Physics Term Paper

8/3/2019 Physics Term Paper

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TERM PAPER(1st SEMESTER-1ST YEAR)

ON

ELECTROSTATIC FIELD IN MATTER(DIELECTRICS).BEHAVIOUR ANDRESPONSE OF A DIELECTRIC TO

EXTERNAL ELECTROSTATIC FIELD ANDMICRO AND MACROSCOPIC LEVELS

SUBMITTED TO:

MR.RAVI BUSHAN

SUBMITTED BY:

JAGTAR SINGH

SECTION-K1004

CLASS-B.TECH (CSE)


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I Jagtar student of B.Tech(CSE)-MBA Ist termexpressing my deep gratitude to my Physics teacherMr.Ravi Bushan. I am very much thankful to him. Ibenefited a lot discussing with him.

I am also thankful to my parents who encouraged meand provided such a motivation, so I became ableto perform this.

I am also thankful to all my friends and those whohelped me directly or indirectly in completion of myproject.

JAGTAR SINGH

B.Tech(CSE)MBA

Roll no-RK1004b31

CONTENTS: ELECTROSTATIC FIELD

DIELECTRIC

DIELECTRIC MATERIAL

EFFECT ON DIELECTRIC

BEHAVIOUR AND RESPONSE OF DIELECTRIC

ENERGY IN DIELECTRIC SYSTEM

FORCE ON DIELECTRICS


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INTRODUCTION:-

ELECTROSTATIC FIELD: When two objects in each other's vicinityhave different electrical charges, an electrostatic field exists between them. Anelectrostatic field also forms around any single object that is electrically charged with

respect to its environment. An object is negatively charged (-) if it has an excess ofelectrons relative to its surroundings. An object is positively charged (+) if it is

deficient in electrons with

Atom in external electric field

Electrostatic fields bear some similarity to magnetic fields. Objects attract if their

charges are of opposite polarity objects repel if their charges are of the same polarity .

The lines of electrostatic fluxin the vicinity of a pair of oppositely charged objects aresimilar to lines of magnetic flux between and around a pair of opposite magnetic

poles. In other ways, electrostatic and magnetic fields differ. Electrostatic fields are

blocked by metallic objects, while magnetic fields can pass through most metals.Electrostatic fields arise from a potential difference or voltage gradient, and can exist

when charge carriers, such as electron, are stationary. Magnetic fields arise from the

movement of charge carriers, that is, from the flow of current.

When charge carriers are accelerated (as opposed to moving at constant velocity), afluctuating magnetic field is produced. This gives rise to a fluctuating electric field,

which in turn produces another varying magnetic field. The result is a leapfrog effect,

in which both fields can propagate over vast distances through space. Such asynergistic field is known as an electromagnetic field, and is the phenomenon that

makes wireless communications, broadcasting, and control systems possible
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WHAT IS DIELECTRIC AND DIELECTRIC MATERIAL:A dielectric material is a substance that is a poor conductor of electricity, but an

efficient supporter of electrostatic fields. If the flow of current between oppositeelectric charge poles is kept to a minimum while the electrostatic lines of flux are not

impeded or interrupted, an electrostatic field can store energy. This property is useful

in capacitors, especially at radio frequencies. Dielectric materials are also used in theconstruction of radio-frequency transmission lines.

In practice, most dielectric materials are solid. Examples include porcelain , mica,

glass, plastics, and the oxides of various metals. Some liquids and gases can serve as

good dielectric materials. Dry air is an excellent dielectric, and is used in variablecapacitors and some types of transmission lines. Distilled water is a fair dielectric. A

vacuum is an exceptionally efficient dielectric.

