Kinds of Material - Chapter Notes, Material Science, Semester, Engineering Class 11 Notes | EduRev

Class 11 : Kinds of Material - Chapter Notes, Material Science, Semester, Engineering Class 11 Notes | EduRev

 Page 1


  
 
 
 
D: KINDS OF MATERIALS 
D1: Dielectric Materials 
D2: Magnetic Materials 
D3: Superconductors 
D4. Semiconductors 
D5. Nanomaterials 
  
Prof. J.K.Goswamy’s Lecture Notes on Materials Science: Properties of Materials. Page 185 
 
Page 2


  
 
 
 
D: KINDS OF MATERIALS 
D1: Dielectric Materials 
D2: Magnetic Materials 
D3: Superconductors 
D4. Semiconductors 
D5. Nanomaterials 
  
Prof. J.K.Goswamy’s Lecture Notes on Materials Science: Properties of Materials. Page 185 
 
D1: DIELECTRIC MATERIALS 
16.1 Introduction 
On the basis of electrical conduction, the materials 
can be classified into three basic categories i.e. 
conductors, insulators and semiconductors. The 
conductors have large number of free electrons 
which participate in electrical conduction on 
imposing external electric field. Such materials are 
characterized by high electrical conductivity and 
find diversified applications. Rather conductors 
have been one of the indices to adjudge the 
growth of civilizations since historical times. 
In the same spirit, the semiconductor materials 
have moderate number of free electrons available 
for electrical conduction at low temperatures. As 
the temperature is raised, the increasingly number 
of electrons are set free to participate in the 
conduction process. These materials are 
characterized with electrical conductivity 
increasing as a function of temperature. Further 
such materials have two types of charge carriers – 
electrons and holes, which contribute to the 
current. These materials have wide applications in 
electronic devices ranging from diodes, transistors, 
integrated circuits and many other devices. To 
summarize, this class includes wide variety of 
materials which form the backbone of the present 
day technology. 
The dielectric materials are defined to be those 
which have few free or loosely bound electrons. 
These materials suffer charge polarization on 
application of external electric field resulting in 
buildup of charges on their surface. This surface 
polarization results in modification of electric field 
inside these materials. As a consequence of this 
feature, their dielectric and optical properties 
assume importance. The insulators can be 
conceived as an ideal dielectric which has all the 
electrons bound tightly. The properties of 
dielectric materials are governed by the behavior 
of electric dipole in different environment. It is 
instructive that we should first be conversant with 
basic terminology of an electric dipole. 
 
16.2 Electric Dipole 
A system of equal and opposite charges separated 
by some distance constitutes an electric dipole. An 
electric dipole has two axes of interest which are 
shown in the figure 16.1. 
 
 
 
 
 
 
 
Figure 16.1: This diagram depicts the basis 
terminology of an electric dipole. 
Axial Line 
+q -q 
p 
L 
Equatorial line 
Prof. J.K.Goswamy’s Lecture Notes on Materials Science: Properties of Materials. Page 186 
 
Page 3


  
 
 
 
D: KINDS OF MATERIALS 
D1: Dielectric Materials 
D2: Magnetic Materials 
D3: Superconductors 
D4. Semiconductors 
D5. Nanomaterials 
  
Prof. J.K.Goswamy’s Lecture Notes on Materials Science: Properties of Materials. Page 185 
 
D1: DIELECTRIC MATERIALS 
16.1 Introduction 
On the basis of electrical conduction, the materials 
can be classified into three basic categories i.e. 
conductors, insulators and semiconductors. The 
conductors have large number of free electrons 
which participate in electrical conduction on 
imposing external electric field. Such materials are 
characterized by high electrical conductivity and 
find diversified applications. Rather conductors 
have been one of the indices to adjudge the 
growth of civilizations since historical times. 
In the same spirit, the semiconductor materials 
have moderate number of free electrons available 
for electrical conduction at low temperatures. As 
the temperature is raised, the increasingly number 
of electrons are set free to participate in the 
conduction process. These materials are 
characterized with electrical conductivity 
increasing as a function of temperature. Further 
such materials have two types of charge carriers – 
electrons and holes, which contribute to the 
current. These materials have wide applications in 
electronic devices ranging from diodes, transistors, 
integrated circuits and many other devices. To 
summarize, this class includes wide variety of 
materials which form the backbone of the present 
day technology. 
The dielectric materials are defined to be those 
which have few free or loosely bound electrons. 
These materials suffer charge polarization on 
application of external electric field resulting in 
buildup of charges on their surface. This surface 
polarization results in modification of electric field 
inside these materials. As a consequence of this 
feature, their dielectric and optical properties 
assume importance. The insulators can be 
conceived as an ideal dielectric which has all the 
electrons bound tightly. The properties of 
dielectric materials are governed by the behavior 
of electric dipole in different environment. It is 
instructive that we should first be conversant with 
basic terminology of an electric dipole. 
 
