UNIT 1 ELECTRICITY AND MAGNETISM

Modules 1 – 2

Content Standard: The learners demonstrate an understanding of:

1. Electric charge
2. Insulators and conductors
3. Induced charges
4. Coulomb’s Law
5. Electric forces and fields
6. Electric field calculations
7. Charges on conductors

Performance Standard: The learners shall be able to use theoretical and experimental
approaches to solve multi-concept and rich-context problems
involving electricity and magnetism

Lesson Objectives: At the end of the lesson, the students should be able to:
1. Describe using a diagram charging by rubbing and charging by induction.
2. Explain the role of electron transfer in electrostatic charging by rubbing.
3. Describe experiments to show electrostatic charging by induction.
4. State that there are positive and negative charges, and that charge is measured
in coulombs.
5. Predict charge distributions, and the resulting attraction or repulsion, in a
system of charged insulators and conductors.
6. Calculate the net electric force on a point charge exerted by a system of point
charges.
7. Describe an electric field as a region in which an electric charge experiences a
force.
8. Draw electric field patterns due to systems with isolated point charges.
9. Use in calculations the relationship between the electric field and the electric
force on a test charge.
10. Calculate the electric field due to a system of point charges using Coulomb’s
law and the superposition principle.
11. Predict the trajectory of a point charge in a uniform electric field.
12. Calculate electric flux.
13. Use Gauss’s law to infer electric field due to uniformly distributed charges on
long wires, spheres, and large plates.
14. Solve problems involving electric charges, dipoles, forces, fields, and flux in
contexts such as, but not limited to, systems of point charges, classical models
of the atom, electrical breakdown of air, charged pendulums, control of
electron and proton beams, electrostatic ink-jet printers.

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 DEVOTIONAL

In The Image of God

The phrase “the image of God” has captivated interpreters of the Bible for
centuries. What is this image in which the first humans were created? For example, does
it mean that God looked in a mirror and formed His new creation to look like Himself?
Or does it mean that humans are more like God than all other forms of life are? Or does it
refer to a spiritual and intellectual similarity and compatibility between the Creator and
His human creation? The Scriptures do not give any precise explanation of this
expression even though scholars have derived from Scripture many interpretations of
what it could mean.

However, we can see that, after sin, this image had been changed, which is why
Ellen G. White wrote that the goal of education is to restore in man the image of his
maker (Education, pp. 14-16).

How can education achieve such a remarkable goal?

First, we need to remember that God made us have a relationship with Him,
somewhat as parents do with their children. He made us in His image, the same way
human parents have children in their image (Gen. 5:1) so that He can bring us up to be
His children, who belong to His family; He can communicate with us and form a lasting
relationship with us. The image of God, therefore, is more of a “mental image” that
enables two beings, one divine, and the other human, to have a meeting of minds. This is
precisely what happens in education, first at home between parents and children, and later
at school when teachers take over the work of education. God intended this process of
education we know so well when, distinguishing us from many other life forms, He made
us in His image – He did it so that He can teach us and we can learn from Him until His
image (His mind) is reflected in ours.

DEVOTIONAL QUESTION
The story of redemption is a story of education from creation to incarnation, and
from incarnation to re-creation. God is a teacher, and heaven is a school for all
time (see Ellen G. White, Education, p. 301). What are the implications of this
thought for our commitment to Christian education at home, in church, in school,
in the university, and throughout life?
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 START – OFF

PURPOSE
Electricity plays a significant role in society. Nearly all technologies today use
electrical energy to work. As technology made human life more convenient, you can say
that electricity is associated with convenience as well. Magnetism, on the other hand, is
an effect of the presence of electricity.

The conversion from electrical energy to work is useful in your daily activities.
This conversion also provides further opportunities for technological advancement.

As future professionals in the field of science and technology, you have to

understand the principles of electricity and magnetism because these concepts, just to
name a few, will help you make wise decisions in your respective careers.

