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In the last chapter, We considered electrostatic fields in
free space or a space that has no
materials in it.
NOW WE WILL STUDY
The theory of electr ic phenomena in
mater ial space.
Most of the formulas derived in chapter 4
are still applicable, with some
modification.
5.1 INTRODUCTION:
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5.1 INTRODUCTION:
Just as electric fields can exist in free space,they can exist in material media also.
Mater ials are broadly classif ied in terms of
their electrical properties as:
conductors and nonconductors.
Non-conducting mater ials are usually referred to
as:
insulators or dielectrics.
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5.1 INTRODUCTION
:
A brief discussion of the electrical
properties of materials in general will be
given to provide a basis for understandingthe concepts:
Conduction
Electr ic cur rent Polarization
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Further discussion will be on some properties
of dielectric materials such as:susceptibility,
permittivity,
linearity,isotropy
homogeneity,
dielectr ic strength,
and relaxation time.
NOTE The concept of boundary conditions for
electric fields existing in two different
media will be introduced in Chapter # 06
5.1 INTRODUCTION:
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5.2 PROPERTIES OF MATERIALS
Questions such as:
Why an electron does not leave a conductor surface?
Why a current-carrying wire remains uncharged?
Why mater ials behave differently in an electric f ield?
Why waves travel with less speed in conductors than in
dielectrics ?
are easily answered by consider ing theelectr ical properties of mater ials
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5.2 PROPERTIES OF MATERIALS
Here a brief discussion will suffice to help us
understand the mechanism by which materialsinfluence an electric field.
In a broad sense, materials may be classified in
terms of their conductivity , in mho per meter
or siemens per meter (S/m) ,
As conductors and non conductors,( technically as
metals and insulators - dielectrics) .
The conductivi ty of a mater ial usually depends on
temperature and frequency.
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5.2 PROPERTIES OF MATERIALS
A material with high conductivity ( 1)is referred to as a metal
where as one with low conductivity
( 1) is referred to as an insulator. A material whose conductivity lies
somewhere between those of metalsand insulators is called a
semiconductor.
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Copper and aluminum are metals,
Silicon and germanium are semiconductors,
Glass and rubber are insulators.
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5.2 PROPERTIES OF MATERIALS
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5.2 PROPERTIES OF MATERIALS
The conductivity of metals generally
increases with decrease in temperature.
At temperatures near absolute zero (T = 0K),
some conductors exhibit infinite conductivity
and are called superconductors.
Lead and aluminum are typical examples of
such metals. The conductivity of lead at 4
K is of the order of 1020 mhos/m.
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5.2 PROPERTIES OF MATERIALS
We shall only be concerned with metals andinsulators in this text.
Microscopically, the major difference between ametal and an insulator lies in the amount of
electrons available for conduction of current.
Dielectric materials have few electrons available
for conduction of current in contrast to metals,
which have an abundance of free electrons.
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5.3 CONCEPT OF CONVECTION
AND CONDUCTION CURRENTS
Two fundamental quantities in electrical engg.
I. Electric voltage (or potential difference)
II. CurrentWe considered potential in the last chapter.
Before examining how electric field behaves in a
conductor or dielectric, it is appropriate to considerelectric current.
Electric current is generally caused by the
motion of electric charges.
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Current:The current ( in amperes ) through a given area
is the electric charge passing through the area
per unit time
1 AMPERE CURRENT
the movement caused within a fluid by the tendency of hotter and
therefore less dense material to rise, and colder, denser material to
sink under the influence of gravity, which consequently results in
transfer of heat.
"the final transfer of energy to the surface is by convect ion"
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5.3 CONCEPT OF CONVECTION AND
CONDUCTION CURRENTS
CURRENT DENSITY
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5.3 CONVECTION AND ONDUCTION
CURRENTS
The current is depending on how I is produced. There are
different kinds of current densities:
Convection current density,
Conduction current density,
Displacement current density.
We will consider convection and conduction current densities here;
Displacement current density will be considered in Chapter # 09.
