Download Q.1 what is dielectric loss?

JRE SCHOOL OF Engineering
Class Test 1- March 2015
Subject Name Engineering. Physics-II
Roll No. of Student
Date
Subject Code
Max Marks
Max Duration
Time
27 Mar 2015
NAS-201
30 Marks
1 Hr.
9:20 am to 10: 20 am
SECTION – A
(3x5=15)
Q.1 what is dielectric loss?
Ans: When the relaxation time and the frequency of the applied field are similar, a
phase lag occurs and energy is absorbed. This is called dielectric loss.
Q.2 Define Curie temperature.
Ans:
At certain temperature, the ferromagnetism converted into para magnetism
.that temperature is known as Curie temperature.
Q.3 what are the characteristics of core of a transformer?
Ans (1) Low hysteresis loss
(2) High specific resistance
(3) High initial permeability
Q.4 Define magnetic susceptibility and permeability. Also write relation between them.
Ans:- Magnetic susceptibility – The intensity of magnetization for a material is
proportional to the magnetic field. The magnetic susceptibility of a specimen
measures the ease with which the specimen can be magnetized. It is defined as
the ratio of the intensity of magnetization induced in it to the magnetized field,
m =
M
H
Permeability – when ever magnetic substance is placed in a magnetic
field ,it acquires induced magnetism. The lines of force of the magnetizing
field,
H,
concentrate
inside
the
sample
which
results
into
the
magnetization of the substance .the measure of the degree to which the
lines of force can penetrate the substance is called permeability.
Relation between magnetic susceptibility and permeability---
r  1   m
Q.5 Write Maxwell’s IVth equation in differential and integral form, along with physical
significance.
(IV)But using Lenz’s law, electro motive force can also defined as work
done in carrying a unit charge round a closed loop i.e. line integral dl of
electric field intensity E gives as equation
e.m. f .   E.dl
B
 E.dl   t ds
Using Stroke’s theorem to convert line integral in surface integral
 E.dl   curl.E.ds
B
 curl.E    t ds
B
t
B

t
curlE  
xE 
SECTION – B
(5x1=5)
Q.6 The atomic weight and density of sulphur are 32 and 2.08 gm (cm) -3 resp. The
electronic polarizability of the atom is 3.28 x 10 -40 Fm2. If sulphur has cubic
symmetry, what will be its relative dielectric constant?
Or
Find the polarization P in a homogenous and isotropic dielectric material of
relative permeability 4, when the electric displacement density D is 2 x 10 -8 C/m2.
According to Classius mossotti relation
 r  1 N e

 r  2 3 0
If NA is the Avogadro number
N 
N A
M
 the density and M the molecular weight ,then
 r  1 N e 

 r  2 3M 0
=
6.023x10 26 x(2.08 x10 3 ) x3.28 x10 40
3x32 x8.85 x10 12
 r 1
=0.483
r  2
r =
1.966
 3.8 Ans:
0.517
SECTION – C
(10x1 =10)
Q.7 What is molecular polarizability? Explain different types of Polarizabilities.
Ans: The induced electric moment per unit volume of the dielectric is called dielectric
polarization (P).
The induced dipole moment μ is proportional to electric field acting on the molecule 𝐸
E
or
  E
(1)
If there are N molecules per unit volume then
Dielectric Polarization:
P  N or
P  NE
(2)
Types of Polarization:
A.
B.
C.
D.
Electronic Polarization
Ionic Polarization
Orientational Polarization
Space charge Polarization
A. Electronic Polarization [Pe]: In non-polar dielectric polarizability arises due to
displacement of electrons relative to nucleus by the action of electric field.
At equilibrium
Lorentz force = Coulomb force
 Ze 
1( Ze)(ch arg edisplaced )
4o d 2
We know Volume charge density  
The equation becomes  ZeE 
 Ze  3Ze

