In this PPT contains ,Dia,Para,Ferromagnetism,Clausius-Mossoti equation,Dielectric Loss ,Hysteresis,Hysteresis loss and its Applications,Determination of susceptibility,types of polarisation in mateials,relative permability

1. 1/15/2017 1
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
Engineering Physics II
Presentation by
Dr.A K Mishra
Associate Professor
Jahangirabad Institute of Technology, Barabanki
Email: akmishra.phy@gmail.com
Arun.Kumar@jit.edu.in

2. Dielectrics Introduction
• Dielectrics are basically nonconductors of electricity because
usually do not have any free charge for conduction.
• They have positive and negative charge tightly bound together.
• Under the influence of external field positive and negative
charges are displaced from their equilibrium and form dipole
which are responsible for dielectric behavior of these materials
it may solid, liquid or gases.
• There is a slight difference between dielectric and insulators.
The main function of dielectrics is to store electrical energy,
while the function of insulators is to obstruct the flow of
current.
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2

3. Dielectric Constant
• Michel faraday discovered that the capacitance of a capacitor
increased if the space between the conductors plates is filled with a
dielectric materials.
• If is the capacitance of the condenser filled with air between its
plates.
• C is the capacitance when the space filled with dielectric materials.
Then dielectric constant defined as
K = = …………………….(1)
Where is known as
relative permittivity or dielectric constant, of the medium.
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JIT Jahangirabad
3
0
C
r
r0
C
C

4. continued
•If a parallel plate capacitor with metal plates of area A and separation d, then its capacity
can be expressed as
……………..(2)
Where is the permittivity of free space between the plates of the capacitor.
If the space filled with dielectric material of permittivity then the capacitance of the
same capacitor will be given as
………………….(3)
where K is constant having its value more than unity and it is also known as relative
permittivity ( ). Now equation (3) can be written as
1/15/2017
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JIT Jahangirabad
4
d
C 0
0
A


0

0
K 
r

d
A
C



5. continued
From equation (2) & (4)
…………………..(5)
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Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
5
00
C




Cr
K
d
A
0
K
C 
d
C rA 0



6. • Dielectrics are the materials having electric dipole moment permanently.
• Dipole: A dipole is an assembly in which equal positive and negative
charges are separated by a small distance.
• DIPOLE moment: The product of magnitude of either of the charges and
separation distance b/w them is called Dipole moment. All dielectrics are
electrical insulators and they are mainly used to store electrical energy.
• All dielectrics are electrical insulators and they are mainly used to store
electrical energy.
Ex: Mica, glass, plastic, water & polar molecules
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6
+q -q
X

7. Dielectric polarization
Dielectric polarization of non conductors of electricity can be
discussed in the context of polar and non polar molecules.
Non polar dielectric materials in an electric field:
when materials placed in the electric field its properties is modified.
The +ve and –ve charges of the molecules feel electrostatic force in
opposite directions. Therefore the center of gravity of two charges are
separated from each other. the molecule thus acquire an induced
electric dipole moment in the direction of the field. this process is
known as polarization of dielectrics the dielectric material that are
polarized only when they are placed in an electric field are known as
non polar dielectrics.
Examples :H2, N2, O2, CO2
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JIT Jahangirabad
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8. 1/15/2017
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Unpolarized
Polarized by an applied electric field
+ + + + + + + + + + +
- - - - - - - - - - - - -
• Unpolarized and Polarized

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JIT Jahangirabad
9
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
- + - + - + - +
- + - + - + - +
- + - + - + - +
- + - + - + - +
- + - + - + - +
- + - + - + - +
- + - + - + - +

0
Field EApplied

) and
i.e.
) and
i.e.
Induced charge appear in such a way
that the electric field set by them ( )
opposes the internal field .the resultant
field E in the dielectric is the vector sum
of ( ) and i.e.
E = - …………………..(1)
Continued
E 
E 
E0
E0
E  E 