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5.3 CONVECTION AND ONDUCTION
CURRENTS
we will keep in mind
the general concept
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5.3 CONVECTION AND ONDUCTION
CURRENTS
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CONDUCTION CURRENT
According to Newton's law, the
average change in momentum of
the free electron must match the
applied force. Thus,
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CONDUCTION CURRENT DENSITY
CONDUCTION CURRENT DENSITY
COMPARING EQ. 5.9 AND EQ. 5.10
POINT FORM OF OHMS LAW
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5.4 CONDUCTORS
THE FREE CHARGES DO TWO THINGS:
First, They accumulate on the surface of the conductor.
Second, The induced charges set up an internal induced field
Ei, which cancels the external applied field Ee.
The result is illustrated in Fig. 5.2 (b). This leads to an
important property of a conductor:
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A PERFECT CONDUCTOR CANNOT
CONTAIN AN ELECTROSTATIC
FIELD WITHIN IT
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5.4 CONDUCTORS
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The SI units of the field
are newtons per coulomb (NC1) or,
equivalently, volts per metre(V
m1
),
http://en.wikipedia.org/wiki/SIhttp://en.wikipedia.org/wiki/Newton_(unit)http://en.wikipedia.org/wiki/Coulombhttp://en.wikipedia.org/wiki/Volthttp://en.wikipedia.org/wiki/Metrehttp://en.wikipedia.org/wiki/Metrehttp://en.wikipedia.org/wiki/Volthttp://en.wikipedia.org/wiki/Coulombhttp://en.wikipedia.org/wiki/Newton_(unit)http://en.wikipedia.org/wiki/SI -
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5.4 CONDUCTORS
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5.4 CONDUCTORS
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5.4 CONDUCTORS
ready reference
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5.4 CONDUCTORS
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EXAMPLE 5.1
SOLUTION
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PRACTICE EXERCISE 5.1
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EXAMPLE 5.2
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0
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PRACTICE EXERCISE 5.2
SOLUTION
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EXAMPLE 5.3
SOLUTION
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PRACTICE EXERCISE 5.3
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EXAMPLE 5.4
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EXAMPLE 5.4
FOR EXAMPLE 5.4FOR PRCTICE EXERCISE 5.4
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PRACTICE EXERCISE 5.4
PLZ SEE FIGURE IN PREVIOUS SLIDE
EXAMPLE 5 6
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EXAMPLE 5.6
EQ. 5.34
EQ. 4.60 ( PAGE NO. 133)
EQ. 5.32
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PRACTICE EXERCISE 5.6
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5.5 P0LARIZATION IN DIELECTRICS
The main difference between a conductor and a
dielectric lies in the availability of free electrons in the
atomic outermost shells to conduct current.
But on the other hand, although the charges in a
dielectric are not able to move about freely, they are
bound by finite forces and we may certainly expect a
displacement when an external force is applied.
To understand the macroscopic effect of an electric
field on a dielectric, consider an atom of the dielectric
as consisting of a negative charge - Q (electron cloud)
and a positive charge +Q (nucleus) as in Figure 5.6(a).
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CONTS P0LARIZATION IN DIELECTRICS
A similar picture can be adopted for a dielectricmolecule; we can treat the nuclei in molecules as point
charges and the electronic structure as a single cloud of
negative charge.
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1. Since we have equal amounts of positive and
negative charge, the whole atom or molecule is
electrically neutral.
2. When an electric field E is applied, the positive
charge is displaced from its equilibrium position in
the direction ofEby the force :
F+ = QE3. While the negative charge is displaced
in the opposite direction by the force:
F_ = QE
A dipole results from the displacement of
the charges and the dielectric is said to
be polarized.
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CONTS P0LARIZATION IN DIELECTRICS
In the polarized state, the electron cloud is distorted by the
applied electric field E. This distorted charge distribution isequivalent, by the principle of superposition, to the original
distribution plus a dipole whose moment is :
p = Qd (5.21)
where d is the distance vector from Q to +Q of the dipole
as in Figure 5.6(b).