16.2 Electric Dipole 
A system of equal and opposite charges separated 
by some distance constitutes an electric dipole. An 
electric dipole has two axes of interest which are 
shown in the figure 16.1. 
 
 
 
 
 
 
 
Figure 16.1: This diagram depicts the basis 
terminology of an electric dipole. 
Axial Line 
+q -q 
p 
L 
Equatorial line 
Prof. J.K.Goswamy’s Lecture Notes on Materials Science: Properties of Materials. Page 186 
 
Electric Dipole Moment(p) is defined as product of 
magnitude of one of the charges and distance of 
separation between them and is always directed 
from negative to positive charge. Mathematically 
we have  
( ) ) 1 . 16 ( 2l q p
r
r
= 
The dimensions of electric dipole moment are 
[LTA] and SI units are Coulomb-metre. However 
the practical unit of this quantity, for consideration 
in microscopic systems (such as atoms, molecules, 
nuclei etc), is Debye (D), which is defined as the 
dipole moment due to charges of magnitude 10
-
10
Stat-Coulomb separated by a distance of 1Å. The 
magnitude of 1 Debye in SI units is: 
Cm D
Cm
statCm m statC D
30
9
20
20 10 10
10 33 . 3 1
10 3
10
10 10 10 1
-
-
- - -
× =
×
=
= × =
 
 
16.2.1 Field Due to an Electric Dipole 
The electric field due to a dipole can be defined at 
three different positions, which are discussed in 
the text to follow in this section: 
 
Field at an oblique location: The electric field at a 
point P (see figure 16.2) lying at a distance r from 
the centre of a short electric dipole and making an 
angle ? with axis of dipole is  
( )
) 2 . 16 (
4
3
5
0
2
r
p r r p r
E
ob
pe
r r r r
r
- ·
=
 
 
 
 
 
 
 
 
    
Figure 16.2: Electric field due to an electric dipole 
at an oblique position. 
 
The direction of electric field is given as 
) 3 . 16 (
2
tan
tan
?
a = 
 
Axial Field: The electric field intensity, due to an 
electric dipole, at a point lying on axial line at a 
distance r from the centre of electric dipole having 
length l 2 , will be : 
) 4 . 16 (
) ( 4
2
2 2 2
0
l r
p r
E
axial
-
=
pe
r
r
 
The axial field points along the direction of the 
electric dipole moment vector. 
 
Equatorial field: The electric field at a pointlying 
on the equatorial line at a distance r from centre 
of electric dipole is 
( )
) 5 . 16 (
4
2 / 3
2 2
0
l r
p
E
eq
+
-
=
pe
r
r
 
The equatorial field is opposite to the direction of 
electric dipole moment vector. 
 
 
r 
P 
+q 
-q 
E
ob
 
? 
a 
Prof. J.K.Goswamy’s Lecture Notes on Materials Science: Properties of Materials. Page 187 
 
Page 4


  
 
 
 
D: KINDS OF MATERIALS 
D1: Dielectric Materials 
D2: Magnetic Materials 
D3: Superconductors 
D4. Semiconductors 
D5. Nanomaterials 
  
Prof. J.K.Goswamy’s Lecture Notes on Materials Science: Properties of Materials. Page 185 
 
