dielectrics- lecture notes
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Dielectrics are the materials having electric dipole moment permanently.
Dipole: A dipole is an entity in which equal positive and negative charges are separated by a small distance..
DIPOLE moment (µEle ):The product of magnitude of either of the charges and separation distance b/w them is called Dipole moment.
µe = q . x coulmb.m
All dielectrics are electrical insulators and they are mainly used to store electrical energy.
Ex: Mica, glass, plastic, water & polar molecules…
Xq -q
Introduction
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Electric field
Dielectric atom
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dipole
The relative permittivity(εr) is often known as dielectric const. of medium it can given by,
εr=ε/ε0
Dielectric constant is ratio of permittivity of medium to permittivity of free space.
The value of capacitance of capacitor is given by, C0=εrε0A/d
By this eqn we can say that high εr increases capacity of capacitor.
Polar and Nonpolarized MoleculesNon-polar Molecules : The Dielectric material in which there is no permanent dipole existence in absence of an external field is …..
O=O N N Cl-Cl F-F Br-Br I-I
2 – Compounds made of molecules which are symmetrically shaped
carbon tetra fluoride CF4
propaneC3H8
methane CH4
carbon tetra fluoride CCl4,
carbon dioxideO=C=O
Polar Molecules The Dielectric material in which there is permanent dipole existence even in absence of an external field is …..
HClhydrogen chloride
carbon monoxideC O
2 – molecules with O, N, or OH at one end – asymmetrical e.g.; CH2Cl2,CH3Cl
waterH2O
unbounded electron pairs bend the molecule
ammonianitrogen trihydrideNH3
alcoholsmethanolCH3OH
Identify each of the following molecules as 1) polar or 2) nonpolarized. Explain.
A. PBr3
B. HBr
C. Br2
D. SiBr4
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Identify each of the following molecules as 1) polar or 2) nonpolarized. Explain.
A. PBr3 1) pyramidal; dipoles don’t cancel; polar
B. HBr1) linear; one polar bond (dipole); polar
C. Br2 2) linear; nonpolarized bond; nonpolarized
D. SiBr4 2) tetrahedral; dipoles cancel; no polar
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As shown in fig. when an electric field is applied to dielectric material their negative & positive charges tend to align in equilibrium position.
They produce electric dipole inside the material. This phenomenon is known as Polarization. It can be represented by,P=polarizationμ= dipole momentV=Volume Unit=Cm-2 Now dipole moment depends upon applied electric field.
α polarizability of material.
PV
E
P E
P E
9999999999999999999999999999
9999999999999999999999999999
9999999999999999999999999999
++++++++
--------
E0
----------------------
++ -- ++ -- ++ -- ++ -- ++ -- ++
-- ++ -- ++ -- ++ -- ++
-- ++ --
+q
-q
-q
+q
-q
+q
++++++++++++++++++++++
E0
In absence of dielectric
In presence of dielectric
0
00
00
.E ds q
qE A
qE
A
0
0 0
0 0
. '
'
'
E ds q q
q qEA
q qE
A A
V=Ed So
Now
0 0
d
E Vk
E V
0
0
0 0
0 0 0
'
',
1, ' (1 )
E qE
k kA
q qE
A A
q q qSokA A A
then q qk
0
0
So, . '
1(1 )
q
.
E ds q q
q qk
k
k E ds q
This relation true is for parallel plate
capacitor Which is Gauss’s law for dielectrics
The resultant dielectric field is given by,
Where,E=Electric fieldD=Flux Density or
Displacement vectorP=Polarization
0 0
0 0
0
0
'
',
,
,D
p
q qE
A A
qnow P
Aq P
EA
qE P
Aq
now DA
So E P
Electric susceptibility:The polarization vector P is proportional to the total electric flux density and direction of electric field.Therefore the polarization vector can be written
0
0
0
0
( 1)
1
e
e
r
e r
P E
P
E
E
E
Displacement vector,
0
0
0
r 0 0
0
D E P
Now,P=
( - ) E P
(or) ( . - ) E P
( 1) . P
Where,( 1)r
r
E
E
1. Electron polarization2. Ionic polarization3. Orientation polarization4. Space charge polarization
When no external field is applied nucleus of atom is like in fig. (a)
When external field is applied, displacement in opposite direction is observed between nucleus & electrons due to this dipole moment is induced.
This type of polarization is called Electronic polarization.
Ex. Germanium, Silicon, Diamond etc…
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Electric Field Electric Field (a) (b)
Some materials like ionic crystal does not possess permanent dipole moment.
Fig. (a) shows natural arrangement of ionic crystal. When Ele. Field is applied on this type of material displacement of ions is observed.
Due to an external electric field a positive & negative ion displaces in the direction opposite to each other due to which distance between them is reduced & ionic polarization is generated.
Ionic polarization is observed in materials like NaCl, KBr, KCl etc…
Let us consider simple example of NaCl crystal.
As shown in fig. when crystal is placed in an external electric field Na+ ion displaces in one direction & Cl- ion goes in opposite direction.
Some molecules like H2O, HCl having permanent dipole moment p0.
In the absence of a field, individual dipoles are arranged in random way, so net average dipole moment in a unit volume is zero as shown in fig. (b).
A dipole such as HCl placed in a field experiences a torque that tries to rotate it to align p0 with the field E.
In the presence of an applied field, the dipoles try to rotate to align parallel to each other in direction of electric field fig (d).
This type of polarization is Orientation polarization.
This type of polarization occurs only in polar substances like H2O, CH3Cl when they are placed in external field.
A crystal with equal number of mobile positive ions and fixed negative ions.
In the absence of a field, there is no net separation between all the positive charges and all the negative charges.
In the presence of an applied field, the mobile positive ions migrate toward the negative charges and positive charges in the dielectric.
The dielectric therefore exhibits Space charge or interfacial polarization.
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dW F dr
F
dW qE dr
dW E dp
p pP
lA V
0
0
0
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20
( 1) .
. .( 1) .
. .( 1) .
1( 1) E
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( 1) E2
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r
r
r
r
r
p PV
dW EVdP
P E
dW EV dE
dW EV dE
W V
W
VU
References:Engineering physics By Dr. M N Avadhnulu, S Chand publicationEngineering physics by K Rajgopalanhttp://web.mit.edu/viz/EM/visualizations/coursenotes/modules/guide05.pdf
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