10. Polar dielectric materials and electric field
•The dielectric materials which have Permanent dipole moments with their
random rotation in the absence of external electric field are known as polar
dielectric materials.
•When external field is applied to the polar dielectric the partial alignment is
take place. In the absence of external electric field the dipole have their
random orientation but due to thermal agitation etc. some dipole moment
may be contributed by the existing dipoles. The dipole moment of polar
dielectric in an electric field is given as
•There is permanent dipole exists even in the absence of an electric field
.Centroids of positives and negative charges of molecules constituting the
dielectric material do not coincide even in the absence of electric field
Examples : HCL , CO
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10
ip
PP P-

11. Non Polar Dielectrics
• There is no permanent dipole existence in the
absence of an electric field .
• Centroids of positive and negative charges of
molecules constituting the dielectric material
coincide .
• Examples :H2, N2, O2, CO2
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12. Electric field
• The region surrounded by charged body is always
under stress because of electrostatic charge . If a small
charge q or a charged body is placed in this region
,then the charge q or a charged body will experienced a
force according Coulomb s law . This stressed region
around charged body is called electric field .
• Electric field at a point define as the force that acts on
a unit positive charge placed at that point thus E.
• According to coulomb law when two point charges Q1
and Q2 are separated by a distance r, the force of
attraction or repulsion between two charges is given by
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13. Electric Polarization vector (P)
The process of producing electric dipoles by an electric field is called
polarization in dielectrics.
The induced dipole moment is proportional to the intensity of the electric
field.
Induced surface charge per unit area i.e surface density of bound charges in
dielectric medium.
……………………………(1)
The induced charge appears when the dielectric is polarized hence is
Known as electric polarization vector .
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JIT Jahangirabad
13
A
P
Q


Q
A
Q
P


14. Electric Displacement vector (D)
• A charge is sending line of forces received by an area
then no. of line of forces received by an unit area is called flux density
or electric displacement vector ( ).
• From the above discussion, the displacement
vector can expressed as
…………………..(1)
Let us consider another charge at a
` distance r from .
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JIT Jahangirabad
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1
q
1
q 24 r
D

1
q r
P
Line of forces from 1
q
A
q
D
q 1
24 r
1 


1
q
q2

15. continued
• if the force feel by is .then the electric field can be expressed as
………………………..(2)
on putting the values of F we get
.
………….(3)
using the equation (1),we get
.
where is the relative permittivity for free space, = 1 and hence the
above equation becomes
The unit of displacement vector or electric flux density is coulomb/
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JIT Jahangirabad
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q2 F

q 2
F


E

1
44
F
r
qq
q 2
1
2
2
2
1
2

r
q
q
E


E
r
E







0
D
ED
D


 r
E
0

D
M 2
 r

16. Relation between , ,
1/15/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
16
E

D

P

If a dielectric slab is placed in a parallel plate capacitor,then the resultant
Electric field within the material is given by
. Where is the applied field and is
The induced field.
From the Gauss law of electrostatics, we have
.
or
- EE 0 

E E

0
Q.dE s00
 


E
A
Q
0

E


17. Electric flux density (D)
• The flux density or electric displacement D at
a point in a material is given by D=єr є0E.
• Where E is the electric field strength, є0 is the
dielectric constant and єr is relative permitivity
of the material.
• The 3 vectors D,E and P are related by the
equation D= є0 E+P
P= є0 (єr -1)E
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18. Various polarization processes:
When the specimen is placed inside a d.c.
electric field, polarization is due to four types
of processes.
1.Electronic polarization
2.Ionic polarization
3.Orientation polarization
4.Space charge polarization
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19. Electronic Polarization
• When an EF is applied to an atom, +vely charged nucleus displaces in the
direction of field and ẽ could in opposite direction. This kind of displacement
will produce an electric dipole with in the atom.
i.e, dipole moment is proportional to the magnitude of field strength and is
given by where is the electronic polarizibility.
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JIT Jahangirabad
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E
e
E
ee  
e







 
























 

















(a) (b)
(a) Charge distribution in atom in the absence of field
(b) Charge distribution in atom in the presence of field

