Dielectrics and Magnetic Materials

Electric Polarization :
When a dielectric is placed in an external electric field, dipole moment is induced
by stretching or re-orienting of molecules along the field direction. This is called
polarization.
Various Polarization Processes :
1)Electronic Polarization : The displacement of negatively charged electron cloud and
positively charged nucleus of an atom in opposite directions, on application of electric field,
result in electronic polarization As the nucleus and the centre of electron cloud are
separated by a certain distance, dipole moment is created within each atom.
electron cloud
E

  

2) Ionic polarization : The ionic polarization is due to the displacement of cations and
anions in opposite directions and occurs in an ionic solid.
3) Orientational Polarization : When an electric field is applied on molecules which posses
permanent dipolemoment, they tend to align themselves in the direction of applied field.
The polarization due to such alignment is called orientation polarization, which is dependent
on temperature.
4) Space charge polarization : Space charge polarization occurs due to accumulation of
charges at the electrodes or at the interfaces of multiphase materials. The ions diffuse over
appreciable distance in response t the applied field, giving rise to redistribution a charges in
the dielectric medium.

Electric susceptibility e :
In many substances polarization is proportional to the field,
P  o e E provided E is not too strong.
The constant of proportionality e is called the electric susceptibility of the medium. A
factor o has been extracted to make e dimensionless. The value of e depends on the
microscopic structure of the substance. The materials that obey the above equation are
called linear dielectrics.
Dielectric Constant (K):
It is the ratio of the permittivity of the medium to the permittivity of free space.
Electric displacement D  (o E  P )  o E  o e E  o (1  e ) E
or, D   E where   o (1  e ) is called permittivity of the material.

The dimensionless quantity K= 1  e  is called dielectric constant.
o
Polarizability ( ) :
Polarizability is defined as induced dipole moment per unit electric field.


E

Expression for electronic polarizability :

In classical model of an atom, the nucleus of charge ze is surrounded by an electron cloud of
charge  ze distributed in a sphere of radius R. The charge density  is given by
 ze

4 3
R
3
E

 R x

When electric field of intensity E is applied, the nucleus and the electrons
experience Lorentz forces of magnitude ZeE in opposite directions. Hence nucleus and
electron cloud are separated. Now a Coulomb force which tends to oppose displacement
develops between them. Equilibrium is reached when Lorentz force and coulomb force are
equal and opposite.
Lorentz force FL  ZeE
4
Ze  x3
1 3
Coulomb force FC 
4o x2
In equilibrium FL=FC
4
Ze  x3
1 3
ZeE =
4o x2
4
Ze  x3
1 3 ze
ZeE =  
4o x 2 4 3
R
3
Ze x
 E=
4o R3
 Induced electric dipole moment e  Zex
 4o R3E
Electronic polarizability 
e  e  4o R3
E
If N is number of atoms/ m3 e  o (r 1)
Frequency dependence of polarization
On application of an electric field polarization occur. This polarization depends on time. The
polarisationP(t) as a function of time is given by
P(t) = P[1- exp(-t/tr)]
Where P is the maximum polarization and tr is the relaxation time. The relaxation time is
defined as the time taken for polarization process to reach 0.63 of maximum value.
If we draw a graph b taking frequency along X-axis and the corresponding polarization along
Y-axis the nature of the graph will be like the figure.
From the figure it is clear that
1. All the four types of polarization take place at a frequency of 102 Hz.
2. At a frequency range of 106 to 1010Hz all three polarization takes place except space
charge polarization.
3. At a frequency ~1013 Hz both electronic and ionic polarization takes place.
4. At a frequency of ~1015 Hz only electronic polarization takes place.
Internal field in solids : (Lorentz method)
Let a dielectric be placed between the plates of a parallel plate capacitor and let there be an
imaginary spherical cavity around the atom A inside the dielectric. It is also assumed that
the radius of the cavity is larger is larger compared to the radius of the atom.