ESSENTIAL QUESTION
Why study Physics and its relevance?
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PURSUE CONTENT/BIG IDEAS

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MODULE 1: Electric Charges

You learned from Chemistry that the atom is the basic building block of matter. It
comprises the following subatomic particles: proton, electron, and neutron. These three
differ in the charge that they carry. Protons are positively charged (+e), whereas
electrons have negative charges (-e). Neutrons have no charge or are electrically neutral.

Fig 1.1 An early representation of the three subatomic particles of an atom

proton, electron, and neutron. Eventually, this was replaced with a model that
corresponds to the modern atomic theory.

Electric Charge
At the atomic level, an electric charge determines the electric interaction and magnetic
interaction between subatomic particles and other charged particles.

Fig 1.2 An experiment using a glass rod and a rubber rod shows that like charges
repel each other, and unlike charges attract each other.

As shown in the figure here, a glass rod and a rubber rod are used to demonstrate the
interaction between electric charges. It was found out that after rubbing the rubber rod
with fur and the glass rod with silk, both pairs of objects acquired charges. Two glass
rods are found to repel each other, whereas a glass rod is found to be attracted to the
rubber rod. Based on these observations, the law of charges is stated as follows: Like
charges repel each other, and unlike charges attract each other.
As a derived SI (or International System of Units) quantity, an electric charge is
represented by the symbol “q” and measured using the unit coulomb (C). In Chemistry,
you learned that the charges of subatomic particles are measured in terms of e. The
relationship between e and coulomb is

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 1 coulomb = 6.242 x 1018e

Furthermore, electric charge is quantized. This means that the charge is either
zero or a multiple of the basic unit of e.
In an atom, the subatomic particles provide the net charge. An electrically neutral
atom contains an equal number of protons and electrons. An atom that has an imbalance
in the number of protons and electrons is called an ion. Cations are positive (more
protons than electrons), and anions are negative (more electrons than protons).
Macroscopically, a body is electrically charged if the number of positive charges
it has is not equal to the number of negative charges. In other words, the charge of a
particle depends on the sum of its electrical charges.

BIG IDEA
Opposite charges in an atom attract each other. If the positive charges of an
atom outnumber the negative charges, the atom is a positive ion. If there are
more negative charges than positive charges in an atom, the atom is a
negative ion.

Conductors are materials that allow electrical charges to move from one material to
another. Conductors may be charged through different methods – rubbing, conduction, ad
induction. The following section discusses these charging methods in detail.

a. Charging by Rubbing
An electrically neutral body can gain a charge by rubbing or friction. Consider
two different uncharged bodies. Because of the difference in their material compositions,
the nuclei of their atoms pull their electrons with different strengths. Rubbing these two
bodies will force their atoms to interact with each other, resulting in the “ripping off” of
electron(s) from the body with a weaker electron hold. The “ripped off” electrons are
then transferred to the other body. After rubbing, one of the bodies will have more
electrons, and the other one will have fewer. Thus, both will now be electrically charged.

Fig 1.3 Both the glass rod and the silk cloth become electrically charged after
rubbing them together.

An example of charging by rubbing is shown in figure 1.3. A glass rod acquired a

positive charge after being rubbed with the silk cloth, and the silk cloth acquires a
negative charge. Charging by rubbing also explains why we experience a weak electric
shock when we suddenly touch a metallic object after walking on a carpeted floor.

BIG IDEA
An object that holds its electrons weakly will eventually lose them when

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 rubbed with another object that has a stronger hold in its electrons.
Similarly, you should strongly hold on to whatever is important to you so

that you won’t lose it when rough times come or when you need it. 😊

The charge acquired by rubbed materials can be determined using the triboelectric series.
The triboelectric series is a list of common materials that were experimented on and
found to behave predictably. When these materials are rubbed together, those that appear
first in the list tend to lose their electrons, making them positive. Meanwhile, those latter
in the list tend to gain electrons, making them negative. In other words, if you rub any
two of the materials in the series, the material in the upper part of the list will be positive,
and the other material in the lower part will be negative.

