APPLIED PHYSICS

MAGNETISM AND DIELECTRICS

The fundamental thing responsible for electric field or magnetic field is charge. The static
electric field is associated with charge. But we do not have magnetic charge in nature. A moving
charge gives rise to a magnetic field.
In every atom electrons are revolving around the nucleus with –ve charge in electronic
orbits create current in orbit. This current creates magnetic field. So atom or molecule behaves as
a magnet. So that it consist of magnetic moment.
In magnetizing substances the net magnetic moment is not zero, but in non magnetizing
substance like wood the net magnetic moment is zero.

MAGNETIC DIPOLE MOMENT (µM)

The arrangement of two equal and opposite charges separated by a distance is called magnetic
dipole. The magnetic moment of a magnet is defined as the product of length of magnet (2l) and
its pole-strength (m)

Magnetic moment µm = 2l x m amp-m2

It is vector quantity. Its direction is south to North Pole.

TORQUE (Τ)

Torque is defined as a couple acting on the bar magnet when placed at right angles to the
direction of uniform magnetic field. Because of this torque magnetic dipole rotates and finally
comes along the direction of field.

τ = µm B sinө where B is magnetic induction

Bar magnets, current loops, current carrying coils etc., all experience a torque in magnetic field
and can be regarded as magnetic dipole.

MAGNETIC FIELD

The space around the magnet where its magnetic influence is experienced is called magnetic
field. It is a scalar quantity.

MAGNETIC INTENSITY OR MAGNETIC FIELD STRENGTH (H)

Magnetic field intensity at any point in the magnetic field is defined as the magnetizing force
experienced by a unit North Pole placed at that point. It is measured in Amp/m. It is a vector
quantity. It is independent of the medium.

H=

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MAGNETIC INDUCTION OR MAGNETIC FLUX DENSITY (B)

The total no. of magnetic lines of force passing through the unit cross sectional area of the
substance due to both magnetizing field and induced magnetism is called magnetic flux density.

B= It is vector quantity. It is measured in N/amp-m or wb/m2 or Tesla.
A
INTENSITY OF MAGNETIZATION (I or M)
When a magnetizing substance is placed in an external magnetic field, the two ends of the
substance acquire equal and opposite pole strength, hence substance possess some magnetic
moment. The induced magnetic moment per unit volume of the substance when it placed in an
external magnetic field is called intensity of magnetization. It is vector quantity and is measured
in amp/m.

Inducedmag neticmomen t
According to definition I=
Volume

2lm m
I= = amp/m
A.2l A

So intensity of magnetization is defined as the induced pole strength per unit area of the
substance when it is placed in an external magnetic field.

MAGNETIC PERMEABILITY (µ)

Permeability of a medium is measure of the conducting power of the magnetic lines of force
through that medium. Consider a magnetizing substance is placed in uniform magnetic field. The
magnetic lines of force passing through unit area in a substance is directly proportional to the
field strength H. Therefore

BH B = µH
B
Where µ permeability of medium µ=
H
Permeability is the ratio of magnetic induction to field strength.

If the material is placed in air or free space then the above equation can be written as

B0
µo = where B0 is flux density in air or free space, µo is permeability of air or free space,
H
µo = 4 x 10-7 H/m

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
µr = is called relative permeability. It is the ratio of permeability of medium to permeability
0
of air or free space.

For air and non magnetic materials µr = 1.

MAGNETIC SUSCEPTIBILITY χ

The magnetic susceptibility of the specimen gives how free the specimen can be magnetized. The
intensity of magnetization I or M of the substance is directly proportional to the magnetic
intensity H.

i.e., M  H or M = χH

where χ is proportionality constant known as magnetic susceptibility.

M
χ= dimension less quantity.
H

MAGNETIZATION

The term Magnetization is defined as the process of converting non-magnetic material into
magnetic material.

RELATION BETWEEN RELATIVE PERMEABILITY µr AND SUSCEPTIBILITY χ

When a material is placed in an external magnetic field, the total flux is sum of the flux in air or
free space produced by external field and flux in free space produced by magnetization of the
material.