The internal field at the atom site A can be considered to be made up of the following three
components namely E, E1, E2,
Field E :
E is the external field
Field E1 :
E1 is the field intensity at A due to other atoms contained in the cavity. We are assuming a
cubic structure , so E1 = 0 because of symmetry.
Field E2 :
E2 is the field intensity due to polarization charges on the surface of cavity.

d
r

A

If d A is the surface area of the sphere of radius r lying between  and   d  , where  and
  d  , where  is the direction with reference to the direction of the applied force,
dA  2r 2 sin d 
The charge dq on the surface dA is equal to the normal component of the polarization
multiplied by surface area.
 dq = P cos  . dA  P(2r 2 sin  cos d  )
The field due to this charge at A denoted by dE4 is
1 dq
dE2  cos 
4o r 2
 Total field E2 due to charges on the surface of the entire cavity is obtained by
integrating.
P  2 P  2
E2   dE2   cos  sin  d    cos d ( cos  )
2o 0 2o 0

P  Cos3   P
  
2o  3   3
  0 o
P
 Internal field E i =E+E1 +E 2 =E+
3 o
Clausius- Mosotti Relation
Now polarization P = NαeEi = Nαe(E + P/3ε0)
So, P[1 – (Nαe/3 ε0)] = NαeE
Or P = NαeE / [1 – (Nαe/3 ε0)]
But P = Eε0 (εr-1)
So, P = Eε0 (εr-1) = NαeE/ [1- (Nαe/3ε0)]

Where N is the number of molecules per unit volume. The above relation is known as
Clausius- Mosotti Relation

Magnetics
 Unit of Magnetic pole strength is Amp-meter
 Unit of magnetic dipole moment is Amp-m2
Magnetic flux density
The number of magnetic lines of force per unit area, area being perpendicular to the lines of
forces is known as magnetic flux density. It is denoted by B.
 B is a vector quantity.
 Its unit in MKS system is Tesla or Weber/ M2.
 In CGS system its unit is Gauss or Maxwell/cm2.
 1Tesla = 104 Gauss
Magnetization (M)
When a magnetic material is placed in a magnetic field, the elementary current loops in the
material become aligned parallel to the field and the material is magnetized and acquires
magnetic moment.
The magnetic moment per unit volume of the material is known as magnetization and
is denoted by M.
Thus M = m/V
 It is a vector quantity.
 It’s MKS unit is Amp/meter
 If ‘a’ is the cross sectional area of the material and ‘l’ be the length of the material
then
mxl m
M= 
axl a

Hence M can be defined as the pole strength per unit area of the specimen.
Magnetic Intensity (H)
When a magnetic material is placed in a magnetic field, it becomes magnetized. The
capability of the magnetic field to magnetized a material is known as magnetic intensity of
the field and is denoted by H.
 It is a vector quantity
 It’s MKS unit is Amp/meter
 B= µ H
Relative permeability (µr)
The degree to which the magnetic field can penetrate to a magnetic material is known as its
relative permeability and is defined by the ratio of magnetic flux density in the medium to the
magnetic flux density in vacuum.
B
So, μ r 
B0
 It is a dimensionless quantity.
 Its value for vacuum is 1
Permeability (µ)
The product of the relative permeability (µr) and permeability of the free space (µ0) is known
as permeability of the material medium
Thus μ = μ r μ 0
Where µ0 = 4π x 10-7 Wb/A-m
B B B B B
 Since μ r  and μ 0  0 therefore μ = μ r μ 0 = x 0 =
B0 H B0 H H
 In vacuum B = µ0H but in a magnetic material medium B = µ0(H + M)
Magnetic susceptibility (χm)
For most magnetic materials the magnetisation (M) is directly proportional to magnetic field
intensity (H)
That is M α H So, M = χm H
The constant χm is called magnetic susceptibility of the material and may be defined as the
ratio of the magnetisation(M) to the magnetic field intensity(H)
 χm is a pure number. Its value for vacuum is zero.
 For paramagnetic materials its value is positive.
 Foe diamagnetic materials its value is negative.
 For Ferromagnetic materials its value is positive and very large
Relation between µr and χm
We know that B = µ0(H + M) = µ0H( 1 + M/H) = µ0H( 1 + χm)
B
 =μ 0 1 + χ m 
H
B
μ= So, μ = μ 0 1 + χ m 
H
μ
Again μ r = , Hence μ r = 1 + χ m 
μ0
Origin of Magnetic moment
In atoms the permanent magnetic moment can arise due to the following factors
1. The orbital motion of the electron
The atom of any material consists of a central nucleus and the electrons move around
the nucleus in specific orbit. Each electron orbit is equivalent to a tiny current loop
and behaves as an elementary magnet having a magnetic dipole moment. The total
orbital magnetic moment of an atom is the sum of orbital magnetic moments of
individual electrons.
2. The electron spin
Each electron is spinning about an axis through itself and this spin also gives rise to a
magnetic diple moment.
3. Nuclearspin
In addition to electronic contribution nuclear spin also contributes to magnetic
moment of atoms. Generally nuclear spin is very less in comparision with magnetic
moment of an electron. Therefore we consider the resulting magnetic moment of an
atom is the sum of the orbital and spin magnetic moments of the electron.
Classification of Magnetic materials
Magnetic materials are classified into three categories.
They are, Ferromagnetic material, Paramagnetic material and dia magnetic material.