Table 1.1 A few of the materials in the triboelectric series

Triboelectric Series
1. dry hand 6. wool 11. rubber
2. leather 7. fur 12. polyester
3. glass 8. silk 13. Styrofoam
4. human hair 9. wood 14. polyurethane
5. nylon 10. amber 15. PVC

Example: Using the information presented in table 1.1, determine the acquired charges of
the bodies in each of the following pairs if they are rubbed together.
a. wood and Styrofoam c. glass and leather
wood: + glass: –
Styrofoam: – leather: +
b. nylon and silk d. rubber and rubber
nylon: + rubber: none
silk: – rubber: none

b. Charging by Conduction
A body can also be electrically charged through conduction. Consider a neutral
body A. Charges in A are evenly distributed throughout the material. Suppose a strongly
negative body B is brought near A. The negative charges of A will move to the side
farther from where B is. Consequently, the positive charges of A will be attracted toward
the side near B. If B will touch A, some of B’s negative charges will transfer to A as these
spread away from each other. If B will be separated from A, B is now less negative than
before, while A is now more negative. See figure 1.4.

Fig 1.4 When a negatively charged

rod comes into physical contact with B
a metal sphere, some of the electrons
of the rod transfer to the sphere. A
Thus, the metal sphere becomes
more negative than the rod.
BIG IDEA

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 Bringing an object with a strong positive charge near an object with a
neutral charge can make the latter acquire a charge similar to the strong
one. Likewise, mingling with people with positive dispositions can make

you acquire their positivity. 😊

c. Charging by Induction
Another method of electrically charging a body is through induction. Charging by
induction is illustrated as follows:

Fig 1.5 Charging by induction shown using a tin can be resting on an insulating
stand and a balloon.

A negatively charged balloons are placed near (but without physical contact) a
neutral tin can. Asa result, the positive charges of the can move to the left, near the
negatively charged balloon because of attraction. Meanwhile, the negative charges move
to the right side of the tin can, away from the balloon because of repulsion. The excess
negative charges at the right side of the tin can are known as induced charges.
Being near a negatively charged object, the tin can’s electrical charges separate ---
the negative charges move to the right side, and the positive charges move to the left side.
The separation of electrical charges to opposite poles due to induction is known as
polarization. If the balloon is removed, the charges of the tin can simply rearrange, and a
neutral condition is achieved.
Charging an object by induction may also occur through a process called
grounding. Grounding is a process similar to conduction, but it includes a grounding
wire that connects the neutral body A (the metal sphere in figure 1.6) to the ground,
which is a reservoir of charge. If a strongly positive body B (the rod in figure 1.6) is
brought near A, the negative charges of A will move to the side near B. negative charges
from the ground will also travel to the same side via the grounding wire. If the grounding
wire is suddenly cut, the negative charges that went to A from the ground will stay in A,
thus making the body more negatively charged. See figure 1.6.

Fig 1.6 An illustration showing

how charging by induction
works with a ground
connection.

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Electric Dipoles
In the previous discussion, you have learned that when you bring neutrally
charged body A near a strongly negative body B, its positive charges will be drawn near
B, and the negative charges will be pushed to the other side. This resulting condition
polarizes the body and forms a dipole. Polarization is the process wherein an electrically
neutral body becomes polar by the rearrangement of its molecules. As the molecules
realign or move, particles with similar charges group together and move toward the
opposite ends of the body. Hence, the body becomes positive at one end and negative at
the other, making it a dipole.

What is the role of polarization in the formation of dipoles?

Point dipoles refer to atoms bearing a positive side and a negative side. In such
atoms, the electrons converge or gather on one side and the protons on the other. An
extension of this concept gives rise to molecular dipoles. This type of dipole involves a
molecule having a negatively charged side and a positively charged side. The
electronegative atoms of the molecule form the negative end of the molecule, and the
electropositive ones are responsible for the positive end.
Another way to classify dipoles is whether they are permanent or temporary
(instantaneous). An instantaneous or a temporary dipole is an atom or a molecule with
most of its negative charges shifted only to one side as a result of their random
movement.

