PHY102 - General Physics II: WEEK 2

(2-Credit Units)

Department of Physics and Materials Science.

Kwara State University, Malete, Nigeria.

Lecturer: Mr. O. K. AZEEZ

May 30, 2024

Course Outline: Forces in nature. Electrostatics (electric charge and its properties, meth-
ods of charging). Coulomb's law and superposition.Solved problems

Contents
1 Introduction 2
1.1 Conductors and Insulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Methods of Charging a Body 2

3 Electric Field and Lines of Electric Force 3

3.1 Law of Force Between two Charges . . . . . . . . . . . . . . . . . . . . . . . . . 3
3.1.1 Permittivity and Relative Permittivity . . . . . . . . . . . . . . . . . . . 3
3.2 Electric Field Strength OR Electric Field Intensity . . . . . . . . . . . . . . . . 3
3.2.1 Field Strength E due to a point Charge . . . . . . . . . . . . . . . . . . . 3

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1 Introduction
A charge is an amount of electricity. It is denoted by the letter Q. There are two kinds of
charges. These are:

1. Positive charge (+)

2. Negative charges (−)

Charging a rod by rubbing does not create or make electricity. The rubbing simply transfers
energy. A fundamental law of action between charges states that: like charges repel, unlike
charges attract. It must be noted that any uncharged body must contain equal number of
protons and electrons. A body which is negatively charged contains an excess of electrons
while one that is positively charged is decient in the number of electrons.

1.1 Conductors and Insulator

An electric conductor is a substance which is able to carry electric charges from one point
to another through it. In metals, conduction takes place by the movement of free electrons
and this explain why metals are good conductor of electricity. Insulators are substances which
do not allow electric charges to move easily through them. They contain no free electrons.
Examples are rubber, plastic materials, glass, silk, wool, fur, cotton, wood etc. There is a third
class of material that shares both the properties of conductors and insulators simultaneously
under a controlled condition. They are known as semi-conductors. Examples are silicon and
germanium.

2 Methods of Charging a Body

There are various methods of charging a body
1. Charging by Friction: When two substances are rubbed against each other, electrons are
transferred from one substance to the other. For example, if you comb dry hair with a dry
plastic comb and bring the comb near a small piece of paper, it will be attracted by the
comb. Similarly, when a plastic rod is rubbed with wool or a glass rod rubbed with silk or
cotton, the rod can attract a small piece of paper. The substance which acquires an excess
of electrons becomes negatively charged, while the other which losses electron becomes
positively charged. N OT E : A glass rod rubbed with silk acquires positive charge and
an ebonite rod after it has been rubbed with fur carries negative charge.
2. Charging by Induction: When a charged body is brought close to an uncharged body, but
not directly touching it, there will be distribution of charges on it. The redistribution of
charge on the conductor is according to the law that likes charges repel, unlike charges
attract. If the charged rod is removed, the positive and the negative charge on the
conductor return to their undisturbed positions. The separation of charges in a conductor
due to a charge body nearby is known as electrostatic induction. A conductor can be
given a permanent charge if it is earthed momentarily while still under the inuence of the
charged body. When the conductor is touched with a nger, we say it has been earthed.
3. Charging by Contact: This occurs when a charged conductor A, shares its charges with
another initially uncharged conductor B, by coming in contact with it. When separated,
both bodies now carry charges of the same sign such that the total charge on them is
equal to that carried by A initially.

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3 Electric Field and Lines of Electric Force
An electric eld is a region or space where an electric force is felt by a charged body brought into
that region. Electric eld is a vector quantity which has both direction and magnitude. The
direction of an electric eld at a point is dened as the direction of the force on a small positive
charge placed at that point. The magnitude of the eld is called the electric eld strength or
intensity. Electric eld may be represented by electric lines of force. An electric line of force is
the path that would be followed by a positive charge if it were free to move within the electric
eld. Line of forces emanates from the positive charges and end on the negative charges.

3.1 Law of Force Between two Charges

The inverse square law also known as Coulomb law states that the force between two electrically
charged bodies is inversely proportional to the square of the distance (r). i.e. F α r12 inverse
square law. The electric force between two point charges q1 and q2 separated by a distance r is
directly proportional to the product of the charge and inversely proportional to the square of
the distance between the charges. That is:
q1 q 2 kq1 q2
Fα → F = (1)
r2 r2
where k is a constant given by k = 4πϵ1 0 . ϵ0 denotes the permitivity of free space, if the charges
are in vacuum, The S.I unit of charges is the coulomb (C).
q1 q2
F = (2)
4πϵ0 r2

3.1.1 Permittivity and Relative Permittivity

The relative permittivity ϵr , of a medium is the ratio of its material permittivity ϵ to that of a
vacuum,ϵ0 . So, relative permittivity:
ϵ
ϵr = (3)
ϵ0

3.2 Electric Field Strength OR Electric Field Intensity

An electric eld can be dened as a region where an electric force is felt by a charge body. The
electric eld strength E at any point is dened as the force per unit charge which it exerts.
The direction of E is that of the force on a positive charge.
NOTE: The eld strength E is a vector quantity and so its direction is very important
when adding two or more values of E.
F
E= = N C −1 (4)
Q

It follows that the eld strength E has the unit of Newton per Coulomb (N C −1 ). A more
practical unit of E is the volt per metre (V m−1 )

3.2.1 Field Strength E due to a point Charge

The strength E of the electric eld due to a very small or point charge Q situated in a vacuum
can be derived as follows:
since F = kqr12q2 , assuming q1 = q2 = q ,

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 then
kq 2
F = . (5)
r2
But E = Fq → E = Fq = kqr2 ÷ q → kq
2

r2
Hence E = r2 , but k = 4πϵ0 so this can be rewritten as E =
kq 1 q
4πϵ0 r2

Example
Three charges +15C , −20C and −17C are distributed as shown in the diagram below. Find
the resultant force acting on the +15C charge.

Solution

The force of attraction between +15C and ˘20C is given by:

kq1 q2
F1 = r2

F1 = 9×109 ×15×20
32
= 3 × 1011 N

The force of attraction between +15C and −17C , is given by

9×109 ×15×17
F2 = 22
= 5.74 × 1011 N

net force F =
p p
F12 + F22 = (3 × 1011 )2 + (5.74 × 1011 )2 = 6.5 × 1011 N

F1 3×101 1
tan θ = F2
= 5.74×1011
→ θ = arctan(0.52) = 27.60

Assignment
1. Two similar but opposite point charges ˘q and +q each of magnitude 5×10−8 are separated
by a distance of 8.0cm in a vacuum as shown in the diagram below. Calculate the
magnitude and direction of the resultant electric eld intensity E at the point P.

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 2. Two point charges +30C and +20C are separated by a distance of 12cm. compute the
electric eld intensity and the force on a +5 × 10−6 C charge placed midway between the
charges.

Assignment submission deadline: Monday, June 3, 2024, at 10:00 AM. Point of Submission
Physics lab SL2.