20. Ionic Polarization
• The dielectric material having ionic bond such as NaCl. after applying
external electric field the Na and Cl ions displaced from their equilibrium
in opposite direction to each other.
• The displacement between ions causes an increase or decrease in distance
between the atoms.
• This polarization is time independent like electronic polarization.
.
Where is ionic polarizibility.
If there are N molecules then
Polarization can be given as
1/15/2017
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JIT Jahangirabad
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E
E
ii
p


p i
EN ip i
Na Cl
No Field E= 0
r0
(a)
Na Cl
Field E
(b)
r0
x
x

21. Orientational Polarization
• Occurs in polar substance, which shows dipole moment in the absence of
external electric field.
• Due to random orientation the net dipole moment is zero.
• When material is placed in an external electric field ,dipoles rotate about
their axis of symmetry and align with the field.
• Where is ionic polarizability.
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JIT Jahangirabad
21
Ep
p
o
o

 o
E


o
a
b

22. Space Charge Polarization
• Due to external electric field charges accumulate at electrodes.
• Occurs sudden change in the conductivity of the dielectrics.
• Under the influence of applied field ,the ions are diffused over an
appreciable distance, due to which the redistribution of charges takes
place.
• The tendency of redistribution of charges in the dielectric medium in the
presence of external electric field is known as space charge polarization.
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

 
 

 



 
 

 


   
 

 

   
 

 
No Field
E=0
Field E

23. Total Polarization
• The dielectric materials are classified into different groups based on
their mode of polarization .if the material feels all type of polarization
then total polarizability can be given as
where are the function of molecular structure due to this
also known as deformation polarizability and is denoted by .
therefore the above equation can be written as
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JIT Jahangirabad
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 oei

 i
&e
 i
&e
d
 od


24. Internal field equation in Liquid & Solids
• When liquid or solids materials are place in an external field then not only
its molecules feels external field but also influence by the field of
surrounding dipoles. The net field (sum of applied & surrounding) is
known as Local field or Internal field. In order to determine the internal
field we will use the model suggested by Epstein known as
One-Dimentional atomic array method
.
………….
Linear array of atoms in an electric field
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JIT Jahangirabad
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pi
pi pi
pi
pi
d
d d
A B C D E

25. Continued…………….
• We have taken five atom in linear array named A,B,C,D &E for
convenience of calculation. We will calculate the internal field at the atom
C due to A,B at its left and D,E at its right and then it extended foe all atom
of the array.
• Let be the dipole moment induced in each atom due to applied field .
Now the field produced at C due to dipole B is given by
. ……………………(1) .
similarly the field at C due to D is given as
.
…………………….(2)
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E

pi
d
ECB 2
0
i
4
2p



d
p
d
p
3
0
i
3
0
i
4
2
)(-4
2
 
E CD


26. Continued…………….
From eq (1) & (2)
………………………(3) similarly the
induced electric field contributed by E and A at C can be given as
. ………..(4)
………………………………….(5)
Then the local/internal field at the atom site C due to all atomic dipoles wil
be given as
- ………………(6)
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JIT Jahangirabad
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d
p
E 3
0
i
CD



E CB
(2d)
p
E 3
0
i
CE
4
2


ECA
(-2d)
p
3
0
i
4
2


(2d)
p
E 3
0
i
CE


ECA
(d)
p
3
0
i
E



Ei
(2d)
p
3
0
i



27. Continued…………….
• Now the calculation for rest atomic dipole at left and right hand side of atom site C can be
given as
+ + …………….
.
(7) where n is an Integer , the value of is 1.2. ………… now the equation
.in
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JIT Jahangirabad
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(d)
p
3
0
i
E


 
Ei
(2d)
p
3
0
i


(3d)
p
3
0
i


(d)
p
3
0
i
E


 
Ei 







 .................................
11
1
(3)(2)
33








 

1 33
0
i 1
E
(d)
p
ni
n
E


 










1 3
1
n
n
(d)
p
3
0
i
2x1
E



Ei

28. Lorentz field
• Internal field equation in three dimension is also known as Lorentz field.
We can get it by simply replacing by number of density N (atom per
unit volume).Thus,
Let us put (a constant) usually known as internal field
coefficients, and is known as polarization vector.
Now the above equation can be written as
.
Internal field coefficient ( ) depend on the internal arrangement of the
atom in dielectric. For cubic crystal the value of is .hence the
Lorentz field equation can be written as ,
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JIT Jahangirabad
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d
3
1
 0
i
N2x1
E
p

 
E i


2
x1 
ppi
N

pE
0



E i
 0
l
3
p
EE

E i

3
1

29. Claussius-Mossotti equation
• Equation gives the relation between macroscopic dielectric constant and
microscopic polarizability of non polar dielectric materials (do not posses
permanent dipole moment).when placed in external field then dipole
moment induced.
• Let induced dipole moment due to local field then,
…………………….(1)
where is the polarizibility per atom.
If dielectric material have N molecules per unit volume, then electric
polarization is given by
.
. …………………..(2)
. We know that
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JIT Jahangirabad
29
pi

El

E L
p i

p

Ep Li
NN 

p
E L
N
p


 0
l
3
p
EE

E i

30. Continued……….
Putting the value of local field in the equation (2) we get,
……………..(3)
but we know the relation
By putting the value of in equation (3) we get
or
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JIT Jahangirabad
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











0
3
p
EN
p


 E1-r0

p
 1-
p
r0 

E
E

  











0r0
3
p
1-
p
N
p


  









3
1
1-
1
1
r
0


N
 






 

1-3
2
1
r
r0


N
 
 2
1-r
03 





r
N

31. Relation between Dielectric constant and
Refractive index (Lorentz-Lorentz formula)
• According to Maxwell, the velocity of propagation of electromagnetic
waves in unbounded medium is given as
……………….(1)
where is the magnetic permeability and is the absolute permittivity.
For non magnetic medium, permeability is thus
……………(2)
We know the refractive index is defined as
.
…………….(3)
Using the value of n,we get Lorentz-Lorentz formula.
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31


 

r
0
0
00
1
1
mediuminwaveofVelocity
in vaccumewaveofVelocity
n

1
v
 
0

1
0
v m
 
 2
1-
3 n
n2
2
0 


N

32. Frequency dependence of dielectric constant
• It is observed that polarization behavior of different material at different
frequencies is different.
• This is due to orientation contribution of dipoles in total polarization. The
polarization behavior of dipoles is varied at different frequencies. The
variation of polarization at different frequencies be explained as below.
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ppp eio

p
Polarization
Frequency
Variation of dielectric constant with frequency
pe
pe
pi
pp oe
pi
Microwave Infrared Ultraviolet

33. Continued………..
• (Below the frequency Hz):The behavior of material in this region can
be explained on the basis of relaxation time (The average time taken by
the dipole ton orient themselves in the direction of the field in one
complete cycle)of dipole. At low frequency dipole get time to orient
themselves in the field direction.
• In audio frequency range or Microwave band region ( to Hz): In this
region the orientational polarization is ceases. Hence total polarization is
due to ionic and electronic as a result the polarization rapidly decreases.
• Infrared region( to Hz):In this region the dipole follow the ionic
polarization but at higher frequency the contribution of ionic polarization
is zero in this way only electronic polarization contribute the total
polarization. the variation of dielectric constant with frequency shows a
bell shaped profile.
• Ultraviolet region (> ):In this range all the electron cloud unable to
follow the field reversal and total polarization (p=0) becomes unity.
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33
10
6
10
6
10
11
10
11
10
14
10
15

34. Dielectric Losses or Loss tangent
• It can be understand by taking the case of charging and discharging of a
capacitor, if V is the potential of then amount of energy stored in the
form of electrostatic potential energy in the dielectrics.
during discharging the same energy should be released but it is an
observation only a part of it is released while rest is disappeared as a heat.
The amount of energy dissipated in the form of heat is known as dielectric
loss.
Expression of dielectric loss:
.
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JIT Jahangirabad
34
Current Voltage
Ic
IR
O

I
(a)
c
Dielectric
c
IR
Ic
R
(b)

35. Continued……………………
Let the plate of capacitor is placed in an electric field (fig.a) ,due to field
dipoles orient in a particular direction and opposes by internal friction. The
opposition by dipoles is equivalent to resistance of capacitor.
When ac flows then current ( ) and voltage (V) are in same phase.
When voltage is applied to the capacitor the current flowing ( ) leads the
voltage by . Thus, & perpendicular to each other shown in fig. c
Let angle between & is called dielectric loss angle is denoted by . The
tangent of this angle is known as loss tangent which gives the electrical loss of
dielectric material.
Dielectric loss = V = V I cos ( - ) = VI sin ………………………..(1).
from fig. C we get = cos
. ……………………………………..(2)
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IR
IC
90
0
IC IR
IC I 
IR 90
0
 
IC I 
cos
I c
I 

36. Continued…………
Putting he value of I in equation (1) we get
Dielectric loss =
= ………………..(3)
we know that if is reactance, then
where f is frequency and c is capacitance of the
capacitor. Now current can be given in terms of V and as
therefore the dielectric loss in terms of frequency and
capacitance .
Dielectric loss = = is the expression of dielectric loss.
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36


sin
cos
Ic








V
tancIV
X c
cf2
1

X c
X cIc
 cf2V
V
Xc
Ic
 cf2V V  cf2
2
V

37. Important applications of dielectric material
• Dielectric material have large application in the field of engineering,
medicine, industry and research as follows,
• Low dielectric constant materials are widely used in engineering,
microelectronics , industry ,computers and medical equipments, etc.
• High dielectric constant materials are used in semiconducting
manufacturing processes in which silicon dioxide is not suitable but widely
used in microchip,integratedcircuit,transistors,microprocessors,computers
and so on.
• The heating property is used in dehydration of food,tobacco,etc.
• Used in microwave ovens and other home appliances.
• Used as an insulators and wide used in ceramic appliances.
• Heating is used to laminate important documents ,in xerox machine .
• Liquid dielectrics used in filling medium for transformers, circuit breakers.
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38. Ferro electricity
• Most of the dielectric materials depends directly on the applied field and
known as linear dielectrics. The dielectric which shows polarization in the
absence of electric field is known as ferroelectrics and have the following
property.
• Ferroelectric have permanent electric dipole without influence of external
electric field.
• In such materials the Polarization and applied field is non linear in nature.
• Dielectric constant of ordinary dielectrics do not varry much with
temperature but he dielectric constant of ferroelectrics is highly depend
on temprature.
• Dielectric constant drops significantly above critical temprature known as
Curie temprature.
• Ferroelectric materials shows hysteresis.
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39. Magnetic property of materials
• There are two type of motion when external field is applied ,
• Orbital motion
• Spin motion about their axis
• When magnetic moment is applied the dipoles are align in the direction of
the field and then material is said to be magnetized.
Useful parameter: When magnetic material is place in the external fielfd
(H) the number of line of forces inside the material crossing per unit area
is called magnetic flux density (B) and the phenomenon is called magnetic
induction. its unit is weber/meter or tesla.
Inensity of magnetization: When magnetic moment is placed in the
external field it acquires magnetic moment (m).The magnetic moment per
unit volume is known as the intensity of magnetization (I) and given as
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39
V
I
M


40. Magnetic Suceptibility
Magnetic Susceptibility: The intensity of magnetization (I) is
directly proportional the intensity of magnetizing field (H). i.e
where is called magnetic susceptibility of the magnetic material. it is
dimensionless quantity and is the characteristic of the material.
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HI
H
m
I
H
I
m

m

41. Relative permeability ( )
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r
• The capability of magnetic line of force to penetrate the materials is called
permeability ( )e.
we know the magnetic flux density (B) is related to magnetizing field as
Where is the permeability. if the
medium is vacuum or air then the expression become
Where is called absolute
Permabieatility.

HB
HB
H
00 B 0


42. Relative between and
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 r
m
The magnetic flux (B), magnetizing field (H) and he intensity of magnetization
(I) Are related a below
……………………..(1)
Putting the value of B we get
we knows the value of susceptibility
.
.
we can write now
.
)I(H
0
 B
HB
I)(H
0
  H
)
H
I
H(1
0
  H
)(1
m0
 



m
0
1
 m
1 
r

43. Magnetic moment of an atom: Bohr magneton
• In an atom electron revolve around the nucleus due to which electric
current produces, The rate of flow of charge is current,
if r be the radius of the orbit and v be the speed of the electron then
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JIT Jahangirabad
43
T
e
i
Magneton.Bohrclledisandofmomentmagnetictheshowsthis)
m4
eh
(n
m22
e
Mthus
m2
nh
rv
2
rvm
iselectronofmomentunangularpostulate,Bohr
2
evr
.
r2
ev
AiM
bygivenismomentmagneicnow
r2
ev
)
speed
distance
Time(
v
r2
r
2













M
nh
nh
from
i
T

44. Classification of magnetic materials
On the basis of magnetic properties different materials are classified as,
• Diamagnetic Substances
• Paramagnetic Substances
• Ferromagnetic Substances
Diamagnetic Substances:
• Occurs in all materials.
• Atom do not posses net magnetic moment their orbital & spin magnetic moments
becomes zero after adding vectorically.
• Acquire induced dipole moment when placed in an external field.
• Shows perfect conductivity and demagnetization when cooled at low temperature.
• Diamagnetic materials are Type I superconductors
when suspended in a uniform magnetic field ,align their longest axis at right angle.
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45. Continued……………….
• Material in U-Shaped tube depressed when placed in magnetic field.
• The line of forces do not prefers to pass through the materials.
• The permeability of substance is less than 1 i.e
• Diamagnetism losses soon when field is removed.
• Substance not magnetized easily because susceptibility is negative.
Ex:
Bismuth, Antimony, Copper,
gold,quartz,mercury,water,alcohol,air,hydrogen etc.
Paramagnetic substances:
• These substance are weakly attracted by magnets.
• Atomic dipoles are randomly oriented but when place in external field
then align in the direction of the field.
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1r

46. Continued………………
• Substance develop weak magnetization in the direction of field.
• When paramagnetic rod suspended in uniform magnetic field then align in
the direction of the field.
• The line of forces prefer to pass through the material and their
permeability is greater than 1 i.e .
• When magnetic field is removed the substance loss their magnetization.
• In non – uniform field substance move from weaker part of field to
stronger part.
• Material in u shaped tube elevated when external field is created.
E.g
Alluminiun , Platinum, chromium , magnese, copper sulphate ,oxygen.
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JIT Jahangirabad
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1r

47. Ferromagnetic
• Atom have permanent magnetic dipole moment, the strong interaction
between neighboring atomic dipole, keep them align even the field is
removed.
• Substance strongly magnetized in the direction of the field.
• Line of forces prefers to pass through the material rather than air,its
permeability is greater than 1 i.e
• In non-uniform field substance moves from weaker part to stronger part of
the field.
• Material in U-shaped tube elevated when external field is created.
• The permeability of material is large so the susceptibility s positive.
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1r

48. Langevin theory of diamagnetism
• According to Langevin In 1905,electrons revolve in different orbits are
paired ( ) the vector sum of total magnetic moment is
zero.when external field is applied orbits starts precessional motion,this is
known as Larmor Precession.
Let electron revolve in circular orbit of radius r with angular frequency
then the centripetal force acting on the electron is
……………….(1)
In the presence of external field the flux density B is perpendicular to the
plane of orbit, therefore the Lorentz force ( ) is given by
……………………..(2)
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2
1
-and
2
1

0
 o0
2
02
0
rrewhe
r
m
rm v
v f e
Fm
)Bxv(eF m

49. Continued……………..
• This force is perpendicular to motion of the electon and direction is
determined by the Fleming left hand rule
using Faraday law of electromagnetic induction ,the emf induced due to
application of external field
………………………….(3)
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49
v
e

Fm
Fe
Fe
Fm
e

v
(a) (b)
dt
d
-

 

50. Continued……………..
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(6)....................
dt
d
r2
e
-
dt
dv
dt
d
-.
r2
e
dt
dv
m
Hence)5.(....................
r2
E
electronfor theusecanweere
V
Ecapaitorplateparallelinknowwe.......(4)..........Ee
dt
dv
m
i.eelectrontheaccelaratefme
















m
H
d
This

51. Continued……………..
• When magnetic field is applied its value changes from 0 to B.
Hence the corresponding change in flux is
.
change in angular velocity or angular frequency is
.
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51
2m
eBr
-
r2
e
-dv
d.
r2
e
-dvm
getwe,6eqfronhence
A)B(0-
r
rr
2
22