B = B0 + Bi

B0 = flux in air or free space due to external field = µ0H

Bi = flux in air or free space due to induced magnetism = µ0I

B = µo[ H+I ] --------(1)

This is the relation between B, H and I.

Divide the above equation by H, we get

B I
= µo[ 1 + ]
H H

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
µ = µo(1 + χ) =1+χ
0
µr = 1 + χ ---------- (2)

SPIN MAGNETIC MOMENT

A spin magnetic moment is the magnetic moment induced by the spin of elementary particles.
For example, the electron is an elementary spin-1/2
spin fermion. Quantum electrodynamics gives the
most accurate prediction of the anomalous magnetic moment of the electron.

ORIGIN OF MAGNETIC MOMENT

Every substance is made with large number of molecules or electrons. The magnetic properties
of the materials are due to the motion of the electrons around the nucleus in the atoms. Every
electron is associated with the orbital and spin motions. The orbita
orbitall motion of the electron around
the nucleus is imagined as current carrying circular having no resistance. As a result it sets up the
magnetic field around the atom. Hence every atom in the material acts as a tiny magnet. In
general the magnetic moment of atom originate from 3 sources:

1) Orbital magnetic moment of the electrons

2) Spin magnetic moment of the electrons
3) Spin magnetic moment of the Nucleus

Orbital Motion of Electrons: Bohr Magneton

The motion of the electron constitutes a current and the circular

cir path
of electron is identical to current loop. Such a current loop behaves
as an elementary magnet having magnetic moment. The total orbital
magnetic moment of magnetic moment of an atom is sum of orbital
magnetic moments of individual electrons.
Let us consider an atom in which there is single electron of mass m and
charge e revolving around the positive nucleus in a circular orbit of radius r. Let v be the velocity
of electron, ω be the angular velocity of the electron. The magnetic moment possessed by an
electron which is revolving around the nucleus is given by

Magnetic moment µm = I x A ------------ (1)

where I is current in the circular loop of orbit. A= ᴨ is the area enclosed by the circulating
current.

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ev
We know I = , r is the radius of the circular orbit ( I = e /t, t = distance/speed)
2r
ev 2
From equ. (1), µm = r
2r
evr
= ---------- (2)
2
The angular momentum of the electron in the circular orbit of radius r is L = mvr or r = L/mv
eL
From equ (2), we get µm = - ----------- (3)
2m
The negative sign indicates that the dipole moment is opposite to the vector representing the
angular momentum.
e
The constant is called gyromagnetic ratio. It is the ratio of magnetic moment to angular
2m
momentum.

According to the modern atomic theory the angular momentum of electron in the orbit is
determined by the orbital quantum number l which is restricted to a set of values
l = 0, 1, 2…. (n -1). Where n is principal quantum number. Which determine the energy of orbit.
It can accept only integers.
lh
The angular momentum of electron associated with a particular value of ‘l’ is
2

 e  lh  eh 
 µm = -   = -  l = -µB. l -------- (4)
 2m  2  4m 

 eh  -24 2
The quantity µB =   is called Bohr magneton and has value 9.27x10 A-m
 4m 
Bohr magneton is a fundamental unit of atomic magnetic moment. Electron possess the magnetic
moment not less than Bohr magneton. For filled electronic shells the total angular momentum is
zero.
 Atoms or ions which are having only filled shells have no permanent magnetic moment, they
are diamagnetic.

Spin Motion of Electron

The spinning electron also associated with a magnetic moment, which is given by the relation
 e 
μes =    S, where  is spin gyromagnetic ratio depends on the structure of the spinning
 2m 

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particle, experimental value of  = -2.0024, the negative sign indicates that μes is opposite to that
h
of S in direction. Since S = for electron, μes = 9.24 x 10-24 A-m2
4

Spin magnetic moment of Nucleus

eh
The magnetic moment of the nucleus is given by μps = = 5.05x10-27 A-m2 where Mp
4 M p
represents the mass of proton which is nearly 1/2000 as much as that of an electron. The
magnetic moment due to the nuclear spin is neglected. The two factors namely orbital motion
and spin motion of electron are contributed to the permanent magnetic moment in atoms.