D1: DIELECTRIC MATERIALS 
16.1 Introduction 
On the basis of electrical conduction, the materials 
can be classified into three basic categories i.e. 
conductors, insulators and semiconductors. The 
conductors have large number of free electrons 
which participate in electrical conduction on 
imposing external electric field. Such materials are 
characterized by high electrical conductivity and 
find diversified applications. Rather conductors 
have been one of the indices to adjudge the 
growth of civilizations since historical times. 
In the same spirit, the semiconductor materials 
have moderate number of free electrons available 
for electrical conduction at low temperatures. As 
the temperature is raised, the increasingly number 
of electrons are set free to participate in the 
conduction process. These materials are 
characterized with electrical conductivity 
increasing as a function of temperature. Further 
such materials have two types of charge carriers – 
electrons and holes, which contribute to the 
current. These materials have wide applications in 
electronic devices ranging from diodes, transistors, 
integrated circuits and many other devices. To 
summarize, this class includes wide variety of 
materials which form the backbone of the present 
day technology. 
The dielectric materials are defined to be those 
which have few free or loosely bound electrons. 
These materials suffer charge polarization on 
application of external electric field resulting in 
buildup of charges on their surface. This surface 
polarization results in modification of electric field 
inside these materials. As a consequence of this 
feature, their dielectric and optical properties 
assume importance. The insulators can be 
conceived as an ideal dielectric which has all the 
electrons bound tightly. The properties of 
dielectric materials are governed by the behavior 
of electric dipole in different environment. It is 
instructive that we should first be conversant with 
basic terminology of an electric dipole. 
 
16.2 Electric Dipole 
A system of equal and opposite charges separated 
by some distance constitutes an electric dipole. An 
electric dipole has two axes of interest which are 
shown in the figure 16.1. 
 
 
 
 
 
 
 
Figure 16.1: This diagram depicts the basis 
terminology of an electric dipole. 
Axial Line 
+q -q 
p 
L 
Equatorial line 
Prof. J.K.Goswamy’s Lecture Notes on Materials Science: Properties of Materials. Page 186 
 
Electric Dipole Moment(p) is defined as product of 
magnitude of one of the charges and distance of 
separation between them and is always directed 
from negative to positive charge. Mathematically 
we have  
( ) ) 1 . 16 ( 2l q p
r
r
= 
The dimensions of electric dipole moment are 
[LTA] and SI units are Coulomb-metre. However 
the practical unit of this quantity, for consideration 
in microscopic systems (such as atoms, molecules, 
nuclei etc), is Debye (D), which is defined as the 
dipole moment due to charges of magnitude 10
-
10
Stat-Coulomb separated by a distance of 1Å. The 
magnitude of 1 Debye in SI units is: 
Cm D
Cm
statCm m statC D
30
9
20
20 10 10
10 33 . 3 1
10 3
10
10 10 10 1
-
-
- - -
× =
×
=
= × =
 
 
16.2.1 Field Due to an Electric Dipole 
The electric field due to a dipole can be defined at 
three different positions, which are discussed in 
the text to follow in this section: 
 
Field at an oblique location: The electric field at a 
point P (see figure 16.2) lying at a distance r from 
the centre of a short electric dipole and making an 
angle ? with axis of dipole is  
( )
) 2 . 16 (
4
3
5
0
2
r
p r r p r
E
ob
pe
r r r r
r
- ·
=
 
 
 
 
 
 
 
 
    
Figure 16.2: Electric field due to an electric dipole 
at an oblique position. 
 
The direction of electric field is given as 
) 3 . 16 (
2
tan
tan
?
a = 
 
Axial Field: The electric field intensity, due to an 
electric dipole, at a point lying on axial line at a 
distance r from the centre of electric dipole having 
length l 2 , will be : 
) 4 . 16 (
) ( 4
2
2 2 2
0
l r
p r
E
axial
-
=
pe
r
r
 
The axial field points along the direction of the 
electric dipole moment vector. 
 
Equatorial field: The electric field at a pointlying 
on the equatorial line at a distance r from centre 
of electric dipole is 
( )
) 5 . 16 (
4
2 / 3
2 2
0
l r
p
E
eq
+
-
=
pe
r
r
 
The equatorial field is opposite to the direction of 
electric dipole moment vector. 
 
 
r 
P 
+q 
-q 
E
ob
 
? 
a 
Prof. J.K.Goswamy’s Lecture Notes on Materials Science: Properties of Materials. Page 187 
 
16.2.2 Electric Potential due to a Dipole 
The electric potential at any point P (see figure 
16.2) lying at a distance r at an angle of ? with the 
axis of dipole is given as: 
 
) 5 . 16 (
4
cos
2
0
r
p
V
pe
?
=
 
Hence the electric potential at any point P lying on 
the axial or equatorial lines are obtained as 
 
o
eq
o
axial
V
r
p
V
90 0
0
4
2
0
= =
= =
?
?
pe
 
 
16.2.3 Electric Dipole in an Electric Field 
If an electric dipole is placed in a uniform electric 
field, then two charges experience equal and 
opposite force (see figure 16.3) as a result of which 
net force on it is zero. Since these forces are acting 
opposite in direction and operate along different 
lines of action, they constitute a couple which 
tends to rotate the electric dipole. The torque 
exerted on the dipole is E p
r
r r
× = t .This torque 
tends to align the electric dipole moment along 
the direction of applied electric field. 
 
