Tho.lecture 2

8/20/2019 Tho.lecture 2

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GENERAL PHYSICS II

Electromagnetism

&

Thermal Physics


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Chapter VIII

Dielectrics

§1. Induced charges and polarization of dielectrics§2. Molecular model of induced charges

§3. Piezoelectric effect


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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 +Q -Q

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 it. It means that the charge Q is

constant . V


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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 flowfrom one atom (or molecule) to another. The electric asymmetry of atoms(molecules) leads to the existence of electric dipoles. These dipoles arerandomly 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 σ 0, the electric field E 0 between plates exretstorques on the dipoles. These torques tend to align the dipoles with the

field (pic. b). By this effect there exits a net charge density σ i induced in the surfaces of

the dielectric (pic. c).

a) b) c)


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2.3 The dielectric constant:

The induced charges on the surfaces of the dielectric creates aninduced electric field E i . The direction of E i is opposite to the electric fieldE 0. Therefore, the net electric field inside the dielectric is

We define the dielectric constant

+σ 0 -σ 0-σ i +σ i

+

+

-

-

-

-

+

+

E 0

E i

1 < k < ∞

perfect dielectric(vacuum)

perfect conductor

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


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In summary, when a dielectric is inserted in a electric field, a

redistribution 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 for some dielectrics: mica → 3-6; glass → 5-10; water → 80.


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1.4 Permitivity of dielectric:

The electric field between two plates is calculated through surface

charge density σ

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

σ - σ i , and we have

From the formular we can write

Therefore where

The definition of permitivity

of dielectricThe meaning of permitivity ε :

If in the vacuum then in the dielectric


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In other word, the effect of dielectrics can be take into account by the

replacement ε 0 → ε in expressions for the elctric field .

ε 0

can be called the permitivity of vacuum .

The units: k is a number which has no unit.

The units of ε is the same as of ε 0 → C2 / Nm2 = F/m

(recall ε0 = 8.85 Х 10-12 F/m)

1.5 Dielectric breakdown:

When any dielectric material is subjected to a sufficiently strong electricfield, 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 dielectric strength. (For example,

for dry air it’s about 3 x106 V / m.


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§ 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 themolecular structure of dielectrics and consider inmore detail about these molecular dipoles.

2.1 The case of nonpolar molecules:

+ The simplest case of a monatomic gas (for

instance, helium) → the centers of gravity of the

negative and positive charges coincide (pic. a).+ The molecular of some gases, like oxygen, has

a symmetric pair of atoms (pic. c).

+ The moleculars of this type, in the absent of

external electric field, have not permanent dipole

moment. They are called nonpolar moleculars.

In a electric field the centers of positive andnegative charges are displaced. As a result, the

nonpolar molecules will become asymmetrical

and have a electric dipole moment (pic. b).

a/

b/

c/


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+ 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 The 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.

Polar molecules behave in an external field as rigid dipoles.


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(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.

(b) 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 theaxis a of the crystal. The second axis is c.

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

This effect is called longitudinal piezoelectric.

+ The same charges arise as before, if the plate

is stretched along the direction OO which isperpendicular 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 OO).+ 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.


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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 .

If we insert on the panels an alternating voltage, the crystall plate will be

stretched and compressed in accordance withthe frequency of the voltage → oscillations arise

in the plate.

~

a

O

O

V

There is also resonance phenomenon:

when the frequency of the alternating

voltage coincides with the own frequencyof 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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