CLASSIFICATION OF MAGNETIC MATERIALS BASED ON ATOMIC MAGNETIC

MOMENT

The materials may be classified on the basis of permanent magnetic moment in to five groups.
Magnetic properties other than diamagnetism, which is present in all substances, arise from the
interactions of unpaired electrons. Is as shown in the figure

Diamagnetic
Materials composed of atoms or molecules having zero magnetic moment are
called diamagnetic.

Paramagnetic
If the atomic magnetic dipoles are orient in random direction in the absence
of external field, the material will be paramagnetic. The orientation of
magnetic moments in paramagnetic substances is as shown in fig A.

Ferromagnetic
If the individual dipoles of the material orient in the same direction, the
material will be Ferro magnetic. The orientation of dipole moment in ferro
magnetic materials is shown in fig B.

Antiferro magnetic
If the neighboring dipoles in the material orient in opposite direction to each
other and with same magnitude, the materials are called antiferro magnetic as
shown in fig C.

Ferri magnetic
If the neighbouring dipoles are orient anti parallel and with unequal
magnitudes, the materials are called ferri magnetic as shown in fig D.

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DIAMAGNETIC MATERIALS

The materials which are magnetized in the direction opposite to the magnetic field are called
diamagnetic materials. or The materials which cannot
cannot be magnetized in the external magnetic
field are called diamagnetic materials.

Examples: All inert gases, hydrogen,

drogen, air, water, gold, silver, bismuth etc.,

Properties

 Diamagnetic substances exhibit negative susceptibility. The value of susceptibility is

small and is the order of 10-6

 As the diamagnetic susceptibility is negative, the relative permeability µr is slightly less

than unity.

 When a small rod of diamagnetic material is placed in magnetic field it

turns to a position perpendicular to the field lines. Diamagnetic
materials pulled aside the field lines

 The magnetic susceptibility of diamagnetic materials is independent of temperature.

Note that when the field is zero the magnetization is zero. The other characteristic
behavior of diamagnetic materials is that the susceptibility is temperature independent. Some
well known diamagnetic substances, in units of 10-8 m3/kg, include: quartz (SiO2) -0.62 ,Calcite
(CaCO3) -0.48 ,water -0.90

 The magnetization varies linearly with the applied field H, when the field is too strong.

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 When the diamagnetic substance is placed in non uniform magnetic field, it move
towards the weaker region of the field.

 The lines of force show less preference to pass through these substances than through
vacuum or air.

 The liquid level of diamagnetic solution solution taken in the U-tube depresses when it is
placed in a uniform magnetic field as in below

PARAMAGNETIC MATERIALS

Materials or substances which acquire weak magnetism in the direction of the field when placed
in magnetic field are called paramagnetic materials.

Examples: oxygen, solutions of iron salts, copper chloride, chromium and platinum.

Properties
 Paramagnetic materials exhibit +ve magnetic susceptibility, the susceptibility is of the
order of 10-3
 The relative permeability µr is slightly more than unity and move from the region of low
intensity to high intensity in magnetic field.
 A paramagnetic material magnetized in the direction of field. Field lines are pulled
towards the materials and penetrate through the material when it is placed in a magnetic
field.

 The paramagnetic susceptibility is positive. It is dependent on temperature. The

susceptibility is inversely proportional to temperature. Thus
c
χpara = where c is curie’s constant and relation is called curie’s law.
T

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At normal temperatures and in moderate fields, the paramagnetic susceptibility is small (but
larger than the diamagnetic contribution). Unless the temperature is very low (<<100 K) or the
field is very high paramagnetic susceptibility is independent of the applied field. Under these
conditions, paramagnetic susceptibility is proportional to the total iron content. Many iron
bearing minerals are paramagnetic at room temperature. Some examples, in units of 10-8 m3/kg,
include: Montmorillonite (clay) 13 Nontronite (Fe-rich clay) 65 Biotite (silicate) 79
Siderite(carbonate) 100 Pyrite (sulfide) 30.

