physics term paper
TRANSCRIPT
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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
Refrences
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