An important property of a dielectric is its ability to support an electrostatic field

while dissipating minimal energy in the form of heat. The lower the dielectric loss

(the proportion of energy lost as heat), the more effective is a dielectric material.Another consideration is the dielectric constant, the extent to which a substance

concentrates the electrostatic lines of flux. Substances with a low dielectric constantinclude a perfect vacuum, dry air, and most pure, dry gases such as helium and

nitrogen. Materials with moderate dielectric constants include ceramics, distilled

water, paper, mica, polyethylene, and glass. Metal oxides, in general, have highdielectric constants

EFFECT OF ELECTROSTATIC FIELD ON

DIELECTRIC: Most dielectric materials become polarized when they areplaced in an external electric field. In many materials the polarization is proportional

to the electric field:

Where is the total electric field. The constant of proportionality, , is called the

electricsusceptibility. Materials in which the induced polarization is proportional tothe electric field are called linear dielectrics.

The electric displacement in a linear dielectric is also proportional to the total electric

field:

where is called the permittivity of the material which is equal to


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The constant is called the dielectric constantKof the material.

Consider a volume Ventirely filled with linear dielectric material with dielectric

constantK. The polarization of this material is equal to

and is therefore proportional to everywhere. Therefore

and consequently

The electric displacement therefore satisfies the following two conditions:

and

The electric field generated by the free charges when the dielectric is not presentsatisfies the following two equations:

and

Comparing the two sets of differential equations for and we conclude that

The displacement can also be expressed in terms of the total field inside thedielectric:

These two equations show that


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The presence of the dielectric material therefore reduces the electric field by a factor

K.

EFFECT ON DIELECTRIC:

Place a dielectric layer between two parallel charged metal plates with an electric fieldpointing from right to left. The positive nuclei of the dielectric will move with the

field to the right and the negative electrons will move against the field to the left. Fieldlines start on positive charges and end on negative charges, so the electric field within

each stressed atom or molecule of the dielectric points from left to right in our

diagram opposite the external field from of the two metal plates. The electric field is avector quantity and when two vectors point in opposite directions you subtract their

magnitudes to get the resultant. The two fields don't quite cancel in a dielectric as they

would in a metal, so the overall result is a weaker electric field between the twoplates. Capacitors

Let me repeat that the overall result is a weaker electric field between the twoplates. Let's do some math.

Electric field is the gradient of electric potential (better known as voltage).

Ex =

V& Ey =

V& Ez =

V

E = Vx y z

Capacitance is the ratio of charge to voltage.

C =

Q

V

Introducing a dielectric into a capacitor decreases the electric field, which decreases

the voltage, which increases the capacitance.

& 1 (Q constant) 1 (d, Q constant)


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V E (d constant)

C C V E

BEHAVIOUR AND RESPONSE OF

DIELECTRIC TO EXTERNALELECTROSTATIC FIELD: Dielectric response in polardielectrics with respect to external

Temperature, frequency, electric field, and pressure is

An important issue in dielectric/ferroelectric physics. In theliterature, the dielectric spectra as a function of frequency or

temperature have been extensively studied both experimentally

and theoretically. For instance, analysis of dielectric relaxationis available via the Debye model including Cole

Cole equations and related treatments!, and the dielectricrelaxation rate can be described by the Arrhenius relation,

the Vogel-Fulcher relation, or a complicated relaxation-timedistribution function.16 However, the dielectric response asa function of electric field, especially up to high field levels,

has been studied less due to such difficulties as ~i! the difficultyOf dielectric measurements under a wide electric field

range, especially up to high electric fields, and ~ii! lack of aconvenient theory ~for instance, a simple explicit function !todeal with dielectric spectra as a function of electric field in awide range.

In fact, the electric-field dependence of the dielectric response

Can provide very useful information on the basic

physics of dielectric polarization. In some cases, such informationIs critical in understanding the dielectric/ferroelectric

behavior in polar dielectrics. In addition, a new type of electronicdevice making use of the variation of the dielectric

constant of polar dielectrics under dc electric fields has been

developed recently for allocations in next-generation radarand microwave communication systems.79 Therefore, a

study of the dielectric nonlinear behavior under electric

fields is also technologically important.In this paper, we first review the Landau- Ginzburg-Devonshire LGD!

theory and the existing approximatethe electric-field dependence of the dielectric response. It is found that these

treatments are insufficient treatments on

in describing the observed experimental data, whichinclude more than one polarization mechanism. A

multi polarization -mechanism model is suggested by taking


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into consideration both the intrinsic lattice polarization

and the extrinsic polarization. These equations are tested

by experimental data obtained from KTaO3 and Bi-dopedSrTiO3 and good agreement between theory and experimental

data is achieved.