B
BBd





)8.....(..........
2
e
xex
2
M
areaxchargexFrequencyAiM
bygivenismomentmagneticThen the
momentmagneticinchangea
producesitandfrequencyLarmorcalledisfrequencyinchange
)7.......(..........
2m
eB
-
r
dv
rr
2
2 B
This
d








52. Continued……………..
• Thus the change in magnetic moment is
.
The above expression for change in magnetic moment for only one
electron, the total change in magnetic moment due to randomly oriented
orbits is
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JIT Jahangirabad
52
)........(9..........
m2
Be
-
2
e
2
e
M rr
22






 
Hence
smean valueshowingarey&on xbarswheresay)(
3
atonsymmetricysphericallforand
can writethen weaxis-zalongisfieldtheif
r)ofprojectionthebe(......(10)..........
4m
eB
-
ryx
yxr
r
2
22
222
1
1
2
1


 rM

53. Continued……………..
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53
strength.fieldaswellas
etempraturoftindependenandve-issubstancediamagneicofitysuceptibilshows(12)equation
..(12)..........
m6
n
-
Hm6
Hn
-
H
I
bygivenisitysuceptibilthehence
m6
Bn
I
iseunit volumper
moleculesofnumbernaforionmagnetizatofintensitytheHBand
V
M
I
thatknowbut we11).........(..........
3
2
m4
B
-M
gives(9)equationtheretherefo
3
2
ree
re
re
ryx
2
2
2
2
m
2
2
2
2
2
222
1










 r
r

54. 1/15/2017
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54
Hysteresis
When a ferromagnetic material is placed
in magnetized field ,it is observed that
flux density does not vary linearly with
magnetizing field B due to ferromagnetic
material have not unique value of relative
permeability ( ). The relationship
between flux density B and magnetizing
field H is a curve known as hysteresis
curve.
r
O
a
b
C
d
e
f
g

55. Energy loss due to hysteresis
• When external field is applied the dipoles try to align themselves in the
direction of the field, during this process work done by the field in
rotating the dipoles against their attractive forces.
• When field becomes zero some (molecular magnet) dipoles remains
align and the material is said to b permanent magnet.
• To meet the initial condition a coercive field is applied this shows that a
cycle of magnetization is involves a loss of energy.
Let us consider a magnetic material having n molecular magnets per
unit volume, if m be the magnetic moment of each magnet making an
angle with the field H.
then the magnetic moment per unit volume along the direction of the
field is given as.
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 .....(1)....................cosm M

56. Continued……………….
Now, the torque acting on dipole is
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56
m
cosm
sinm










.....(4)....................dsinm-dM
(1)equsinginincreasetoduemomentmagneticinChange
)........(3..........dSinHm-dW
d-dW
isdtofromrotatingindoneworktheTherfore
HB
..(2)....................sinHM
sinBm
0
0
0











57. Continued……..
From eq (3) and (4)
Now
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57
 

.....(6)dM........HdMHW
iscyclecompleteafor
materialtheofeunit volumperfieldgmagnetizinhebydoneworktheThus
.(5)....................dMH
00
0

dW
dHH-dBHdMH
dMHdHHdBH
dMdHdB
)M(HB
knowwenow
.(7)..........loop......H-Mofareax
00
00
00
0
0









W

58. Continued……………..
• Thus eq (6) changes to
Use of Hysteresis Curve:
Construction of permanent magnets have the following characteristics:
.High retentively for strong magnetic field.
.High coactivity, magnetization is not destroyed by strong external field.
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curve.H-Bofareatoequaliseunit volumperionmagnetizatof
cyclecompleteaduringdiscipatedenergyordoneworktheThus
CurveHBofArea
0dHHSincedHH-W
)dHH-dBH(
0
0





W
HdB
W



59. Continued………………….
• These characteristics makes steel a better permanent magnet than
soft iron because iron has low coercivity.Material used for magnets
are,cobalt-steel, tungusten –steel,and chromium-steel,Alnico
(Al+Ni+co)
Electromagnets: Material used for making core of magnet have
• Low coercivity
• High retentivity
• Low hysteresis loss
• More flux – density
• high initial permeability
All these characteristics are found in soft iron.
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59