electricity 4

7/25/2019 Electricity 4

1/30

B.Tech Physics Course NIT Jalandhar

electrostatics Lecture 4

Dr. Arvind Kumar Physics Department

e.mail. : [email protected]
mailto:[email protected]:[email protected]


2/30

Electric field in matter:

Dielectrics: These are the insulator (which do not conduct electricity) which are polarized in presence o !lectric ield . These can "e solid# li$uid or gases. %or e&ample glass mica# air etc.

'ets understand how dielectric get polarized:

ormally we now that atoms are electrically neutral

*o we may e&pect that nothing will happen to these neutral

atoms in presence o electric ield .

+owever# atoms consist o positively charged nucleusand negatively charged electrons.


3/30

he response o the dielectric to the !.%. depends upon the nature oolecules o which the dielectric is made up o . There are two inds o olecules.

,) Polar molecules: A polar molecule is the one in which the centre gravity o positive charge does not coincides with the centre gravity o negative charge. e.g. + - # * - # / etc. A polar

olecule possess permanent dipole moment.

ote the centre o gravity o positive charge means the point wherentire 12e charge is supposes to "e concentred. *imilarly the centre o

ravity o 42e charge means the point where entire 42e charge isuppose to concentrated.)


4/30

(-) on5polar molecules: +ere the centre o gravity o positivecharge coincides with the centre o gravity o 42e charge. Anon5polar molecule does not posses the permanent dipolemoment.


5/30

esponse o dielectric material to e&ternal electric ield:

1 !es"onse of Polar dielectric : 7e consider a dielectric materialhich is made o the polar molecules. 8n the a"sence o the e&ternalield these molecules will "e randomly oriented and there ore theet dipole moment per unit volume will "e zero. ote that althoughe individual molecule has the inite dipole moment "ut the average

ipole moment o the sample is zero .


6/30

+owever when the !.%. is applied to such dielectric then themolecules will "e oriented in the direction o the !.%. This is

"ecause the molecules "ehaving as dipole will e&perience ator$ue

This tor$ue will align the molecule in the direction o !.%.

9 E p =

The degree o alignment dependsupon the strength o the applied!.%. ! 9 and also on the temperature.The degree o the alignment

increases with the strength oapplied ield and decreases with increase in the temperature o thesample.


7/30

Effect of the E.#. on the non$"olar dielectric:7e consider a non5polar dielectric . 8n the a"sence o the !.%. these molecules do not have dipole moment. +owever when the!.%. is applied to non5polar dielectric then the 12e and 42e charges get separated. The 12e charges get displaced in the direction o the ield whereas the 42e charges get displaced in direction opposite to the !.%. the a dipole moment is induced due to e&ternal ield.This ind o dipole moment which is induced due to e&ternal applied

ield is nown a induced dipole moment.


8/30

!lectric ield due to Polarization o Dielectric:

7hen a dielectric is placed in the presence o the ield then themolecules o the dielectric get aligned in the direction o theield.This can "e either due to rotation o the molecules (in case o dielectric made o polar molecules) or due to separation o the charges (in case o dielectric made o non5polar molecules).

Due to this alignment o molecules the positive charge o themolecule inside the dielectric is ollowed "y the negative charge o the ne&t molecule and so on. The 12e charge o the molecule is cancelled "y the 42e charge o the molecule ad acent to it. The net charge in the macroscopic region is zero e&cept at the sur ace.


9/30

There le t un"alanced charge at the sur aceand this lead to the polarization o the dielectric. These chargesare nown as the polarization charges or "ound charges.

Due to these charges there is now new ield denoted "y ! p.This ield acts in direction opposite to the e&ternal applied ield.*o the net ield is now#

! ; ! 9 4 ! p


10/30

8n presence o !.%. positively charged nucleus shi t in directiono electric ield and negatively charged cloud to opposite side and these are separated "y inite distance.

7e say that the atom has got the dipole moment which is proportional tothe applied !.%.

8n a"ove % is atomic polariza"ility and " is induced dipole momentin atom due to e&ternal !.%.

