Tài liệu Chapter VIII Dielectrics ppt

Induced charge and polarization of dielectrics: 1.1 Effects with dielectrics in an electric field: @ One might at first believe that there should be no effect with dielectrics in respon

GENERAL PHYSICS II

Electromagnetism

7

Thermal Physics

Chapter VIII Dielectrics

§1 Induced charges and polarization of dielectrics

§2 Molecular model of induced charges

§3 Piezoelectric etfect

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We have known how can describe the electric field in vacuum

How is the electric field in a matter environment?

In this chapter we consider the case that the environment is a nonconducting material

Recall that in a conducting body (conductor) the charges move freely in respond to an electric field, but in nonconducting bodies the charges can not move freely

Nonconducting bodies are called dielectrics or insulators

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§1 Induced charge and polarization of dielectrics:

1.1 Effects with dielectrics in an electric field:

@ One might at first believe that there should be no effect with dielectrics in respond to an electric field But Faraday discovered that this was not so!

@ A simple experiment is shown in the picture:

- Two conducting plates with magnitude of charge Q

- The electrometer that measures the potential difference V between two conducting plates

Am Experiment shows that the potential difference V between plates decreases when we insert an uncharged sheet of dielectric (glass, paraffin, polystyrene., )

Note that the electrometer measures only potential difference, there is no current

through tt It means that the charge Q is

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1.1 Induced charges and polarization:

Why the potential difference between two conducting plates decreases?

In an dielectric there are not free charges, electrons are not free to flow from one atom (or molecule) to another The electric asymmetry of atoms (molecules) leads to the existence of electric dipoles These dipoles are randomly aligned, therefore the net electric field inside the electric is zero (pic a)

When the dielectric is placed between charged plates of magnitude Q,

surface charge density dp, the electric field Ey between plates exrets

torques on the dipoles Tnese torques tend to align the dipoles with the field (pic b)

By this effect there exits a net charge density o; induced in the surfaces of the dielectric (pic c)

2.3 [he dielectric constant:

The induced charges on the surfaces of the dielectric creates an induced electric field E, The direction of E;is opposite to the electric field E, Therefore, the net electric field inside the dielectric is

| BoE =

We define BE SN — (ie dieleciric constant

1<k<o

km—9—

›E¡ =[I— =]E,

E) The potential difference between the plates is smaller by a factor of k

In summary, when a dielectric is inserted in a electric field, a redistrioution of positive and negative charges takes place, and as a result, the induced charges arise on the surface of dielectric

This phenomenon is called the polarization of dielectric

The electric field E inside the dielectric, and the potential difference V decrease by a factor k (dielectric constant)

Note: The field and potential difference decrease only when the charge

on the plates is held constant !

+ Values of k tor some dielectrics: mica — 3-6; glass — 5-10; water — 80

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1.4 Permitivitv of dielectric:

The electric field between two plates is calculated through surface charge density o on the plates:

@ Without the dielectric:

@ With the dielectric: Suppose that the electric completely fills the space between the plates, the net surface charge density is

O - 0; , and we have =0=Ø

a >

K

where

The definition of permitivity

of dielectric

= In other word, the effect of dielectrics can be take into account by the replacement €,— € in expressions for the elctric field

Ey can be called the permitivity of vacuum The units:

@ kis a number which has no unit

¢ The units of ¢ is the same as of €, > C2 / Nm? = F/m (recall €) = 8.85 X 10°12 F/m)

1.5 Dielectric breakdown:

When any dielectric material is subjected to a sufficiently strong electric field, the phenomenon of dielectric breakdown takes place and the

dielectric becomes a conductor

Interpretation: when the electric field is enough strong, electrons are ripped off from their molecules and crash into other molecules, liberating even

more electrons This process often starts quite suddenly and creates a short circuit between the conducting plates

The maximum electric field magnitude that a material can withstand without the occurrence of breakdown is called its alelectric strength (For example,

for dry air it’s about 3 x10° V/m

§2 Molecular model of induced charge:

We have known that the phenomenon of

polarization is caused by the rearrangement of

dipoles inside electrics We go inside to the

molecular structure of dielectrics and consider in

more detail about these molecular dipoles

ELECTRON DISTRIBUTION

+ The simplest case of a monatomic gas (for

instance, helium) — the centers of gravity of the

itive charges coincide (pic a)

some gases, like oxygen, has

of atoms (pic C)

this type, in the absent of

d, have not permanent dipole alled nonpolar moleculars

he centers of positive and

ioole moment (pic b)

I9

+ The polarization of nonpolar molecules takes place as if there exists an elastic forces between positive and negative charges

= Nonpolar molecules behave in an external field as elastic dipoles

2.2 [he case of polar molecules:

The example of this type is the water molecules Since the centers of grvity of positive and negative charges do not coincide — even in the absent of external field, the molecules have a permanent electric dipole

The effect of an external field is mainly to try rotate molecular dipoles and direct them along the direction of the external electric field

7 Polar molecules behave in an external field as rigid dipoles

CENTER OF

— CHARGE

CENTER OF 1/29/2008 + CHARGE

(a) In the absent of an external electric field, the individual dipoles of polar molecules are oriented at random — the average moment in a small volume is zero

(ob) When there is an external electric field

— there is some average aligment of the molecules

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§3 Piezoelectric effect:

3.1 Straight piezoelectric effect:

The piezoelectric effect is related to some crystal solid dielectrics

From a quartz crystal we cut a plate whose surface is perpendicular to the axis a of the crystal The second axis is Cc

+ When the plate is compressed in the direction along the axis a, in the surface of the plate the surface charges arise

This effect is called /ongitudinal piezoelectric

+ The same charges arise as before, if the plate

is stretched along the direction OO which is perpendicular to both axes a and c

This effect is called transvers piezoelectric

+ The sign of the surface charges will change,

as if we change the sign of the deformations (that is, stretching along a and compressing along OÓỚ))

+ To use this effect we put on the plate metal panels and connect them in

a close circuit It is the principle of piezoelectric microphones: the pressure from a sound wave Creates a alternative currents in the circuit

The interpretation of the piezoelectric effect: In some crystalls, a deformation can lead to a displacement of sublattices This displacement breaks the electrical symmetry inside the crystall and creates a electric dipole moment

3.2 Reverse piezoelectric effect:

The described before effect is called straight piezoelectric effect This name means that there is also the reverse piezoelectric effect

lf we insert on the panels an alternating voltage, the crystall plate will be stretched and compressed in accordance with

the frequency of the voltage — oscillations arise

in the plate

There is also resonance phenomenon:

when the frequency of the alternating voltage coincides with the own frequency

of the plate — the oscillations become

very strong

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The reverse piezoelectric effect and resonance phenomenon are applied

to stimulate ultrasonic waves, to stabilize frequencies of generators of radio signals

The dielectric materials which have piezoelectric property are:

@ Some natural minerals: quartz, turmatin,

@ Synthesized materials: piezoceramics, piezopolymers

(they are the most of the materials which have practical application)

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