 
 
 
 
 
Figure 16.3: The electric dipole placed in an 
uniform electric field. 
If the electric dipole is placed in a non-uniform 
field then net force on it is not zero. As a 
consequence, the electric dipole suffers translation 
in space (due to net force) as well as rotation (due 
to the torque exerted by the field). 
Work done to rotate the electric dipole from 
angular position a to ß with respect to the uniform 
electric field E
r
 is given as: 
 ) 6 . 16 ( ) cos (cos ß a - = pE W 
If the a = 90
o
 is taken as the reference position 
then the work done on the dipole is  
 ) 7 . 16 ( cos E p pE W
r
r
· - = - = ß 
This work is stored as the potential energy of the 
electric dipole.  
 
16.3 Dielectric Properties of a Medium 
 
16.3.1 Properties of Dielectric Medium 
When a dielectric medium is placed in an external 
electric field ( )
0
E
r
, then it suffers surface charge 
polarization resulting in alteration of its 
electromagnetic properties. The electric field 
inside the dielectric medium ( ) E
r
 is related to the 
applied electric field ( )
0
E
r
as: 
) 8 . 16 (
0 0 0
P E E D
r r r r
+ = = e e 
where
o
E D
r r
0
e = is the electric displacement 
vector dependent purely on the applied external 
field. 
   
E q F
r r
- =
-
 
-q 
? 
E
r
 
+q 
E q F
r r
+ =
+
 
Prof. J.K.Goswamy’s Lecture Notes on Materials Science: Properties of Materials. Page 188 
 
Page 5


  
 
 
 
D: KINDS OF MATERIALS 
D1: Dielectric Materials 
D2: Magnetic Materials 
D3: Superconductors 
D4. Semiconductors 
D5. Nanomaterials 
  
Prof. J.K.Goswamy’s Lecture Notes on Materials Science: Properties of Materials. Page 185 
 
D1: DIELECTRIC MATERIALS 
16.1 Introduction 
On the basis of electrical conduction, the materials 
can be classified into three basic categories i.e. 
conductors, insulators and semiconductors. The 
conductors have large number of free electrons 
which participate in electrical conduction on 
imposing external electric field. Such materials are 
characterized by high electrical conductivity and 
find diversified applications. Rather conductors 
have been one of the indices to adjudge the 
growth of civilizations since historical times. 
In the same spirit, the semiconductor materials 
have moderate number of free electrons available 
for electrical conduction at low temperatures. As 
the temperature is raised, the increasingly number 
of electrons are set free to participate in the 
conduction process. These materials are 
characterized with electrical conductivity 
increasing as a function of temperature. Further 
such materials have two types of charge carriers – 
electrons and holes, which contribute to the 
current. These materials have wide applications in 
electronic devices ranging from diodes, transistors, 
integrated circuits and many other devices. To 
summarize, this class includes wide variety of 
materials which form the backbone of the present 
day technology. 
The dielectric materials are defined to be those 
which have few free or loosely bound electrons. 
These materials suffer charge polarization on 
application of external electric field resulting in 
buildup of charges on their surface. This surface 
polarization results in modification of electric field 
inside these materials. As a consequence of this 
feature, their dielectric and optical properties 
assume importance. The insulators can be 
conceived as an ideal dielectric which has all the 
electrons bound tightly. The properties of 
dielectric materials are governed by the behavior 
of electric dipole in different environment. It is 
instructive that we should first be conversant with 
basic terminology of an electric dipole. 
 
16.2 Electric Dipole 
A system of equal and opposite charges separated 
by some distance constitutes an electric dipole. An 
electric dipole has two axes of interest which are 
shown in the figure 16.1. 
 