Essential Learning
Electric charge is the property of subatomic particles that determines their interaction
with other charged particles. The electric charge of a body is expressed in integer
multiples of e, and the unit coulomb (C) is used to measure the electric charge. Charges
can be either positive or negative. similar charges repel, and unlike ones attract.

Electrically neutral bodies can acquire charges by friction or rubbing, conduction, or

induction. In these methods, electron transfer plays a significant role.

A body with a positive charge on one end and a negative charge on the other end is
called an electric dipole. This occurs as an effect of a strongly positive or strongly
negative charge being brought near an electrically neutral body.

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MODULE 2: Electrostatic Force, Electric Field, and Electric Flux

The act of repelling implies pushing and the act of attracting suggests pulling. You know
that a push or a pull pertains to force. You can then say that electric charges exert a force
on each other as they interact.

Fig 2.1 How electric charges using

force when they interact
with each other.

Electrostatic Force
You learned from the previous module that like charges repel each other and
unlike charges attract each other. This attraction and repulsion between electric charges
come from a force is known as electrostatic force. This force can be computed using
Coulomb’s Law for electrostatics as shown here.
→ k q1 q2
FE= 2
r
→
In this equation, F E is the electrostatic force, q1 and q2 are the magnitudes of the
charges, r is the distance between the charges, and k is known as Coulomb’s constant
with the value of
2
9 N .m
k =8.99 x 10 2
C

Because it is a force, the electrostatic force is expressed in newton (N).

Coulomb’s constant is an indication of the strength of electrostatic force compared with
other types of forces.

Coulomb’s Law can be seen as a variation of Newton’s Law of universal

gravitation. While Newton’s Law governs the gravitational force between two bodies,
Coulomb’s law quantifies the electrostatic force between two charges. It states that an
electrostatic force is directly proportional to the product of the charges and is inversely
proportional to the square of the distance between two charges. This means that stronger
charges will result in a stronger force, and weaker charges will result in a weaker force.
Furthermore, the greater the distance between the charges, the weaker is the force
between them. Meanwhile, the force strengthens as the charges move closer to each
other.

Fig 2.2 Illustration of the effects of Coulomb’s Law

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Examples 1: a. What is the electrostatic force of attraction between a -6.0 x 10 -6 C charge
and a 4.0 x 10-6 C charge if they are separated by a distance of 3 meters
(m)?

Solution: →
FE=
(
8.99 x 10 9
N .m2 (
C
2 )
−6.0 x 10−6 C ) ( 4.0 x 10−6 C )
≈ 0.02 N
3 m2

The force of attraction between the given charges is approximately 0.02 N.

b. Two identically charged one–peso coins are 1.5 m apart on a table. What
is the charge of one of the coins if each of them experiences a repulsive
force of 2.0 N?

√ ( F ) (r ) =
√
→
2
E ( 2.0 N ) ( 1.5 m )2 −5
Solution: q= ≈2.23 x 10 C
( )
k N .m 9
2

2
8.99 x 10
C
Each coin carries a charge of approximately 2.23 x 10−5 C .

BIG IDEA
As charges move farther from each other, the electrostatic force between
them weakens. As they move near to each other, this force strengthens. You
can relate this science concept in real life to the concept of relationships. As
two people move farther from each other, their friendship usually weakens
because of their separation. On the other hand, friendship tends to be

stronger when two people find time to be together. 😊

The Superposition Principle

Consider four electric charges in a vacuum. Each pair of charges will interact with
each other, and electrostatic forces are exerted between these charges as they interact.
There are a total of six forces in the described system of four electric charges in a
vacuum. As these forces are vectors, you simply add them to get the resultant force.
Recall from your previous physics class that the resultant force is the sum of all
the forces acting on a body. This means that if you have two or more forces applied to a
body, the body will experience the net effect of all the forces applied. This addition of
forces applied to a body is essentially an application of the superposition principle.
In the study of electrical charges, the superposition principle essentially means
that the overall effect or net effect of the presence of electric charges in a given system is
equal to the individual effects of each pair of charges in the system. In figure 2.3, you can
see how the six electrostatic forces are added and resulted in a single electrostatic force.