S.No Ferromagnetic Paramagnetic Diamagnetic

1 Strongly attracted Feeble attraction towards Feeble repulsion from the
towards magnetic field. magnetic field. magnetic field.
2 Field lines are More number of field lines Less number of field lines
concentrated in the pass through the material pass through the material
material. than outside. than outside.
3 Set along the direction Tend to align along the Tend to align
of the magnetic field. magnetic field direction. perpendicular the
magnetic field direction.
4 Susceptibility, χ is large Susceptibility, χ is less than 1 Susceptibility, χ is small
and positive. but positive. but negative.
5 Relative permeability, µr Relative permeability, µr is Relative permeability, µr
is greater than unity. slightly greater than unity. is less than unity.
6 Susceptibility, χ Obey’s Curie law, χ = 1/T Susceptibility, χ is
decreases with independent of
temperature. temperature.
7 Have definite Curie No Curie point. No Curie point.
point above which they
become paramagnetic.
8 Exhibit phenomenon of Hysteresis is not exhibited. Hysteresis is not exhibited.
Hysteresis.
9 Possess retentivity. No retentivity. No retentivity.
10 Ex: Iron, cobalt, nickle Ex: Platinum, Chromium, Ex: Bismuth, mercury,
Aluminium etc. silver, copper, water etc.

Weiss theory of Ferromagnetism

To explain the phenomenon of ferromagnetism, Weiss proposed a hypothetical concept of

ferromagnetic domains. He postulated that the neighboring atoms of the ferromagnetic
materials, due to certain mutual exchange interactions, from several number of very small
regions, called domains.

Weiss theory of ferromagnetism is also called domain theory of ferromagnetism. It has

following points:

Each domain is spontaneously magnetized and carries a dfinite magnetic moment. In the
absence of an external magnetic field, the magnetic moment of different domains are so
arranged that the net magnetic dipole moment is zero.

When an external magnetic field is applied, the domains which are aligned approximately
along the direction of the applied magnetic field grow in size at the cost of unfavorably
oriented domains, that is, those align opposite to the field direction get reduced. In other
words, the domain boundaries move so as to expand the favorable domains. Hence a net
magnetic dipole moment is induced.
Thus the material is magnetised mostly by the process of domain alignment. When the field is
removed, the domain boundaries do not recover their original positions and thus the material
is not completely demagnetised, but some residual magnetism remains in it.

Hysteresis
When a ferromagnetic material is subjected to increasing or decreasing magnetic
fields, the magnetic field induction B varies as a function of H along a closed loop called
hysteresis loop. The curve begins at O. As H
increases the field B increases slowly , then
more rapidly and finally attaining saturation
value and becoming independent of H. The
maximum value of B is saturation flux
density Bs and the corresponding
magnetization is the saturation
magnetization Ms. If H is now decreased, B
also decreases but following the path AC
instead of original path AO. Thus B lags
behind H. When H becomes zero B does not
become zero but has a value equal to
OC(Br).This magnetic flux density remaining
in the materials is called residual
magnetism. It indicates that the material remains magnetized even in absence of external
field H. The power of retaining magnetism is called retentivity or remanance of the material.
If H is now increased in reverse direction B decreases along the path CD. B becomes zero
when H attains a value equal to OD. To reduce magnetic induction within the material to
zero a field of magnitude Hc must be applied opposite to original magnetizing field. Hc is
called coercivity. On reversing the variation of field H, the curve follows the path EFGA. The
closed curve ACDEFGA is called hysteresis loop.

Differences between Hard and Soft Magnetic Materials

S.No. Hard Magnetic Materials Soft Magnetic Materials

1 Materials which retain their Soft magnetic materials are easy to
magnetism and are difficult to magnetize and demagnetize.
demagnetize are called hard magnetic
materials.
 2 The domain wall is prevented. Hence The domain wall movement is easy.
it is difficult to demagnetize Hence they are easy to magnetize and de-
magnetize..
3 These materials retain their These materials do not retain their
magnetism even after the removal of magnetism even after the removal of the
the applied magnetic field. applied magnetic field.
4 They have large hysteresis loss due to They have low hysteresis loss due to
large hysteresis loop area. small hysteresis area.
5 Susceptibility and permeability are Susceptibility and permeability are high.
low.
6 Coercivity and retentivity values are Coercivity and retentivity values are less.
large.
7 Magnetic energy stored is high. Magnetic energy stored is less.
8 The eddy current loss is high The eddy current loss is less because of
high resistivity.
9 These materials are used for making Used in making permanent magnets,
permanent magnets. magnetic separators, magnetic detectors,
Used in transformer cores, motors, speakers, microphones, etc.
generators, electromagnets, etc.
10 Examples- Alnico, Chromium steel, Example- Iron- silicon alloy, Ferrous
tungsten steel, carbon steel nickel alloy, Ferrites, Garnets