 
 
 
 
 
 
Figure 16.1: This diagram depicts the basis 
terminology of an electric dipole. 
Axial Line 
+q -q 
p 
L 
Equatorial line 
Prof. J.K.Goswamy’s Lecture Notes on Materials Science: Properties of Materials. Page 186 
 
Electric Dipole Moment(p) is defined as product of 
magnitude of one of the charges and distance of 
separation between them and is always directed 
from negative to positive charge. Mathematically 
we have  
( ) ) 1 . 16 ( 2l q p
r
r
= 
The dimensions of electric dipole moment are 
[LTA] and SI units are Coulomb-metre. However 
the practical unit of this quantity, for consideration 
in microscopic systems (such as atoms, molecules, 
nuclei etc), is Debye (D), which is defined as the 
dipole moment due to charges of magnitude 10
-
10
Stat-Coulomb separated by a distance of 1Å. The 
magnitude of 1 Debye in SI units is: 
Cm D
Cm
statCm m statC D
30
9
20
20 10 10
10 33 . 3 1
10 3
10
10 10 10 1
-
-
- - -
× =
×
=
= × =
 
 
16.2.1 Field Due to an Electric Dipole 
The electric field due to a dipole can be defined at 
three different positions, which are discussed in 
the text to follow in this section: 
 
Field at an oblique location: The electric field at a 
point P (see figure 16.2) lying at a distance r from 
the centre of a short electric dipole and making an 
angle ? with axis of dipole is  
( )
) 2 . 16 (
4
3
5
0
2
r
p r r p r
E
ob
pe
r r r r
r
- ·
=
 
 
 
 
 
 
 
 
    
Figure 16.2: Electric field due to an electric dipole 
at an oblique position. 
 
The direction of electric field is given as 
) 3 . 16 (
2
tan
tan
?
a = 
 
Axial Field: The electric field intensity, due to an 
electric dipole, at a point lying on axial line at a 
distance r from the centre of electric dipole having 
length l 2 , will be : 
) 4 . 16 (
) ( 4
2
2 2 2
0
l r
p r
E
axial
-
=
pe
r
r
 
The axial field points along the direction of the 
electric dipole moment vector. 
 
Equatorial field: The electric field at a pointlying 
on the equatorial line at a distance r from centre 
of electric dipole is 
( )
) 5 . 16 (
4
2 / 3
2 2
0
l r
p
E
eq
+
-
=
pe
r
r
 
The equatorial field is opposite to the direction of 
electric dipole moment vector. 
 
 
r 
P 
+q 
-q 
E
ob
 
? 
a 
Prof. J.K.Goswamy’s Lecture Notes on Materials Science: Properties of Materials. Page 187 
 
16.2.2 Electric Potential due to a Dipole 
The electric potential at any point P (see figure 
16.2) lying at a distance r at an angle of ? with the 
axis of dipole is given as: 
 
) 5 . 16 (
4
cos
2
0
r
p
V
pe
?
=
 
Hence the electric potential at any point P lying on 
the axial or equatorial lines are obtained as 
 
o
eq
o
axial
V
r
p
V
90 0
0
4
2
0
= =
= =
?
?
pe
 
 
16.2.3 Electric Dipole in an Electric Field 
If an electric dipole is placed in a uniform electric 
field, then two charges experience equal and 
opposite force (see figure 16.3) as a result of which 
net force on it is zero. Since these forces are acting 
opposite in direction and operate along different 
lines of action, they constitute a couple which 
tends to rotate the electric dipole. The torque 
exerted on the dipole is E p
r
r r
× = t .This torque 
tends to align the electric dipole moment along 
the direction of applied electric field. 
 
 
 
 
 
 
Figure 16.3: The electric dipole placed in an 
uniform electric field. 
If the electric dipole is placed in a non-uniform 
field then net force on it is not zero. As a 
consequence, the electric dipole suffers translation 
in space (due to net force) as well as rotation (due 
to the torque exerted by the field). 
Work done to rotate the electric dipole from 
angular position a to ß with respect to the uniform 
electric field E
r
 is given as: 
 ) 6 . 16 ( ) cos (cos ß a - = pE W 
If the a = 90
o
 is taken as the reference position 
then the work done on the dipole is  
 ) 7 . 16 ( cos E p pE W
r
r
· - = - = ß 
This work is stored as the potential energy of the 
electric dipole.  
 