4R 3
4R 3
3
Ze(
1
(3)
4o
(4)
4d 3 
)
3
d2
Substituting 𝜌 from (4)
 3Ze
)
4R 3 )
3
4d 3 (
 ZeE 
Ze(
1
4o
d
d2
4o R 3
Ze
Hence induced dipole moment
(5)
4o R 3 E
  Zed  Ze
Ze
E
or
  e E
Where  e is called as Electronic Polarizability given by  e  4o R 3
Hence Electronic Polarization Pe  N e  N e E
(6)
(7)
B. Ionic Polarization [Pi]: Ionic polarization occurs in ionic crystals.
On applying electric field, positive and negative charges are further separated in opposite
directions. This leads to increase in separation (d).
The induced dipole moment due to ionic polarization
i   i E
(8)
Where  i is ionic polarizability.
If there are N molecules per unit volume then Ionic polarization
Pi  N i  N i E
(9)
For most of the materials, ionic polarizability is less than electronic polarizability.
i 
1
10 e
C. Orientational Polarization [Po]: Orientational polarization occurs in polar molecules
having permanent dipole moment.
If there are N molecules per unit volume then Orientational polarization
Po  N o  N o E
(10)
Orientational polarization is temperature dependent and frequency dependent.
o 
 o2
(11)
3kT
Or
What is hysteresis curve? Explain retentivity and coercivity. Prove that energy
dissipated
per cycle per c. c. of magnetization is
µo times the area under I-H curve.
Ans: When a ferromagnetic material is magnetized in one direction, it will not relax back to zero
magnetization (B) when the imposed magnetizing field (H) is removed. It must be driven back to
zero by a field in the opposite direction. If an alternate field is applied to the material, its
magnetization will trace a loop called Hysteresis
loop.
Lagging of the magnetization of a ferromagnetic
material, such as iron, behind variations of
the magnetizing field is called Hysteresis.
If the intensity of the magnetizing field is
gradually increased, the magnetic flux
density B rises to a maximum, or saturation, value
at which all of the atomic magnets are aligned in
the same direction. When the magnetizing field is
diminished, the magnetic flux density decreases, again lagging behind the change in field
strength H. In fact, when H has decreased to zero, B still has a positive value called
the remanence, residual induction, or retentivity, which has a high value for permanent
magnets. B itself does not become zero until H has reached a negative value. The value
of H for which B is zero is called the coercive force or coercivity. A further increase in H (in
the negative direction) causes the flux density to reverse and finally to reach saturation again,
when all the atomic magnets are completely aligned in the opposite direction. The cycle may
be continued so that the graph of the flux density lagging behind the field strength appears as a
complete loop, known as a hysteresis loop. The energy lost as heat, which is known as
the hysteresis loss, in reversing the magnetization of the material is proportional to the area of
the hysteresis loop. Therefore, cores of transformers are made of materials with narrow
hysteresis loops so that little energy will be wasted in the form of heat.
To derive expression for heat developed per unit volume per unit cycle, consider a ring of
ferromagnetic material having area of cross section A, circumferential length l having N
number of turns. If i is the current in the coil which produces flux density B
Then magnetic flux through the coil Ф𝐵 = 𝑁 𝐵 𝐴
Magnetizing force due to current 𝐻 =
𝑁𝑖
𝑙
𝑜𝑟 𝑖 =
According to Lenz’s law, induced emf produced:
𝐻𝑙
𝑁
𝑒= −
𝑑 Ф𝐵
𝑑𝑡
= −
𝑑 (𝑁 𝐵 𝐴)
𝑑𝑡
= −𝑁𝐴
𝑑 ( 𝐵)
𝑑𝑡
-ve sigh indicates the opposite nature of induced emf.
Therefore work has to be done against induced emf. This work done in time dt is given by
𝑑𝑤1 = 𝑒 𝑖 𝑑𝑡
𝑑𝑤1 = [𝑁𝐴
𝑑 ( 𝐵)
𝑑𝑡
𝐻𝑙
] [ 𝑁 ] 𝑑𝑡
𝑑𝑤1 = 𝐻𝐴𝑙 𝑑𝐵
Therefore, net work done for a complete cycle of magnetization is then given by
𝐵
𝑊1 = 𝐴𝑙 ∫𝐵 2 𝐻𝑑𝐵
1
And Work done per unit volume
𝑊 = 𝐴𝑙
𝐵
1
∫𝐵 2 𝐻𝑑𝐵
𝐴𝑙
𝐵
= ∫𝐵 2 𝐻𝑑𝐵
1
Also 𝐵 = 𝜇𝑜 (𝐻 + 𝐼) or 𝑑𝐵 = 𝜇𝑜 (𝑑𝐻 + 𝑑𝐼)
𝐵2
𝑊 = ∫ 𝐻 𝜇𝑜 (𝑑𝐻 + 𝑑𝐼)
𝐵1
𝐵
𝑊 = ∫𝐵 2 𝐻𝜇𝑜 (𝑑𝐻 + 𝑑𝐼)
1
𝑊 = 𝜇𝑜 ∮ 𝐻 𝜇𝑜 (𝑑𝐻) + 𝜇𝑜 ∮ 𝐻(𝑑𝐼)
𝑾 = 𝝁𝒐 ∮ 𝑯(𝒅𝑰)
Work done per unit volume per cycle of magnetization = area of B-H loop or 𝝁𝒐 times area
of I-H curve. This loss of energy is dissipated in the form of heat and is known as
hysteresis loss.
************