June 2011
UNIVERSITY
PHYSICSΠ
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June 2011
Electric Charge
&
Electric Field
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June 2011
21.1) Electric Charge
Plastic rods and fur are particularly good for demonstrating electrostatics. Figure
21.1a shows two plastic rods and a piece of fur. After we charge each rod by
rubbing it with the piece of fur, we find that the rods repel each other (fig. 21.1b).
Study figures b, c, d, e and f, we can conclude that:
Two positive charges or two negative charges repel each other. A positive
charge and a negative charge attract each other.
Alternatively:
Like charges repel, and opposite charges attract.
‫ا ٍِ ٗقد‬ٍٞ٘ٝ ‫ش ساعح‬ٞ‫َنْل ذ٘ف‬ٝ
. . . ٙ‫اء أخش‬ٞ‫طعاٍل ٗمالٍل ٗأش‬
.‫ٗسرصْع تٖا اىَعجضاخ‬
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June 2011
Electric Charge and the structure of matter
The structure of atoms can be described in terms of three particles: the negatively
charged electron (fig. 21.3), the positively charged proton, and the uncharged
neutron.
The protons and neutrons in an atom make up a small, very dense core called the
nucleus, with dimensions of the order of
Surrounding the nucleus are
the electrons, extending out to distances of the order of
from the
nucleus.
The protons and neutrons are held within the stable atomic nuclei by an attractive
interaction, called the strong nuclear force that overcomes the electric repulsion
of the protons. The strong nuclear force has a short range, and its effects do not
extend far beyond the nucleus.
Mass of electron
Mass of proton
Mass of neutron
In a neutral atom the number of electrons, equals the number of protons in the
nucleus, and the net electric charge (the algebraic sum of all the charges) is exactly
zero. the number of protons or electrons in a neutral atom of an element is called
the atomic number of the element.
We have two very important principles:
First is the principal of conservation of charge:
The algebraic sum of all the electric charges in any closed system is constant.
The second: is that:
the magnitude of charge of the electron or proton is a natural unit of charge.
‫ سفرشّا‬ٜ‫ٍِ اىٌَٖ جذا ف‬
.‫خ‬ٞ‫سم٘ب اىقطاس اىصذ‬
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June 2011
21.2) Conductors, Insulators, and Induced charges
Some materials permit electric charge to move easily from one region of the
material to another, while others do not.
Most metals are good conductors, while most nonmetals are insulators.
We can charge a metal ball by touching it with an electrically charged plastic rod,
as in fig.21.5a. In this process, some of the excess electrons on the rod are
transferred from it to the ball, leaving the rod with a smaller negative charge.
Methods of charging:
1) By friction
As stated in (fig.21.1)
2) By induction
As shown in (fig.21.6)
.‫ذك‬ٞ‫نِ قشاسك ت‬ٞ‫ى‬
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June 2011
21.3
Coulomb's law
For two point charges:
(Constant for a vacuum)
The charge q of an electron is e where:
Example 21.2
Two point charges,
and
are
separated by a distance of 3.0 cm (fig.21.10a). Find the
magnitude and direction of (a) the electric force that
exerts on
the electric force that
on
Solution:
‫أين ذكر‬a, b‫بالحل‬
fig.21.10
‫خيق‬ٝ ٌٞ‫اإلّساُ اىذن‬
‫جذ‬ٝ ‫فشصا أمثش ٍَا‬
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June 2011
Example 21.3
Two point charges are located on the positive x-axis of a coordinate
system (fig.21.11a). Charge
is 2.0 cm from the origin, and
charge
is 4.0 cm from the origin. What is the total force
exerted by these two charges on a charge
located at the
origin? Gravitational forces are negligible.
Solution:
fig.21.11
‫ففف٘ب‬ٞ‫نشّٕ٘فففل ىع‬ٝ ‫اىْففاط ال‬
.‫اك‬ٝ‫ ٗىنِ تسثة ٍضا‬،‫ل‬ٞ‫ف‬
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June 2011
Example 21.4
In (fig. 21.12) two equal positive point charges
interact with a third point charge
find the magnitude and
direction of the total (net) force on
Solution:
fig.21.11
Summing the forces:
.‫ اىذسب ٗصو‬ٚ‫ٍِ ساس عي‬
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June 2011
21.4) Electric Field and Electric Forces
‫الصور غير واضحة‬
The charge
can be either positive or
negative. If
is positive, the force
is the
same direction as
if
is negative,
and
are in opposite directions (fig.21.14).
ٌ‫اففففذل اىعففففاى‬ٝ ‫اضففففذل‬
.‫ٍعل ٗاتل ذثل ٗدذك‬
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June 2011
Gravitation Field
The gravitational field or gravitational force per unit mass, is a useful concept
because it does not depend on the mass of the body on which the gravitational
force is exerted; likewise, the electric field
or electric force per unit charge, is
useful because it does not depend on the charge of the body on which the electric
force is exerted.
Electric Field of a point Charge in a vector Equation:
If we use a rectangular (
) coordinate system, each
component of at any point is in general a function of
the coordinates (
) of the point.