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 Fig. 2.3 An application of the
superposition principle

Examples 2:
1. Consider the following three-point charges arranged along the x-axis:
a. q1 has a charge of – 8.0 µC and is located at x = – 3.0 m
b. q2 carries a charge of 3.0 µC and is located at the origin
c. q3 has a charge of – 4.0 µC and is located at x = 3.0 m

What is the overall force experienced by q2?

q1 = – 8.0 µC q2 = +3.0 µC q3 = – 4.0 µC

Solution: The force between q1 and q2 is computed as follows:

( )
2
N .m (
−8.0 x 10 C ) ( 3.0 x 10 C )
9 −6 −6
8.99 x 10 2
→
C
F 1, 2=
¿¿

The force between q2 and q3 is computed as follows:

( )
2
N .m (
3.0 x 10 C ) (−4.0 x 10 C )
9 −6 −6
8.99 x 10 2
→
C
F 1, 2=
¿¿

Note that both q1 and q3 will equally attract q2. This implies that q2 will be
suspended at the origin and will experience a net force (resultant force) of
→ →
0 N. F 1, 2can be interpreted as – 0.02 N (going to the left) and F 2 ,3as 0.02
N (going to the right). By the superposition principle, you have
→
F Enet ≈−0.02 N + 0.02 N ≈ 0 N
The charge q2 will not experience any net force.

2. Three-point charges are arranged along the y – axis in a vacuum. The topmost
charge bears a charge of – 4.0 µC, the middle charge has a charge of +3.0 µC,
and the bottom one carries a – 7.0 µC charge. What is the magnitude and
direction of the net electrostatic force that the middle charge experiences?

Solution: The force between the top charge and the middle charge is computed as
follows:

11
 ( )
2
N .m (
−4.0 x 10 C )( 3.0 x 10 C )
9 −6 −6
8.99 x 10 2
→
C
F top−middle =
¿¿

The force between the bottom charge ad the middle charge is computed
as follows:

( )
2
9 N .m
8.99 x 10 2
(−7.0 x 10−6 C ) ( 3.0 x 10−6 C )
→
C
F bottom−middle=
¿¿

The top charge will pull the middle charge upward (positive direction
concerning the y – axis), whereas the bottom charge will pull the middle
charge downward (negative direction concerning the y – axis). Thus, by the
superposition principle, you have
→
F Enet ≈ 2.7 N + (−4.7 N ) ≈−2 N
The middle charge experiences a net electrostatic force of approximately
– 2 N.

BIG IDEA
The superposition principle states that individual electrostatic forces are
added as vectors to yield a single resultant vector. Similarly, you can say
that the positive and negative traits of a person are part of his or her

identity. 😊

Electric Field and Its Representation

The area or field around a charge where the electrostatic force can be experienced
is called the electric field. An electric field coexists with every electrostatic charge; it
associates with each point in space the electrostatic force experienced per unit of electric
charge, by an extremely small (or infinitesimal) test charge at that point. A test charge is
a single charge whose behavior is measured or determined based on the presence of
external factors or stimuli. Its presence is arbitrary. For easier computation, a unit of 1 C
is used.

What is an electric field? What is its importance in an electrostatic charge?