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As a measure of intensity of the polarization, we define
polarization P (in coulombs/meter square) as the dipolemoment per unit volume of the dielectric; that is,
CONTS P0LARIZATION IN DIELECTRICS
If there are N dipoles in a volume Av of the dielectric, the
total dipole moment due to the electric field is
Thus we conclude that the major effect of the electric field E on adielectric is the creation of dipole moments that align themselves in
the direction of E. This type of dielectric is said to be nonpolar.
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POLARIZATION OF A NONPOLAR ATOM/MOLECULES
Examples of nonpolar dielectrics are:1. hydrogen,
2. oxygen,
3. nitrogen,
4. and the rare gases. Nonpolar dielectric
molecules do not possess dipoles until the
application of the electric field as we have
noticed.
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Examples of polar dielectrics are:
1. water,2. sulfur dioxide,
3. and hydrochloric acid : have built-in permanent
dipoles that are randomly oriented as shown in
Figure 5.7(a) and are said to be polar.
POLARIZATION OF A POLAR ATOM/MOLECULES
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1. We conclude that the net effect of the dielectric on the electric
field E is to increase D inside it by amount P
2. . In other words, due to the application of E to the dielectric
material, the flux density is greater than it would be in free
space.
3. It should be noted that the definition of D in eq. (4.35) for freespace is a special case of that in eq. (5.31) because P = 0 in free
space.
THE DIELECTRIC STRENGTH IS THE MAX
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THE DIELECTRIC STRENGTH IS THE MAX.
ELECTRIC FIELD THAT A DIELETRIC CAN
TOLERATE OR WITHSTAND WITHOUTBREAKDOWN
SOME DEFINATIONS TO BE CONSIDERED
FOR BETTER UNDERSTANDING
1. DIELECTRIC CONSTANT
2. DIELETRIC STRENGTH3. DIELETRIC BREAKDOWN
4. PERMITTIVITY OF DIELECTRIC
5. RELATIVE PERMITTIVITY
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5.6 DIELECTRIC CONSTANT AND STREGHTH
5 6 DIELECTRIC CONSTANT AND
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5.6 DIELECTRIC CONSTANT AND
STREGHTH
The dielectric constant (or relative permittivity),is the ratio of the permittivity of the dielectric to
that of free space.
It should also be noticed that and aredimensionless whereas and s are in
farads/meter. The approximate values of the dielectric
constants of some common materials are given in
Table B.2 in Appendix B.
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IMPORTANT POINTS TO BE NOTED
1. The values given in Table B.2 are for static orlow frequency (
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The dielectric strength is the maximumelectric field that a dielectric can tolerate or
withstand without breakdown.
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5.7 LINEAR, ISOTROPIC, AND HOMOGENEOUS
DIELETRICS
a - A material is said to be linear if D varieslinearly with Eand nonlinearotherwise.
b - Material for which or does not vary in the
region considered and is therefore the same at
all points ( i.e. independent of x,y,z ) are saidto be homogeneous.
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5.7 LINEAR, ISOTROPIC, AND HOMOGENEOUS
DIELETRICS
A dielectric material ( in which D = E applies) is linear if
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( pp )
does not change with the applied field E field , homogeneous if
does not change from point to point, and isotropic if does
not change with direction
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EXAMPLE 5.5
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EXAMPLE 5.5
PRACTICE EXERCISE 5 5
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PRACTICE EXERCISE 5.5
SOLUTION
EXAMPLE 5 6
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EXAMPLE 5.6
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PRACTICE EXERCISE 5.6
SOLUTION
EXAMPLE 5.7
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EXAMPLE 5.7
PRACTICE EXERCISE 5 7
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PRACTICE EXERCISE 5.7
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EXAMPLE 5.8
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PRACTICE EXERCISE 5.7
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PROBLEMS
SOLUTION
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SOLUTION
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SOLUTION
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SOLUTION
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SOLUTION
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SOLUTION
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SOLUTION
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SOLUTION
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SOLUTION
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SOLUTION PROBLEM 5.9
SOLUTION
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SOLUTION
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We now consider the case in which the dielectric region containsfree charge. If is the free charge volume density, the total volume
charge density , is given by
Free charges:
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