16.3 Dielectric Properties of a Medium 
 
16.3.1 Properties of Dielectric Medium 
When a dielectric medium is placed in an external 
electric field ( )
0
E
r
, then it suffers surface charge 
polarization resulting in alteration of its 
electromagnetic properties. The electric field 
inside the dielectric medium ( ) E
r
 is related to the 
applied electric field ( )
0
E
r
as: 
) 8 . 16 (
0 0 0
P E E D
r r r r
+ = = e e 
where
o
E D
r r
0
e = is the electric displacement 
vector dependent purely on the applied external 
field. 
   
E q F
r r
- =
-
 
-q 
? 
E
r
 
+q 
E q F
r r
+ =
+
 
Prof. J.K.Goswamy’s Lecture Notes on Materials Science: Properties of Materials. Page 188 
 
) 9 . 16 (
0
0
0 0 0
e
e e
P
E E
P E E
r
r r
r r r
- =
+ =
 
The quantity P
r
is called polarization vector which 
is defined as the amount of electric dipole moment 
developed per unit volume of the dielectric 
medium. If N is the atomic density of the medium 
and p
r
is the dipole moment per atom, then 
polarization vector is expressed as p N P
r
r
= . From 
equation (16.9), it is clearly evident that the 
electric field inside the dielectric medium gets 
modified (i.e. reduced) due to polarization of the 
molecules (or atoms) of the medium itself. 
The electric displacement is also expressed as: 
t cons Dielectric lative
E
E
where
E D
r
r
tan Re
) 10 . 16 (
0
0
= =
=
e
e e
r r
 
The dielectric constant of a medium can be 
measured by providing specific amount of charge 
to plates of capacitor and measuring the potential 
difference ( )
0
V developed. In the next step, the 
dielectric medium is inserted to completely fill the 
space between the plates of capacitor and again 
plates are given same amount of charge. The 
potential difference across the plates ( ) V is 
measured. The dielectric constant can be deduced 
from these two measured voltages as: 
V
V
r
0
= e 
 
 
16.3.2 Concept of Local Field 
When electric field E
r
 acts on the medium, it 
causes polarization by aligning its molecular 
moments ( ) p
r
. The molecular dipole moment, so 
produced, is proportional to the electric field 
acting on the considered molecule. It is expressed 
as: 
 ) 11 . 16 ( E p
r
r
a = 
where a is the polarizability of the molecule. Total 
polarization of the medium is given by: 
) 12 . 16 ( E N p N P
r
r
r
a = = 
Electric displacement is given as: 
) 14 . 16 ( 1
) 13 . 16 ( 1
0
0
0 0
0 0
?
?
?
?
?
?
?
?
+ =
?
?
?
?
?
?
?
?
+ =
+ = + =
e
a
e
e
a
e e e
a e e
N
N
E E
E N E P E D
r
r
 
The polarization can be related to electric 
susceptibility ( ) ? as: 
( )
) 16 . 16 (
) 15 . 16 (
0
0
e
a
?
a e ?
N
E N E P
= ?
= =
 
Putting equation (16.16) in (16.14), we get: 
) 17 . 16 ( 1 1
0
?
e
a
e + =
?
?
?
?
?
?
?
?
+ =
N
r
 
The departure of dielectric constant from unity is 
referred to as the electric susceptibility of the 
medium. Physically it implies the tendency of the 
dielectric material to get polarized under the 
influence of the external electric field.  
Prof. J.K.Goswamy’s Lecture Notes on Materials Science: Properties of Materials. Page 189 
 
Read More
Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

Related Searches

Semester

,

Kinds of Material - Chapter Notes

,

Viva Questions

,

Previous Year Questions with Solutions

,

Material Science

,

study material

,

pdf

,

Engineering Class 11 Notes | EduRev

,

Extra Questions

,

Free

,

shortcuts and tricks

,

past year papers

,

Kinds of Material - Chapter Notes

,

Sample Paper

,

MCQs

,

Semester

,

Material Science

,

video lectures

,

mock tests for examination

,

Semester

,

ppt

,

Summary

,

Exam

,

Engineering Class 11 Notes | EduRev

,

Kinds of Material - Chapter Notes

,

Important questions

,

Semester Notes

,

Engineering Class 11 Notes | EduRev

,

practice quizzes

,

Material Science

,

Objective type Questions

;