Ferrites (Ferrimagnetic materials)

In these materials the net magnetization of magnetic sub-lattices is not zero since antiparallel
moments are of different magnitudes. Above a particular temperature called curie
temperature Tc thermal energy randomizes the individual magnetic moments and the material
becomes paramagnetic.
Ferrites consist chiefly of ferric oxide Fe2O3 , combined with one or more oxides of divalent
metals . They are represented by the general formula MFe2O4 (or) MOFe2O3 in which M
represents any metallic elements such as Fe2+, Co2+, Mn2+, Zn2+, Cd2+, Mg2+etc. The name of
the ferrite depends on the name of the metallic element.
Eg. Fe2+Fe2O4 (Magnetite), Zn2+Fe2O4 (Zinc Ferrite), Ni2+Fe2O4 (Nickel Ferrite)
Characteristics
1. Ferrites exhibit hysteresis loop.
2. They are polycrystalline samples and the coercivity , retentivity and permeability
depend on grain size.
3. Ferrites have high resistivity ranging from 102 to 1010 Ohm-m
4. They possess high permeability
Applications :
1) As the eddy current losses is much less, ferrites are used in transformer core.
2) They are used in radio receivers.
3) They are used in digital data storage devices.
Magnetic device applications
Transformer core-
Transformer core is made of high permeability magnetic materials which concentrate the
magnetic field lines in the core material. The presence of core can increase the magnetic field
of a coil by a factor of several thousand over what it would be without the core.
Different types of core-
(a) Steel Laminated core – These cores are made off a number of E-I shaped very thin
laminated steel plates. Each plate is laminated to decrease the eddy current loss. These
cores are used for transmitting voltage at audio frequency level.
(b) Toroidal core – Torriodal cores are made of a range of materials like steel, coiled
permalloys, powdered iron or ferrite. These cores are circular in nature without any
 opening. Torroidal cores are more efficient than steel laminated core. They can be
made smaller, lighter and with a lower magnetic field but in this case winding is
expensive.
(c) Pot Core – The shape of such core is like a pot. It is round with an internal hollow
that almost completely encloses the coil. Generally a pot core is made in two halves
which fit together around the a coil. These types of core generally shield and used to
reduce electromagnetic interference.
(d) Planar core- A planar core consists of two flat pieces of magnetic material one above
and other below the coil. This design is used for mass production with small volume,
high power transformer at low cost.

Storage Devices
Now a days data storage devices are highly essential requirements of entertainment
electronics and computer system. There are two types of storage devices. (1) Semiconductor
storage devices which are volatile in nature e,g. RAM (2) Magnetic storage devices which are
non-volatile in nature due to which magnetic storage devices are preferable for data storage.
The process of storing data in memory unit is called writing and the process of
retrieving data from memory is called reading.
Hard Disk
Hard disk is the main memory system of magnetic storage devices. It consists of a number of
magnetic disk called platter. A platter is a flat, circular plate which is coated with iron oxide
particles. It also has a read-write head. The platter rotates at very high speed of order 3600
rpm.
The data is recorded by write head in the form of bands. Each band of information on
a particular disk is called a track. The tracks are divided into sectors. The tracks and sectors
are created when the hard disk is first formatted. The tracks are arranged in concentric rings.
There will be several thousand data tracks on one side of a disk in which the bits are recorded
in a track at a density of order 20000 to 100000 bits/inch. A typical outer track contains more
bits than the inner tracks since the circumference of an outer track is greater.
During the operation of the memory the disks are rotated at uniform speed by a disk drive
unit. Each recording surface consists of one read-write head. Using the movable arm
connected with the disks, a particular set of track for reading/writing can be selected.
Advantage
1. They have low access time and high disk transfer rate due to very fast access to data.
2. Data can be read directly from any part of the hard disk (random access.
3. The access speed is about 1000 KBPS.
4. The storage capacity can be increased by mounting several disks on common drive
unit.