. ِ‫ذَرع تاىخيق اىذس‬
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June 2011
Example 21.5
What is the magnitude of the electric field at a field point 2.0 m
from a point charge
?
Solution:
Example 21.6
A point charge
is located at the origin. Find the electric
field vector at the field point
(fig.21.17)
‫ِ اىذو‬ٝ‫أ‬
Solution:
fig.21.17
‫ اىٖفففضاص‬ٜ‫اىقيفففق ٍثفففو اىنشسففف‬
ٔ‫جعيل ذرذففشك دائَففا ٗىنْفف‬ٞ‫سفف‬
.ُ‫ ٍنا‬ٛ‫ أ‬ٚ‫٘صيل إى‬ٝ ِ‫ى‬
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June 2011
Example 21.7
When the terminals of a battery are connected to two large parallel conducting
plates, the resulting charges on the plates cause an electric field
in the region
between the plates that is very nearly uniform. Charged plates of this kind are used
in common electrical devices called capacitors if the plates are horizontal and
separated by 1.0 cm and the plates are connected to a 100-volte battery, the
magnitude of the field is
if an electron is released from rest at
the upper plate, what is its acceleration?
b) What speed and kinetic energy dose it acquire while traveling 1.0 cm to the lower
plate?
c) How much time is required for it to travel this distance?
An electron has a charge –
and a mass
Solution:
(a)
(b)
We have
and
ٜ‫ثح إرا ّضىففففففد فٖفففففف‬ٞ‫اىَصفففففف‬
‫ٗادفففذج ففففجُ جفففضه صفففادثٖا‬
.ِْٞ‫ماّد اث‬
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June 2011
Example 21.7 ‫ذاتع‬
(c)
،ُٟ‫ِ أّد ا‬ٝ‫ٌٖ أ‬ٝ ‫ال‬
ِٝ‫ أ‬ٚ‫ٗىنِ اىٌَٖ إى‬
.‫ ٕزٓ اىيذظح‬ٜ‫ذرجٔ ف‬
.
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June 2011
21.5) Electric- Field Calculations.
In most realistic situations that involve electric filed and forces, we encounter
charge that is distributed over space. The charged plastic and glass rods in
(Fig. 21.1) have electric charge distributed over their surfaces, in this section we
will learn to calculate electric fields caused by various distributions of electric
charge.
To find the field caused by a charge distribution, we imagine distribution to be
made up of many point charge
etc.
Each point charge produces its own electric field
so a test charge
placed at a force
from charge , a force
from charge ,
and so on.
When charge is distributed along a line, over a surface, or through a volume, a few
additional terms are use useful.
.‫ سالح اىاعراء‬ٙ٘‫اىشن‬
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June 2011
Field of an electric dipole
Example 21.9
Point charge and of +12 nC and -12 nC, respectively, are placed 0.10 m
apart. This combination of two charges with equal magnitude and opposite
sign is called an electric dipole.
Compute the electric field caused by , the field caused by , and the total
field (a) at point a; (b) at point b; and (c) at point c.
Solution:
(a)
The components of
and
are
‫و‬ٞ‫ ذخ‬،ٔ‫ ذشغث‬ٛ‫و اىْجاح اىز‬ٞ‫ذخ‬
‫و أّل قادس‬ٞ‫ ذخ‬،ٔ‫أّل ذسرذق‬
ٜ‫ ٍارا تق‬،ٔ‫ق‬ٞ‫ ذذق‬ٚ‫عي‬
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June 2011
Example 21.9 ‫ذاتع‬
(b)
The components of
and
, and the total field
at point b are
(c)
ِٞ‫ش ىل أُ ذسأه ٍشذ‬ٞ‫خ‬
.‫ٍِ أُ ذخطأ ٍشج ٗادذج‬
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June 2011
Field of a ring of charge
Example 21.10
A ring-shaped conductor with radius ɑ carries a total charge Q uniformly
distributed around it. Find the electric field at a point P that lies on the axis
of the ring at distance from its center.
Solution:
Since does not vary as we move from point to point around the ring, all the
factors on the right side except
are constant.
Our result for shows that at the center of the ring (
) the field is zero.
When we are so far from the ring that its size is negligible in comparison to the
distance , its field is the same as that of a point charge. To an observer far from
the ring, the ring would appear like a point.
In this example, we used a symmetry argument to conclude that had only an
-component at a point on the ring's axis of symmetry. We'll use symmetry
argument many times in this and subsequent chapters.
‫ستَا ادرجد ىسْح ماٍيح‬
ٍِ ِ‫ ىن‬،‫ق‬ٝ‫ىنسة صذ‬
‫قح‬ٞ‫ دق‬ٜ‫اىسٖو خساسذٔ ف‬
.‫ٗادذج‬
ّٜٗ‫ذ االىنرش‬ٝ‫ أٗ تاىثش‬SMS ‫ مـو خطـأ تَزمشاخ اىَ٘قع تشساىح‬ٚ‫ٔ عي‬ٞ‫ح عْـذ اىرْث‬ٝ‫ْاساُ ٕذ‬ٝ‫د‬
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June 2011
Field of a line of charge
Example 21.11
Positive electric charge Q is distributed uniformly along a line
with length , lying along the
between
and
find the electric field at point
on the -axis at a
distance from the origin.
