Surface polarization charge, Physics

Assignment Help:

An atom is said to be polarized if it possesses and effective dipole moment, that is, if there is a separation between the centres of negative and positive charge distribution. It is important to realize that a polarization p=0 does not mean that the material does contain dipole moment , but only the vector sum of all dipole moments zero . This will, always be the case if the dipole moments  vectors are randomly distributed with respect to their directions. Let us consider a simple plate capacitor or condenser with a homogenously polarized material inside its plate's .More generally; this describes an isotropic dielectric slab of material in a homogenous electrical field. We have the subsequent idealized condition. To calculate the polarization p for the polarized dielectric, we need to sum of all the dipoles in the medium and divide by the volume Ad. However, the polarized medium can be represented in terms of surface charge +QP and -QP, which are separated by the thickness distance d. We can view this arrangement as one big dipole moment Ptotal        

 -QP to +QP. Thus Ptotal = Qp.d

                   Since the polarization is defined as the total dipole moment per unit volume, the magnitude of p is                 

                       P= Total /volume = Qp.d /Ad = QP / A

    But QP /A is the surface polarization charge density sigma p, so

            P=sigma p

     Polarization is a vector and equation only gives its magnitude. For the rectangular slab, the direction of P is normal to surface. For +σP, it comes out from the surface and for -σ, it is directed into the surface.

            The polarization P induced in a dielectric medium when it is placed in an electric field depends on the field itself. To express the dependence of P on the field E, we define a quantity called the electric susceptibility ? e by

        P=? e.σ0.E

   An effect P due to a cause E and the quantity ? e relates the effect to its cause. Electric susceptibility, ? e is a material quantity that measures the extent of polarization in the material per unit field. Further, polarizibility is defined by

              Induced=alpha 

          So, P=N induced =N .alpha E

                Where N is the density of dipoles. Then ? e and alpha are related by

                    ? e=N. alpha/epsilen0

              It is important to recognize the difference between free and polarization charges. The charge

Qo and Q, before and after the dielectric insertion are free charges that arrive on the plates from the battery. The polarization charges +QP to -QP on the other hand, are bound to the atoms. They cannot move within the dielectric or on its surface. The field E before the dielectric was inserted is given by

   E=V/d=Q0/co d

          After the insertion of the dielectric, this field remains the same v/d, but the free charges on the plates are different. The free surface charge on the plates in now Q in addition, there are bound polarization charges on the dielectric surfaces next to the plates. It is apparent that the flow of current during the insertion of the dielectric, is due to the additional free  Q-Q 0 needed on capacitor plates to neutralize the opposite polarity polarization charges Up appearing on the dielectric surfaces, Q-Up must be the same as before, Q0 , so that the field, does not change inside the dielectric that is,

            Q-Up=Q0

      Or Q=Q0+QP

 Dividing by A, defining sigma=Q/A as the free surface charge density on the plates with the dielectric inserted, we obtain

      σ=ε0.E+σP

   Since σP=P and P=zie .ε .E, we can eliminate σ P to obtain

         σ=ε0 (1+zie.e) E

From the definition of the relative permittivity ?, we have

     ε.r=Q/Q0=σ/σ.0

 So substituting for σ@, we obtain

   ε.r=1+?

In terms of polarizability, this is

  ε.r=1+N.@/ε.0

There are essentially four types of polarization Mechanisms.

(1)         Electronic polarization

(2)         Ionic polarization

(3)         Orientation Polarization

(4)         Interface polarization


Related Discussions:- Surface polarization charge

Searle''s apparatus, why metallic frame used in searles apparatus

why metallic frame used in searles apparatus

Zener diode, its characteristic and working

its characteristic and working

Physics, A train consists of a 4300-kg locomotive pulling two loaded boxcar...

A train consists of a 4300-kg locomotive pulling two loaded boxcars. The first boxcar has a mass of 12,700 kg and the second has a mass of 16,300 kg. Presume that the boxcar wheels

Practical, We here at Brilliant assume that you work through these problems...

We here at Brilliant assume that you work through these problems using some sort of writing utensil. Take your pen or pencil, balance it on its tip, and let go. It falls over. How

Can you explain solenoidal field, Can you explain solenoidal field? Describ...

Can you explain solenoidal field? Describe with example?

Semiconductor materials: indium antimonide, Melting point: 525 0 C. It ...

Melting point: 525 0 C. It has small band gap and very high mobility around 70,000Cm 2 /V-Sec. It has much easier to prepare in single crystal from the Gallium arsenide. It is

Inertia with a handkerchief and tumbler, Inertia with a handkerchief and tu...

Inertia with a handkerchief and tumbler Spread a handkerchief out on a smooth table top. Place a tumbler full with water near one corner of the handkerchief. Raise the opposite

Force on rocket repulsion, a jet of engine on a test tube takes in 20kg of ...

a jet of engine on a test tube takes in 20kg of air per second at a velocity of 100m/s and burns 0.8kg of fuel per second.after compression and heating the exhaut gases are ejected

Avogadros hypothesis, Avogadro's hypothesis (Count A. Avogadro; 1811) A...

Avogadro's hypothesis (Count A. Avogadro; 1811) At the same temperature and pressure, equal volumes of all of the gases contain equal numbers of molecules. In fact, it is, only

Boltzmann constant, Boltzmann constant; k (L. Boltzmann) This is a cons...

Boltzmann constant; k (L. Boltzmann) This is a constant that describes the relationship among temperature & kinetic energy for molecules in an ideal gas. This is equal to 1.380

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd