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1/15/2017 1
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
Engineering Physics II
Presentation by
Dr.A K Mishra
Ass...
Dielectrics Introduction
• Dielectrics are basically nonconductors of electricity because
usually do not have any free cha...
Dielectric Constant
• Michel faraday discovered that the capacitance of a capacitor
increased if the space between the con...
continued
•If a parallel plate capacitor with metal plates of area A and separation d, then its capacity
can be expressed ...
continued
From equation (2) & (4)
…………………..(5)
1/15/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
5
00
C


...
• Dielectrics are the materials having electric dipole moment permanently.
• Dipole: A dipole is an assembly in which equa...
Dielectric polarization
Dielectric polarization of non conductors of electricity can be
discussed in the context of polar ...
1/15/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
8
Unpolarized
Polarized by an applied electric field
+ + +...
1/15/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
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+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
-
-
-
-
-
-
-
-
-
-
-
-
...
Polar dielectric materials and electric field
•The dielectric materials which have Permanent dipole moments with their
ran...
Non Polar Dielectrics
• There is no permanent dipole existence in the
absence of an electric field .
• Centroids of positi...
Electric field
• The region surrounded by charged body is always
under stress because of electrostatic charge . If a small...
Electric Polarization vector (P)
The process of producing electric dipoles by an electric field is called
polarization in ...
Electric Displacement vector (D)
• A charge is sending line of forces received by an area
then no. of line of forces recei...
continued
• if the force feel by is .then the electric field can be expressed as
………………………..(2)
on putting the values of F...
Relation between , ,
1/15/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
16
E

D

P

If a dielectric slab i...
Electric flux density (D)
• The flux density or electric displacement D at
a point in a material is given by D=єr є0E.
• W...
Various polarization processes:
When the specimen is placed inside a d.c.
electric field, polarization is due to four type...
Electronic Polarization
• When an EF is applied to an atom, +vely charged nucleus displaces in the
direction of field and ...
Ionic Polarization
• The dielectric material having ionic bond such as NaCl. after applying
external electric field the Na...
Orientational Polarization
• Occurs in polar substance, which shows dipole moment in the absence of
external electric fiel...
Space Charge Polarization
• Due to external electric field charges accumulate at electrodes.
• Occurs sudden change in the...
Total Polarization
• The dielectric materials are classified into different groups based on
their mode of polarization .if...
Internal field equation in Liquid & Solids
• When liquid or solids materials are place in an external field then not only
...
Continued…………….
• We have taken five atom in linear array named A,B,C,D &E for
convenience of calculation. We will calcula...
Continued…………….
From eq (1) & (2)
………………………(3) similarly the
induced electric field contributed by E and A at C can be giv...
Continued…………….
• Now the calculation for rest atomic dipole at left and right hand side of atom site C can be
given as
+ ...
Lorentz field
• Internal field equation in three dimension is also known as Lorentz field.
We can get it by simply replaci...
Claussius-Mossotti equation
• Equation gives the relation between macroscopic dielectric constant and
microscopic polariza...
Continued……….
Putting the value of local field in the equation (2) we get,
……………..(3)
but we know the relation
By putting ...
Relation between Dielectric constant and
Refractive index (Lorentz-Lorentz formula)
• According to Maxwell, the velocity o...
Frequency dependence of dielectric constant
• It is observed that polarization behavior of different material at different...
Continued………..
• (Below the frequency Hz):The behavior of material in this region can
be explained on the basis of relaxat...
Dielectric Losses or Loss tangent
• It can be understand by taking the case of charging and discharging of a
capacitor, if...
Continued……………………
Let the plate of capacitor is placed in an electric field (fig.a) ,due to field
dipoles orient in a part...
Continued…………
Putting he value of I in equation (1) we get
Dielectric loss =
= ………………..(3)
we know that if is reactance, t...
Important applications of dielectric material
• Dielectric material have large application in the field of engineering,
me...
Ferro electricity
• Most of the dielectric materials depends directly on the applied field and
known as linear dielectrics...
Magnetic property of materials
• There are two type of motion when external field is applied ,
• Orbital motion
• Spin mot...
Magnetic Suceptibility
Magnetic Susceptibility: The intensity of magnetization (I) is
directly proportional the intensity ...
Relative permeability ( )
1/15/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
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r
• The capability of magnet...
Relative between and
1/15/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
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 r
m
The magnetic flux (B), magn...
Magnetic moment of an atom: Bohr magneton
• In an atom electron revolve around the nucleus due to which electric
current p...
Classification of magnetic materials
On the basis of magnetic properties different materials are classified as,
• Diamagne...
Continued……………….
• Material in U-Shaped tube depressed when placed in magnetic field.
• The line of forces do not prefers ...
Continued………………
• Substance develop weak magnetization in the direction of field.
• When paramagnetic rod suspended in uni...
Ferromagnetic
• Atom have permanent magnetic dipole moment, the strong interaction
between neighboring atomic dipole, keep...
Langevin theory of diamagnetism
• According to Langevin In 1905,electrons revolve in different orbits are
paired ( ) the v...
Continued……………..
• This force is perpendicular to motion of the electon and direction is
determined by the Fleming left ha...
Continued……………..
1/15/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
50
(6)....................
dt
d
r2
e
-
dt...
Continued……………..
• When magnetic field is applied its value changes from 0 to B.
Hence the corresponding change in flux is...
Continued……………..
• Thus the change in magnetic moment is
.
The above expression for change in magnetic moment for only one...
Continued……………..
1/15/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
53
strength.fieldaswellas
etempraturoftin...
1/15/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
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Hysteresis
When a ferromagnetic material is placed
in m...
Energy loss due to hysteresis
• When external field is applied the dipoles try to align themselves in the
direction of the...
Continued……………….
Now, the torque acting on dipole is
1/15/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
56
m
...
Continued……..
From eq (3) and (4)
Now
1/15/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
57
 

