Chapter 23

Electric Fields
Outline

23.1 Properties of Electric Charges

23.3 Coulomb’s Law

23.4 The Electric Field

23.6 Electric Field Lines

23.7 Motion of Charged Particles in a Uniform Electric

Field
23.1 Properties of Electric Charges

There are two kinds of

charges in nature; charges
of opposite sign attract one
another and charges of the
same sign repel one
another.

Total charge in an isolated

system is conserved.

Charge is quantized.
 Types of Materials:

1- Conductors: have some free electrons that can move through

the materials. Ex: copper, aluminum, and silver.

2- Insulators: have bound electrons that can not move through

the materials. Ex: glass, rubber, and wood

3- Semiconductors: electrical properties are somewhere

between those of insulators and conductors. Ex: Silicon
 23.3 Coulomb’s Law

k 9 109 Nm 2 /C2
1 12 C2
k where 0 8.85 10
4 0 Nm 2
0 is the permittivity of free space
Properties of the electric force:

1- is inversely proportional to the square of the separation r between the

particles.
2- is proportional to the product of the charges q1and q2on the two
particles
3- is attractive if the charges are of opposite sign and repulsive if the
charges have the same sign
4- is a conservative force
23.3 Coulomb’s Law

Point Charge:

A particle of zero size that carries an electric charge

The smallest unit of charge known in nature is the

charge on an electron (-e) or a proton (+e) and has a
magnitude:

e = 1.6 x 10-19 C
23.3 Coulomb’s Law
Vector Nature of Electric Forces:

kq1q 2
F12 2
rˆ21
r21
The force F21 exerted by q2 on q1 is equal in
magnitude and opposite in direction to the force
F12 exerted by q1 on q2.

(a) When the charges are of the

same sign, the force is repulsive.

(b)When the charges are of

opposite signs, the force is attractive

When more than two charges are present, the

force between any pair of them is given by:
F1= F21 + F31 + F41
 23.3 Coulomb’s Law

Quick Quiz 23.5

Object A has a charge of +2 μC, and object B has a charge of +6 μC.

Which statement is true about the electric forces on the objects?

1- FAB = –3FBA
2- FAB = –FBA
3- 3FAB = –FBA
4- FAB = 3FBA
5-
6-
FAB = FBA
3FAB = FBA a
II
23.3 Coulomb’s Law
Example (1) Chapter 23 :
Sol
or 04M 93
oh
92
6 15
2 1

3m
f es kl9 3
r2 oh
a lo9 2xlE91C5x1o
5.6 159 w
c4,2

Fox E3 cos 0
5.6 159 cos Iso S 6 159 N

Easy f23 sin 0

5.6 159sin180 ON

Fz
Klotilter
8 N
1592
9 10916159115 1 o 8 10
is o
I
f 13 x Fiz cos

f I I o 8 108 cos 36.8

8.64 159N
f BY Frs
sin 0
1.08 158 sin36.8
6.46 109
X component
Fx Fz Fz X
8.64 159 5.6 0
9 3.04 159N

Y component
Fy Fist G34
6.46 159 o 6.46 159N

Resultant force Resultant angle

F Fifi a tail
s 7 16 159N 65.2
23.3 Coulomb’s Law
Example 23.3 Page 713: Resultant Force
Sol
Resultant force o

i Fez e 523 0
Tito
3 f

kia.fi y k
f
15 6
L U2
15N 24 24N 6N
9N 24 N 24 o

N o 774 in

jj.y.by
d'd
Nz 3.44 m
dU i d is correct
 23.4 The Electric Field
An electric field is said to exist in the region of space around a
charged object (the source charge). When another charged object
(the test charge) enters this electric field, an electric force acts on
it.
The test charge serves as a detector of the electric field.

When using Equation 15.3, we assume that the test

charge q0 is small enough that it does not disturb the
charge distribution responsible for the electric field
 23.4 The Electric Field

- If q is positive, the force and the field are in the same direction.
- If q is negative, the force and the field are in opposite directions.

