President Ramon Magsaysay State University

College of Engineering

Iba, Zambales

A report on

The Concept of Electric Fields

In Partial Fulfillment of the subject

Physics for Engineers II (PHYS 1B)

Submitted by:

John Angelo M. Marzan

BSME 1B

April 21, 2022

Submitted to:

Engr. Oliver A. Sabado Jr.

Instructor
I. Abstract

The concept of electric field is simple. An electric charge produces an electric

field, causing other electrically charged bodies around it to experience a force. The
symbol for an electric field is a capital letter E with a vector symbol on top to emphasize
that it’s a vector quantity (⃗
E ). Electric fields are important in a lot of areas of physics,
and are being applied in electrical technology. The concept of electric field is also used
in other fields such as biology and chemistry.

II. Introduction

This discussion aims to explain the different concepts related to Electric Field.
Specifically, it aims to provide the definition of the word, analyze the formula and give
sample computations, and give real world examples and applications of the topic.
Electric field is defined by the Merriam-Webster dictionary as a region associated with a
distribution of electric charge in which forces due to the charge or field act upon other
electric charges. Electric field is governed by Coulomb’s law and Gauss’s law.
Nowadays, the concept of electric field is being used in different fields such as biology,
medicine, and engineering.

III. Discussion

An electric field is the physical field that surrounds electrically charged particles
and exerts force on all other charged particles in the field, attracting or repelling them
depending on their charges (positive or negative). Electrically charged bodies produce
an electric field, they modify the properties of the space around them. An electric field is
present in all points around a charge. For example, we have a charged particle A. This
electric field is present on the different given points in the figure, whether those points
are charged or not. The force, which causes attraction or repulsion, experienced by an
electrically charged body is caused by the electric field produced by another electrically
charged body as shown in figure 2.

Electric Field Repulsive Force

+ +
A q0
Figure 1
 The electric field can be mathematically defined as the force per unit charge
F
exerted on a positive test charge at rest at that point. In symbols, E= q , where E is the
0

electric field, F is the force experienced by the charge, and q 0 is the test charge. The
q1 q2
force can be computed by Coulomb’s law, F=k 2 , where k is the proportionality
r
9 N m
constant equal to 9.0 x 10 , q1 and q2 are the magnitude of the charges, and r is the
C
distance between the two charges. From this, we can say that the strength of an electric
field depends on the distance from the charge producing it, the closer you are, the
stronger it is, and vice versa. The SI unit for electric field is N/C since the SI unit for
force is Newton (N) and the SI unit for charge is Coulomb (C). Electric field is a vector
quantity, same as force. Its direction changes based on the charge of the test charge q 0.
If q0 is positive, the direction of the field is the same as the direction of the force. If q 0 is
negative, the electric field and the force will have different directions.

The sources of an electric field may vary, the simplest source distribution is a
point charge, just one electrically charged point in a plane. The location of this charge is
called the source point, which can be represented as q in the formula. The location
where we want to know the electric field is called the field point. The location between
these two points can be represented as r. To determine the electric field, a test charge
q0 must be placed on the field point. With these, we can use Coulomb’s law to calculate
1 ¿
for the electric force. F= 4 π ∈ ¿ q q 0∨ 2 ¿. Then we can compute for electric field by
0 r
¿ q q0 ∨ ¿2
dividing the electric force by the test charge q0 E= F = 1 r
=
1
¿ q∨ ¿2 ¿ ¿ .
q0 4 π ∈0 q0 4 π ∈0 r
 The source of an electric field is not always a point, however. The source can be
electrically charged throughout their line, rod, sphere, donut-shaped body. An example is
the charged balloon and glass rod in Figure 3.

Figure 3

The charges throughout the body of the balloon and the glass rod all produce an
electric field. In these cases, we use geometry techniques, determine whether the
source of a field is a line, surface, or a volume, and solve based on it. For example, there
are two opposite charges with the same magnitude of 9nC, 16cm apart, an electric
dipole with q1 (+) and q2(-), producing an electric field, and the point field a, 10 cm from

Figure 4
both q1 and q2, is affected by both fields. First, we draw a figure to visualize easier.

θ
θ

To find the electric field at point a, we need to have a good understanding of

vectors. The electric field at a point affected by two charges is given by the principle of
Superposition: ⃗E =⃗ E1 + ⃗
E2 + ⃗
E3 +…, where ⃗
E1 , ⃗
E2 ,∧⃗
E3 are the fields that affect a point. In
this case, ⃗
E =⃗
E1 + ⃗
E2 since two fields affect the field point a. We use the formula for point
1 1
charge twice, one for each charge. ⃗ E1= ¿q ∨ ¿ ¿ ⃗
E= ¿q ∨ ¿ ¿
4 π ∈0 1 r 21 and 2 4 π ∈0 2 r 22 . Since the
distance and magnitude are equal,

( )
−9
9 N m 9 x 10 C
⃗
E 1= ⃗
E 2= 9.0 x 10 =8100 N /C
C (0.10 m)2

We also have to consider the x(horizontal) and y(vertical) components or

direction of the field in the field point. For the x component, we can see from figure 4
that the field ⃗
E1∧ ⃗E 2 are both going to the right, they have the same direction, and
therefore are equal. From this,

⃗
E1 x = ⃗
E2 x = ⃗ (
E 1 cos θ=
8100 N
C )( 108 )=6480 NC
 For the y component, the two fields have the same magnitude but opposite
directions, ⃗
E1 goes upwards and ⃗
E2 goes downwards. ⃗ E1 y =−⃗
E2 y . ⃗
E1 y + ⃗
E2 y =0. Hence, we
N
only need to use the x component. ⃗
E1 x =⃗
E2 x =6480 .
C

⃗ N N N
E x =⃗
E1 x + ⃗
E 2 x =6480 +6480 =12960 ¿ the ¿
C C C

At point a, the electric field is 12960 N/C directed to the right.

An electric field can be visualized easier using electric field lines. An electric field
line is drawn is an imaginary line drawn through a region of space so that its tangent at
any point in the direction of the electric field vector at that point.

Figure 5a Figure 5b

Figure 5a shows electric field lines drawn when there are 2 like charges near each other.
Figure 5b show electric field lines drawn when there are 2 opposite charges near each other.
Michael Faraday introduced this way of visualizing electric fields.

The concept of electric fields is applied in chemistry, industrial processes, biology and
medicine. Specific examples can be seen in Figures 6a and 6b.

Figure 6a Figure 6b
IV. Conclusion

An electric field is the physical field that surrounds electrically charged

particles and exerts force on all other charged particles in the field, attracting or
repelling them depending on their charges (positive or negative). Electric fields are
produced by a charged body. The simplest form of charged body is a point charge, but
an electric field can also be produced by a line, a surface, or a volume. The electric field
F 1
can be computed using the formula E= q ∨⃗ E= ¿ q∨ ¿2 ¿ for point charges. For
0 4 π ∈ 0 r
other electric field sources, the electric field on a field point, the point in a plane that we
are trying to solve for the electric field, is computed using the principle of Superposition:
⃗
E =⃗E1 + ⃗
E2 + ⃗
E3 +…. The use of this principle depends on what the source of an electric
field is. An electric field can be visualized easier using electric field lines. An electric
field line is drawn is an imaginary line drawn through a region of space so that its
tangent at any point in the direction of the electric field vector at that point. The concept
of electric fields is applied in chemistry, industrial processes, biology and medicine.

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