Electric fields predict the behavior of the charges present in any location in space.
Physicists compute the value of an electric field because of its direct relation with
electrostatic force. Mathematically, the electric field can be computed using the equation
→
kQ
E= 2
r

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 →
In this equation, E is the electric field, Q is the source charge, and r is the distance
from the source charge where the electric field is being measured. The unit used to
measure electric field is newton per coulomb (N/C). The source charge is the charge
from where the electric field comes from. In simpler terms, you determine how the test
charge will behave as the result of the electric field coming from the source charge.
The equation for the electric field here shows its relationship with electrostatic
→ FE
force, as follows: E=
q
F
In this equation, E is the electrostatic force experienced by the electric charge.
An electric field is also a vector quantity. It has the same direction as the electrostatic
force exerted on an electric charge.

Examples 3:
1. Calculate the electric field that a test charge will experience on the following
distances from the source charge of +5.02 x 10-13 C.

a. Distance from source charge: 2.04 x 10-3 C.

( )
2
9 N .m
8.99 x 10 2
( 5.02 x 10−13 C )
Solution: →
kQ C
E= 2 =
r ¿¿

The source charge will experience an electric field of

approximately 1,084.43 N /C .

2. A charge of +3.0 x 10-8 C experiences an electrostatic force of 6.0 x 10 -8 N.

Compute the force per coulomb that the charge experiences.
→ F E 6.0 x 10−8 N
Solution: E= = =2.0 N /C
q +3.0 x 10−8 C

The electric field of the charge is 2.0 N/C.

Electric Field Lines

An electric field can be graphically represented using electric field lines. The
density or thickness of these lines is directly proportional to the strength of the electric
field at any region in space. If the field lines are close to each other, the electric field is
stronger.
Electric field lines are drawn based on the charge being considered. Positive
charges have field lines drawn from them. Negative charges have field lines drawn to
them.

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 (a) (b)

Fig 2.4 Electric field lines of electric charges: (a) filed lines of positive charges
are drawn outward (away from the positive charge). (b) Field lines of negative
charges are drawn inward (toward the negative charge).

Consider a positive charge and a negative charge in space. Electric field lines are
drawn from the positive charge and directed to the negative charge. See figure 2.5

Fig 2.5 Electric field lines from the

positive charge going to
the negative charge.

BIG IDEA
Electric field lines are represented by arrows showing the direction of the
electric field from the positive charge to the negative charge. In life, people
who have positive values tend to be givers, whereas individuals with

negative attitudes just want to take without giving. 😊

Electric Flux and Gauss’s Law

An electric field is represented by arrows to indicate the flow or movement from a
positive charge or to a negative charge. This flow of an electric field through a given area
is measurable using electric flux. Mathematically, the equation used to compute for
electric flux is as follows:
→
Φ E =(E )( A) ¿
→
In this expression, Φ E stands for electric flux, E for the electric field, A for the
area of the considered surface, and Ɵ for the angle between the electric field lines and the
line perpendicular to the surface of A. the unit used to measure electric flux is a voltmeter
2
N .m
(V – m) or newton-meters squared per coulomb . Note that this equation is useful
C
for both the uniform electric field and the area.

Example 4: What is the electric flux for the following sets of variables?
→
a. E =9.5 x 1013 N /C
−5 2
A=1.6 x 10 m
Ɵ=75 °
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 Solution: Φ E =(9.5 x 1013 N /C )(1.6 x 10−5 m2)¿V – m
The electric flux is approximately 3.93 x 10 8 V – m.

Fig 2.6 A Gaussian surface

For closed surfaces, electric flux is calculated using a technique or law called
Gauss’s law. Gauss’s Law states that the electric flux through any closed surface is equal
to the net charge inside the surface divided by the permittivity of free space.
Electric fields around regularly shaped bodies can be predicted analytically using
the computations made earlier. This is because the charges in these regularly shaped
bodies are uniformly distributed. Qualitative descriptions of the electric field are also
possible as the surfaces concerned are symmetrical.
An example of this is a negatively charged straight wire. Electric field lines can
be drawn toward the wire, implying that the electric field is directed toward the wire.
Meanwhile, for a positively charged hollow ball, you can predict that the electric field
will move away from the surface of the ball. Last, an infinite line of charge will have the
associated electric field lines moving either from or toward its surface depending on the
charge that it possesses.
The treatment of irregular electric fields coming from irregularly shaped surfaces
requires the use of the differential and integral forms of Gauss’s law. An irregularly
shaped surface will have varying electric fields at all points of its body. Your knowledge
of differential and integral calculus will help solve related problems.