Solution:
From symmetry,
‫ ٍِ شاسمل‬ٚ‫قذ ذْس‬
ِ‫ ىنْل ى‬. . . ‫اىاذل‬
.‫ ٍِ شاسمل اىثناء‬ٚ‫ذْس‬
ّٜٗ‫ذ االىنرش‬ٝ‫ أٗ تاىثش‬SMS ‫ مـو خطـأ تَزمشاخ اىَ٘قع تشساىح‬ٚ‫ٔ عي‬ٞ‫ح عْـذ اىرْث‬ٝ‫ْاساُ ٕذ‬ٝ‫د‬
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June 2011
Field of a uniformly charged disk
Example 21.12
Find the electric field caused by a disk of radius with a uniform positive
surface charge density (charge per unit area) at a point along the axis of
disk a distance from its center.
Solution:
A typical ring has charge
We use this in place of
21.10.
inner radius ,
in expression for the field due to a ring found in example
.ِ‫ذظ‬
‫سا مَا‬ٞ‫قذ ال ذنُ٘ ذع‬
ّٜٗ‫ذ االىنرش‬ٝ‫ أٗ تاىثش‬SMS ‫ مـو خطـأ تَزمشاخ اىَ٘قع تشساىح‬ٚ‫ٔ عي‬ٞ‫ح عْـذ اىرْث‬ٝ‫ْاساُ ٕذ‬ٝ‫د‬
Physics I/II, Circuits, English 123, Numerical, Dynamics, Strength, Statics : ‫مواد عامة‬
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June 2011
In the limit that
disk, the term
get.
is much larger than the distance of the field point from the
in Eq. (21.11) becomes negligibly small, and we
Our final result does not contain the distance from the plane. This means that the
electric field produced by an infinite plane sheet of charge is independent of the
distance from sheet. The field direction is everywhere perpendicular to the sheet,
away from it.
Field of two oppositely charged infinite sheets
Example 21.13
Two infinite plane sheets are placed parallel to each other, separated by a
distance d. the lower sheet has uniform positive surface charge density and
the upper sheet has a uniform negative surface charge density
with the
same magnitude.
Find the electric field between the sheet, above the upper sheet, and below
the lower sheet.
Solution:
Because we considered the sheets to be infinite, our result does not depend on the
separation d.
‫خطف‬ٝ ‫ فقذ‬،‫ال ذجاده األدَق‬
.‫ْنَا‬ٞ‫ق ت‬ٝ‫ اىررش‬ٜ‫اىْاط ف‬
ّٜٗ‫ذ االىنرش‬ٝ‫ أٗ تاىثش‬SMS ‫ مـو خطـأ تَزمشاخ اىَ٘قع تشساىح‬ٚ‫ٔ عي‬ٞ‫ح عْـذ اىرْث‬ٝ‫ْاساُ ٕذ‬ٝ‫د‬
Physics I/II, Circuits, English 123, Numerical, Dynamics, Strength, Statics : ‫مواد عامة‬
C++, Java, MATLAB, Data Structures, Algorithms, Discrete Math, Digital Logic, Concepts :‫٘ذش‬ٞ‫ٍ٘اد مَث‬
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June 2011
21.6) Electric Field Lines.
An electric field line is an imaginary line or curve drawn through a region of
space so that its tangent at any point is in the direction-field vector at that point.
Electric field lines show the direction of at each point, and their spacing gives a
general idea of the magnitude of at each point. Where is strong, we draw lines
closely together; where is weaker, they are farther apart. At any particular point,
the electric field has a unique direction, so only one field line can pass through
each point of the field. In other words, field lines never intersect.
Figure (21.26) shows that field lines are directed away from positive charges and
toward negative charges. In regions where the field magnitude is large, such as
between the positive and negative charges in (fig.21.26b), the field lines are
drawn close together.
In regions where the field magnitude is small, such as between the two positive
charges in (fig. 21.26c), the lines are widely separated. In a uniform field, the field
lines are straight, parallel, and uniformly spaced, as in (fig. 21.18.).
fig.21.26
‫جففة أُ ذقفف٘ه مففو ٍففا‬ٝ ‫ال‬
ُ‫جفففففة أ‬ٝ ِ‫ ىنففففف‬،‫ذعفففففشن‬
.‫ذعشن مو ٍا ذق٘ه‬
ّٜٗ‫ذ االىنرش‬ٝ‫ أٗ تاىثش‬SMS ‫ مـو خطـأ تَزمشاخ اىَ٘قع تشساىح‬ٚ‫ٔ عي‬ٞ‫ح عْـذ اىرْث‬ٝ‫ْاساُ ٕذ‬ٝ‫د‬
Physics I/II, Circuits, English 123, Numerical, Dynamics, Strength, Statics : ‫مواد عامة‬
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