8 the dielectric material has atoms per unit volume then total induced dipole moment is P ; " +ere P is nown as polarization.

&tomic "olari'a ility:


11/30

Conce"t of ound char)es:

/onsider long string o dipoles as shown "elow

+ead o one cancel the tail o other and we are le t with two charges.Positive on right and negative on le t

These net charges at the end are nown as "ound charges.


12/30

/harge at the end o tu"e is


13/30

8 polarization is not uni orm then there can "e "ound chargesinside and also on the sur ace

et charge inside the volume depend upon how much is pushed out


14/30


15/30

ow according to 3auss 'aw

8n a"ove ! is now total !.%.

7e can write a"ove e$n "y ta ing divergence eon one side as

7here we write

Thus we have

8n integral orm we can write

!lectric displacementvector


16/30

-usce"ti ility "ermitti/ity and dielectric constant

Polarization o dielectrics is proportional to the !.%.

is electric suscepti"ility o the material and is dimensionless $uantity.

7e now or linear medium we can write electric displacementvector using (,)

7herePermittivity o the medium

-------------------(1)

-------------------(2)

-------------------(3)


17/30

%rom !$. (=) we can de ine a dimensionless $uantity# nown as relative permittivity o the material

555555555555555(>)


18/30

Local #ield or Polari'in) field in ,ielectric:

electric feld at the site o molecule or dipole due to all sou

nown as Polarizing feld or local feld.

nd the local iled at the site o molecule or dipole we consider maginary sphere o radius r such that inside the sphereave large num"er o molecules. Also outsidephere medium "ehaventinuum.


19/30

7e consider that the dielectric is palced "etween the two plates o the/apacitor. The local ield is thus the sumo ollowing ields

555555(,)


20/30

we fnd the !arious felds in "#n. (1) as ollows$know$

-----------(2)

--------------(3)

feld "3 is due to the molecules inside the sphere. 'onsidch molecule eha!ing as dipole the ". . is written as

--------(*)

l feld is o tained + summing o!er all molecules. or per

metric and per ectl+ random case "3 . ------------(/)


21/30

The electric field E4 due to polarization charges is calculated as follows:

/onsider a small area element(ring shaped)on the sur ace o cavity.8t is written as

55555555(?)( ote: area o sur ace element ; circum erence width. 8n a"ove P8s radius and 6 is width)


22/30

ow the charge d$ on this small area element can "e written as the normal component o Polarization multiplied "y the area element.*o we write#

555555(B)The !.%. at centre A due to the a"ove charge element indirection C ; 9 is written as

555555555( )


23/30

Total !.%. at A is o"tained "y integrating

555555555555555(E)

=

=

cos =

-9

9

P


24/30

999 =9 P P P E E L +++=

Thus using !$. (-)# (=)# (F) and (E) the local ield in e$. (,) can "ewritten as

55555555555(,9)

A"ove !$. gives us the value o local ield at the site o a moleculedue to all sources.


25/30

Clausius 0ossotti !elation:

The /lausius50ossotti relation connects the relative permittivity Gr

o a dielectric to the polariza"ility H o the atoms or moleculesconstituting the dielectric.

The relative permittivity is a "ul (macroscopic) property and polariza"ility is a microscopic property o matter and hence the relation "ridges the gap "etween a directly5o"serva"le macroscopic

property with a microscopic molecular property.

The relation is given "y

where G9 is the electric constant (permittivity o the vacuum) and N is the number density (number of atoms or molecules per

volume).


26/30

Derivation: 7e now that the induced dipole moment in an atom is e$ual to and i there are num"er o atom per unit volume then the polarization is written as

555555(,)

ow using !$ns.

And

!$. (,) can "e written as


27/30

7hich is solved urther as "elow#

5555555555(-)

Also the local ield is given "y ollowing de inition

555555555(=)


28/30

Ising !$. (=) in !$. (-) we get#

55555555(>)

i g !$ (>) it ll i g & i


29/30

ow using !$. (>) we write ollowing e&pression:

555555(F)

/lausius 0ossotti 6elation.


30/30

electricity 4

Documents