Chapter VIII Dielectrics

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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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Nội dung Text: Chapter VIII Dielectrics

GENERAL PHYSICS II Electromagnetism & Thermal Physics 1/29/2008 1
Chapter VIII Dielectrics §1. Induced charges and polarization of dielectrics §2. Molecular model of induced charges §3. Piezoelectric effect 1/29/2008 2
 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. 1/29/2008 3
§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 1/29/2008 constant. V 4
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 σ , the electric field E 0 between plates exrets 0 torques 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 induced in the surfaces of i the dielectric (pic. c). 1/29/2008 5 a) b) c)
2.3 The dielectric constant: The induced charges on the surfaces of the dielectric creates an induced electric field E i . The direction of E i is opposite to the electric field E0. Therefore, the net electric field inside the dielectric is We define the dielectric constant - + + - E0 1
 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. 1/29/2008 7
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 , and we have i From the formular we can write Therefore where The definition of permitivity The meaning of permitivity ε : of dielectric 1/29/2008 If in the vacuum then in the dielectric 8
In other word, the effect of dielectrics can be take into account by the replacement ε → ε expressions for the elctric field. 0 in  ε can be called the permitivity of vacuum . 0  The units:  k is a number which has no unit. 2  The units of ε the same as of ε → C / Nm = F/m is 2 0 (recall ε = 8.85 Х10-12 F/m) 0 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 dielectric strength. (For example, for dry air it’s about 3 x106 V / m. 1/29/2008 9
§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 a/ more 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 b/ 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 and negative charges are displaced. As a result, the nonpolar molecules will become asymmetrical c/ and have a electric dipole moment (pic. b). 1/29/2008 10
+ 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. 1/29/2008 11
(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 1/29/2008 12
§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 c. + 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 longitudinal 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 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. 1/29/2008 13
 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 with a the frequency of the voltage → oscillations arise in the plate. There is also resonance phenomenon: O when the frequency of the alternating O ~ voltage coincides with the own frequency V of the plate → the oscillations become very strong. 1/29/2008 14
 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). 1/29/2008 15