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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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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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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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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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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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CURRENTS

we will keep in mind

the general concept

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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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SOLUTION

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EXAMPLE 5.3

SOLUTION

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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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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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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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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,


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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SOLUTION

EXAMPLE 5 6

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EXAMPLE 5.6

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SOLUTION

EXAMPLE 5.7

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EXAMPLE 5.7

PRACTICE EXERCISE 5 7

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EXAMPLE 5.8

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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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