The direction of an electric field:

 23.4 The Electric Field
According to Coulomb’s law, the force exerted by q on the test
Charge is:

At any point P, the total electric field due to a group of source

charges equals the vector sum of the electric fields of all the
charges.
 23.4 The Electric Field

Quick Quiz 23.6

A test charge of +3 μC is at a point P where an external electric field
is directed to the right and has a magnitude of 4 × 106 N/C. If the test
charge is replaced with another test charge of –3 μC, the external
electric field at P

1- is unaffected
2- reverses direction
3- changes in a way that cannot
be determined
23.4 The Electric Field
Example 23.5 Page 718
 9 10917
f Kf 152 3.9 ios Nyc
a 412

L fin E case
3.9 105 cos 90 0

fly E sin 0
3.9 15 sin 90 3.9 18 Mc

f kg
c9 l 5 l
1.8 105
o 5,2

Fax
1.8
Ez cos 0
15 cos 53.1
0
TW
tah lfo.IJ 53

1 08 105

Ey Ez sing
I 8 105 sin 53.1 1.4 105

X comp Fa Eiu E ex
1.08 15 0 1.08 15 Mc

Y comp Ey Ely e Ezy

1.4 105
3.9 18 2.5 105 Nlc
Resultant g
I f E 2 7 x ios

angle tan tail 2.5 1 5

1 08 1 s

66.6
 23.6 Electric Field Lines
Used for visualizing electric field patterns.
The electric field vector E is tangent to the electric field lines at
each point.
E is large when the field lines are close together and small when
the lines are far apart
23.6 Electric Field Lines
23.6 Electric Field Lines
 23.6 Electric Field Lines

Quick Quiz 23.8

Rank the magnitude of the electric field at points A, B, and C shown

B C
in this figure (greatest magnitude first).
A
 23.7 Motion of Charged Particles in a
Uniform Electric Field
When a charged particle is placed in an electric field, it
experiences an electrical force.
If this is the only force on the particle, it must be the net force and
causes the particle to accelerate according to Newton’s second
law.

If E is uniform (that is, constant in magnitude and direction), then

the acceleration is constant.
If the particle has a positive charge, its acceleration is in the
direction of the electric field. If the particle has a negative charge,
its acceleration is in the direction opposite the electric field
23.7 Motion of Charged Particles in a
Uniform Electric Field
Example 23.10 Page 726: An Accelerating Positive Charge

A positive point charge q of mass m is released from rest in a

uniform electric field E directed along the x axis, as shown
in the Figure. Describe its motion

s f Fsb 3
i
II 29
a 9
Vf GET

KE Kamui IE au
 23.7 Motion of Charged Particles in a
Uniform Electric Field

An electron of charge -e is projected

horizontally into this field from the

origin with an initial velocity vi

Because the electric field E in

the Figure is in the positive y

direction, the acceleration of

the electron is in the negative y

direction
23.7 Motion of Charged Particles in a
Uniform Electric Field
Example 23.11 Page 727: An Accelerated Electron

An electron enters the region of a uniform electric field

as shown in previous Figure, with vi =3.00x106 m/s and
E=200N/C. The horizontal length of the plates is
L= 0.100m.

A- Find the acceleration of the electron while it is in the

electric field. 9 1.4151912
a 3.5 1 Mlse
31
9 I o

B- If the electron enters the field at time t =0, find the

time at which it leaves the field. t
5 6 3.33 1585
C- If the vertical position of the electron as it enters the field
is y= 0, what is its vertical position when it leaves the field?
o
yi Yf
Yf Eat YzC 3.5 103 3.33 158 o.o 195
Chapter Problems

1) Three point charges are located at the corners of an equilateral

triangle as shown in the Figure below. Calculate the resultant electric
force on the 7.00-μC charge.
Chapter Problems

El