15
 Fig 2.7 Examples of electric fields around closed surface: (a) a positively charged
hollow ball and (b) an infinite line of charge.

Applications of Electrostatics
Now that you know how electric charges behave, you can now understand how
they are applied in the development of technology through the years. The following
sections will discuss various applications of the predictable behaviors of electric charges.

Atomic Models
Atoms are made of electric charges. The interaction between these charges can
predict how each atom will behave.

Example 5: Consider the Bohr model of a hydrogen atom. An electron orbits a proton at
a radius of 5.3 x 10−11m. what is the force of attraction between the said
particles? How fast is the electron orbiting the proton? Consider the mass of
the electron to be 9.1 x 10−31 kg.

( )
2
N .m (
1.6 x 10 C )( −1.6 x 10 C )
9 −19 −19
8.99 x 10 2
Solution: →
C −8
FE= 2
≈ 8.19 x 10 N
( 5.3 x 10 −11
m)

The force of attraction between the electron and the proton is approximately
−8
8.19 x 10 N . this implies that the proton is pulling the electron toward it
with a force as computed. This force is referred to as the centripetal force,
which is the force experienced by a body in a uniform circular motion as it
revolves around its orbit.

Recall the equation for centripetal force.

→
→
mv2
F C=
r
Then, you have

√ ( 8.19 x 10−8 N ) ( 5.3 x 10−11 m)

→
v= −31
≈ 2.18 x 106 m/s
9.1 x 10 kg

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 The electron orbits the proton with a velocity of approximately 2.18 x 10 6 m/ s.
This high velocity explains why the orbits of electrons are represented as clouds
around the nucleus of an atom. The clouds represent the area in the atom where
there is a high probability of finding an electron.

BIG IDEA
The nucleus of helium has a charge of +2e, whereas the nucleus of neon
has a charge of +10e (e =1.6 x 10−19 C ¿ .

Electrical Breakdown of Air

The electrical breakdown of air is responsible for the formation of lightning and
the presence of other electrical charges in the atmosphere.

Charged Pendulums
One of the hypothetical applications of the concept of electrical charges is their
role in pendulums bearing a respective electric charge.

Example 6: Two identical balls, each with a mass of 0.10 g, carry identical charges
and are suspended by threads of equal lengths. The figure here shows their
equilibrium position. Find the charge on either ball.

Solution: Look at the ball on the left. Three forces place the ball in equilibrium –
(1) the tension in the thread (T), (2) the repulsive force between the two
balls, and (3) the weight of the ball. The equation is as follows:

( )
→
m
W =( 1 x 10 kg ) 9.8 2 =9.8 x 10 N
−4 −4

Note that the ball is in equilibrium. Then you have

→ →
∑ F x =0 N and ∑ F y =0 N
This means that
→
T cos 60 – F x =0 N (1)
→
T sin 60 – W =0 N (2)
Using equation (2),

17
 →
W 9.8 x 10−4 N −3
T = ≈ 1.13 x 10 N
sin 60 sin 60

Using this value of T in equation (1), you have

→
F x =T cos 60 ≈ ( 1.13 x 10−3 N ) ( cos 60 )=5.65 x 10−4 N

This is the force of attraction between the charged balls. Therefore,

→
2 F E r 2 ( 5.65 x 10−4 N ) ( 0.4 m )2 −14 2
q= = ≈ 1.00 x 10 C

( )
k 9 N .m
2
8.99 x 10 2
C
Then, you have
q=√ 1.00 x 10−14 C 2 ≈ 1.00 x 10−7 C

Each ball has a charge of approximately 1.00 x 10−7 C . This means that
the electrostatic force of repulsion between the charged balls is due to
the computed charge that each of them possesses.

