S N

5. Consider a circular coil of 5 turns with radius 1,73 m. The coil is subjected
to a varying magnetic field that changes uniformly from 2,18 T to 12,7 T in an
interval of 3 minutes. The axis of the solenoid makes an angle of 27◦ to the
magnetic field. Find the induced emf.

6. Consider a solenoid coil of 11 turns with radius 13,8 × 10−2 m. The solenoid
is subjected to a varying magnetic field that changes uniformly from 5,34 T to
2,7 T in an interval of 12 s. The axis of the solenoid makes an angle of 13◦ to
the magnetic field.

a) Find the induced emf.

b) If the angle is changed to 67,4◦ , what would the radius need to be for the
emf to remain the same?

7. Consider a solenoid with 5 turns and a radius of 11 × 10−2 m. The axis of the
solenoid makes an angle of 23◦ to the magnetic field.

a) Find the change in flux if the emf is 12 V over a period of 12 s.

b) If the angle is changed to 45◦ , what would the time interval need to change
to for the induced emf to remain the same?

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368 10.3. Faraday’s law of electromagnetic induction

10.4 Chapter summary ESBQ4

See presentation: 2426 at www.everythingscience.co.za

• Electromagnetism is the study of the properties and relationship between electric

currents and magnetism.

• A current-carrying conductor will produce a magnetic field around the conduc-

tor.

• The direction of the magnetic field is found by using the Right Hand Rule.

• Electromagnets are temporary magnets formed by current-carrying conductors.

• The magnetic flux through a surface is the product of the component of the
magnetic field normal to the surface and the surface area, φ = BA cos(θ).

• Electromagnetic induction occurs when a changing magnetic field induces a

voltage in a current-carrying conductor.

• The magnitude of the induced emf is given by Faraday’s law of electromagnetic

induction: E = −N ∆φ
∆t

Physical Quantities
Quantity Unit name Unit symbol
Induced emf (E) volt V
Magnetic field (B) tesla T
Magnetic flux (φ) weber Wb
Time (t) seconds s

Exercise 10 – 3:

1. What did Hans Oersted discover about the relationship between electricity and
magnetism?

2. List two uses of electromagnetism.

3. a) A uniform magnetic field of 0,35 T in the vertical direction exists. A piece

of cardboard, of surface area 0,35 m2 is placed flat on a horizontal surface
inside the field. What is the magnetic flux through the cardboard?
b) The one edge is then lifted so that the cardboard is now inclined at 17◦ to
the positive x-direction. What is the magnetic flux through the cardboard?
What will the induced emf be if the field drops to zero in the space of 3 s?
Why?

4. A uniform magnetic field of 5 T in the vertical direction exists. What is the

magnetic flux through a horizontal surface of area 0,68 m2 ? What is the flux if
the magnetic field changes to being in the positive x-direction?

5. A uniform magnetic field of 5 T in the vertical direction exists. What is the

magnetic flux through a horizontal circle of radius 0,68 m?

Chapter 10. Electromagnetism 369

 6. Consider a square coil of 3 turns with a side length of 1,56 m. The coil is
subjected to a varying magnetic field that changes uniformly from 4,38 T to
0,35 T in an interval of 3 minutes. The axis of the solenoid makes an angle of
197◦ to the magnetic field. Find the induced emf.

7. Consider a solenoid coil of 13 turns with radius 6,8 × 10−2 m. The solenoid is
subjected to a varying magnetic field that changes uniformly from −5 T to 1,8 T
in an interval of 18 s. The axis of the solenoid makes an angle of 88◦ to the
magnetic field.

a) Find the induced emf.

b) If the angle is changed to 39◦ , what would the radius need to be for the emf
to remain the same?

8. Consider a solenoid with 5 turns and a radius of 4,3 × 10−1 mm. The axis of the
solenoid makes an angle of 11◦ to the magnetic field.
Find the change in flux if the emf is 0,12 V over a period of 0,5 s.

9. Consider a rectangular coil of area 1,73 m2 . The coil is subjected to a varying

magnetic field that changes uniformly from 2 T to 10 T in an interval of 3 ms.
The axis of the solenoid makes an angle of 55◦ to the magnetic field. Find the
induced emf.

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370 10.4. Chapter summary