Energy in dielectric systems

Consider a capacitor with capacitance Cand charged up to a potential V. The totalenergy stored in the capacitor is equal to the work done during the charging process:

If the capacitor is filled with a linear dielectric (dielectric constantK) than the total

capacitance will increase by a factorK:

and consequently the energy stored in the capacitor (when held at a constant potential)is increased by a factorK. A general expression for the energy of a capacitor with

dielectric materials present can be found by studying the charging process in detail.

Consider a free charge held at a potential V. During the charging process the freecharge is increased by . The work done on the extra free charge is equal to

Since the divergence of the electric displacement is equal to the free charge density, the divergence of is equal to . Therefore,

Using the following relation

we can rewrite the expression forWas

The first term on the right-hand side of this equation can be rewritten as


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since the product of potential and electric displacement approach zero faster than 1/r2

when rapproached infinity. Therefore,

Assuming that the materials present in the system are linear dielectrics then

This relation can be used to rewrite :

The expression for can thus be rewritten as

The total work done during the charging process is therefore equal to

Note: this equation can be used to calculate the energy for a system that contains

linear dielectrics. If some materials in the system are non-linear dielectrics than the

derivation given above is not correct ( for non-linear dielectrics).

Example:A spherical conductor, of radius a, carries a charge Q. It is surrounded by lineardielectric material of susceptibilitye, out to a radius b. Find the energy of this

configuration.

Since the system has spherical symmetry the electric displacement is completely

determined by the free charge. It is equal to

Since we are dealing with linear dielectrics, the electric field is equal to .

Taking into account that the susceptibility of vacuum is zero and the susceptibility of

a conductor is infinite we obtain for :


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The scalar product is equal to since and are parallel, everywhere. The

energy of the system is equal to

Forces on dielectrics

A dielectric slab placed partly between the plates of a parallel-plate capacitor will bepulled inside the capacitor. This force is a result of the fringing fields around the

edges of the parallel-plate capacitor . Note:the field outside the capacitor can notbe zero since otherwise the line integral of the electric field around a closed loop,

partly inside the capacitor and partly outside the capacitor, would not be equal to zero.

Figure: Fringing fields.

Inside the capacitor the electric field is uniform. The electric force exerted by the field

on the positive bound charge of the dielectric is directed upwards and is canceled by

the electric force on the negative bound charge . Outside the capacitor the electricfield is not uniform and the electric force acting on the positive bound charge will not

be canceled by the electric force acting on the negative bound charge. For the systemshown in Figure the vertical components of the two forces (outside the capacitor) will

cancel, but the horizontal components are pointing in the same direction and therefore


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do not cancel. The result is a net force acting on the slab, directed towards the center

of the capacitor.

Figure : Forces on dielectric.

A direct calculation of this force requires a knowledge of the fringing fields of the

capacitor which are often not well known and difficult to calculate. An alternative

method that can be used is to determine this force is to calculate the change in theenergy of the system when the dielectric is displaced by a distance ds. The work to be

done to pull the dielectric out by an infinitesimal distance ds is equal to

where is the force provided by us to pull the slab out of the capacitor. This force

must just be equal in magnitude but directed in a direction opposite to the forceexerted by the electric field on the slab. Thus

The work done by us to move the slab must be equal to the change in the energy of the

capacitor (conservation of energy). Consider the situation shown in Figure where the

slab of dielectric is inserted to a depths in the capacitor. The capacitance of thissystem is equal to

Figure: Calculation of .

If the total charge on the top plate is Q then the energy stored in the capacitor is equalto


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The force on the dielectric can now be calculated and is equal to

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