Control of Electron Beams and Proton Beams

Electron beams are industrially used in cross-linking polymers in the field of
materials engineering. For example, in electron beam machining, a narrow beam of high–
velocity electrons are directed toward an object. This setup creates heat that could
vaporize the material. Thus, electron beam machining is useful in the accurate cutting of
metals. Electron beams are also used to produce X – rays, television screens, and
oscilloscope images.

Fig 2.8 Top view of the components of an X-ray machine

Proton beams, on the other hand, have found their use in cancer treatment and other non –
invasive disease treatments.

Inkjet Printers

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 Inkjet printers also make use of the principles of electrostatics to work. An inkjet
printer charges the ink and uses the principle of electrostatic repulsion to propel the
charged ink toward the paper or material to be printed. The computer form where the file
is to be printed provides the codes for the head of the printer and ensures precise
repulsions to the charged ink particulates.

EXTEND YOUR KNOWLEDGE

To understand Gauss’s lawfully, you need to study higher mathematics, particularly
calculus. Visualizing Gauss’s law can also be challenging because the electric flux is
something that you cannot see. The link here will facilitate your understanding of this
especially important scientific principle.
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html

Essential Learning
The electrostatic force is the attraction or repulsion between electric charges. The law of
electric charges states that similar charges repel each other, and unlike charges attract one
another. This force is measured using the unit newton and is computed using Coulomb’s
law for electrostatics. The superposition principle implies that electrostatic forces can be
added as vectors to yield a resultant force.
As you move away from a charge, the electrostatic force weakens. The area around a
charge where an electrostatic force experienced by a test charge is referred to as the
electric field. Furthermore, electric field lines emanate from positive charges and
terminate at negative charges. The electric field is measured using the unit newton per
coulomb.
Gauss’s law for electrostatics quantifies the flow of electric field at any region in space.
This flow is the electric flux and measured using the unit voltmeter.

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 APPLY FORMATIVE ASSESSMENT

1. Compute the charge of the following ions. The first one has been done for you.
a. An ion with a charge of +3

(
( +3 e )
1C
18
6.242 x 10 e) −19
≈ 4.806 x 10 C

b. An ion with a charge of – 2

c. An ion with a charge of +5
d. An ion with a charge of – 3

2. Identify the acquired charges of each material in the following pairs if they are
rubbed together. Use the information presented in table 1.1.
a. Glass and polyurethane
b. Leather and fur
c. Styrofoam and rubber
d. Human hair and wool
e. Polyester and dry hand

3. In the space here, show charging by conduction if a strongly positive body B is

brought near body A. Be guided by the statements provided in each box. Label
your illustrations clearly.
1. An electrically neutral body A and a 2. Body A is brought near, but not in

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 strongly positive body B are apart from physical contact with B.
each other.

3. Body A is brought in contact with B. 4. Bodies A and B are separated from

Electrons transfer from A to B. each other, carrying their respective
charges.

4. In your own words, describe how electrically neutral bodies become charged by
the following methods:
a. Rubbing or friction
b. Conduction
c. Induction

5. Compute the force of attraction between a +1.60 x 10 -19 C charged and a – 2.09 x
10-18 C charged if they are 4.01 x 10-10 m apart.
6. Calculate the repulsive force between a – 1.15 x 10 -19 C charge and a – 1.49 x 10-8
C charge if a distance of 2.01 x 10-20 m separated them.
7. Compute the electric field experienced by a test charge q=+0.80 µC from a
source charge q=+15 µC in a vacuum when the test charge is placed 0.20 m
away from the other charge.

8. What is the electric flux for the given variables?

→
23
E =3.4 x 10 N / C
−2 2
A=2.3 x 10 m
Ɵ=84 °

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References:

 https://ssnet.org/lessons/20d/less08.html
 Senior High School Series: General Physics 2, Philippine Copyright 2017
by DIWA Learning Systems, Inc.

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