.....(6)d...
Continued……………..
• Thus eq (6) changes to
Use of Hysteresis Curve:
Construction of permanent magnets have the following ch...
Continued………………….
• These characteristics makes steel a better permanent magnet than
soft iron because iron has low coerci...
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Dielectric and Magnetic Properties of materials,Polarizability,Dielectic loss,Langevins theory of diamagnetism,Meisner effect

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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

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Dielectric and Magnetic Properties of materials,Polarizability,Dielectic loss,Langevins theory of diamagnetism,Meisner effect

  1. 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. 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. 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 2
  3. 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. 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 3 0 C r r0 C C
  4. 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 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 4 d C 0 0 A   0  0 K  r  d A C  
  5. 5. continued From equation (2) & (4) …………………..(5) 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 5 00 C     Cr K d A 0 K C  d C rA 0  
  6. 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 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 6 +q -q X
  7. 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 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 7
  8. 8. 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 8 Unpolarized Polarized by an applied electric field + + + + + + + + + + + - - - - - - - - - - - - - • Unpolarized and Polarized
  9. 9. 1/15/2017 Dr A K Mishra, Academic Coordinator, 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. 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 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 10 ip PP P-
  11. 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 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 11
  12. 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 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 12
  13. 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 . 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 13 A P Q   Q A Q P 
  14. 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 . 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 14 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. 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/ 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 15 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. 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. 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 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 17
  18. 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 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 18
  19. 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. 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 19 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. 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 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 20 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. 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. 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 21 Ep p o o   o E   o a b
  22. 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. 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 22                                         No Field E=0 Field E
  23. 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 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 23  oei   i &e  i &e d  od 
  24. 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 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 24 pi pi pi pi pi d d d A B C D E
  25. 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) 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 25 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. 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) 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 26 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. 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 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 27 (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. 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 , 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 28 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. 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 1/15/2017 Dr A K Mishra, Academic Coordinator, 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. 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 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 30             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. 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. 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 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. 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. 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 32 ppp eio  p Polarization Frequency Variation of dielectric constant with frequency pe pe pi pp oe pi Microwave Infrared Ultraviolet
  33. 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. 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 33 10 6 10 6 10 11 10 11 10 14 10 15
  34. 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: . 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 34 Current Voltage Ic IR O  I (a) c Dielectric c IR Ic R (b)
  35. 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) 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 35 IR IC 90 0 IC IR IC I  IR 90 0   IC I  cos I c I 
  36. 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. 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 36   sin cos Ic         V tancIV X c cf2 1  X c X cIc  cf2V V Xc Ic  cf2V V  cf2 2 V
  37. 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. 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 37
  38. 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. 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 38
  39. 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 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 39 V I M 
  40. 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. 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 40 HI H m I H I m  m
  41. 41. Relative permeability ( ) 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 41 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. 42. Relative between and 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 42  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. 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 1/15/2017 Dr A K Mishra, Academic Coordinator, 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. 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. 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 44
  45. 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. 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 45 1r
  46. 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. 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 46 1r
  47. 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. 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 47 1r
  48. 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) 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 48 2 1 -and 2 1  0  o0 2 02 0 rrewhe r m rm v v f e Fm )Bxv(eF m
  49. 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) 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 49 v e  Fm Fe Fe Fm e  v (a) (b) dt d -   
  50. 50. Continued…………….. 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 50 (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. 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 . 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 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. 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 1/15/2017 Dr A K Mishra, Academic Coordinator, 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. 53. Continued…………….. 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 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. 54. 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 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. 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. 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 55  .....(1)....................cosm M
  56. 56. Continued………………. Now, the torque acting on dipole is 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 56 m cosm sinm           .....(4)....................dsinm-dM (1)equsinginincreasetoduemomentmagneticinChange )........(3..........dSinHm-dW d-dW isdtofromrotatingindoneworktheTherfore HB ..(2)....................sinHM sinBm 0 0 0          
  57. 57. Continued…….. From eq (3) and (4) Now 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 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. 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. 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 58 curve.H-Bofareatoequaliseunit volumperionmagnetizatof cyclecompleteaduringdiscipatedenergyordoneworktheThus CurveHBofArea 0dHHSincedHH-W )dHH-dBH( 0 0      W HdB W  
  59. 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. 1/15/2017 Dr A K Mishra, Academic Coordinator, JIT Jahangirabad 59

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