 The magnetization M varies linearly with the applied field when the field is not too
strong.
 In no uniform field the paramagnetic substances are attracted towards stronger region of
magnetic field.

 The liquid level of diamagnetic solution taken in the U-tube rises when it is placed in
uniform magnetic field as shown.

FERRO MAGNETIC MATERIALS

Materials which are strongly magnetized in the direction of the field in external magnetic field
are called ferromagnetic.
Example: Iron, Nickel, Cobalt and some steels are examples.

Properties
 Ferro magnetic materials exhibit very high values of magnetic susceptibility and relative
permeability.

 These are very strong the dipoles line up permanently upon the application of external
field.
 The magnetic susceptibility and relative permeability are positive and exhibit very high
values Susceptibilities are in the order of 106 and relative permeabilities are of the order
of 103.

 They conduct magnetic flux much as metals conduct electric current.

 They do not exhibit a linear proportionality between the magnetization and the field
strength.
 The magnetization of these materials is not unique function of field strength but depends
on the field to which it is subjected to.

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 When ferro magnetic material is kept in magnetic field, the field lines crowd in to the
material.

 As the temperature increases susceptibility decreases, aboveabove a certain temperature

ferromagnetic
magnetic material become ordinary paramagnetic and this temperature is called curie
temperature.
c
Susceptibility follows the curie’s
curie law.χ = , where θ is paramagnetic curie’s
T 
temperature. For T >  material transforms into paramagnetic state, T <  material is in
ferromagnetic state.
 Magnetization M varies non linearly with applied field H. as M varies non line
linearly with
the applied field, µr also increases with increase of field, beyond the saturation point
permeability decreases rapidly as shown in fig.

 Ferromagnetic
magnetic material exhibit hysteresis.

WEISS MOLECULAR FIELD THEORY (Spontaneous

Spontaneous magnetization in ferromagnetic
materials)

According to Weiss spontaneous magnetization in a ferromagnetic substance is due to the

interaction between the atomic dipoles in the domain. This interaction produces internal
molecular field Hi. Due to this internal field, the spins would be parallel to the field.

∴ Hi ∝ M or Hi = γM where γ is weiss constant.

∴ Effective field (total field) Heff. = H + Hi
H = H + γM ---------- (1)
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Wheree H is applied field and γ is called molecular field constant which is also known as Weiss
constant. According to Weiss theory every Ferro magnetic substance should initially exhibit
paramagnetism.
M c
∴ Susceptibility of Paramagnetism  = =
H T
M M c
For Ferromagnetic substance, = = =
H eff H  M T

MT = Hc + cM or
M (T-c) = Hc or
M c c
== = --------- (2)
H T  c T  

Where  = c.c. From equ (2) it is clear that magnetization tends to infinity at T = . It means that
the interaction of the individual magnetic moments reinforce each other causing them to align
parallel at T = . Where c is the curie constant, θ is the curie temperature of ferromagnetic
material. This relation is called curie weiss law.
law. For all the temperatures T<  the materials
behave like ferromagnetic. For temperature T > ,, the materials changes into paramagnetic
state.

DOMAIN HYPOTHESIS

In order to explain theory of ferromagnetism weiss introduced the new concept of magnetic
domains. Weiss postulated that entire ferromagnetic material split into a large no. of small
regions of spontaneous magnetization. These regions are called domainsdomains.. Every domain
possesses a definite value and direction of the magnetic moment. Each Domain has a size
ranging from 10-9 to 10-9 m3and contains 1017 to 1021 atoms and whose magnetic axes are aligned
in the same direction even in the direction even in the absence of
magnetic field. In the absence of an external filed the magnetic moment
vectors are randomly oriented and net magnetic moment is zero. When
magnetic field is applied the domains rotate and make to align their
magnetic moments with the field direction. So specimen exhibits a net
magnetization.

When an external field is applied to a ferromagnetic material the magnetization in the material is
increased in two ways.

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1. Due to displacement of the boundaries of the domains

An unmagnetized ferromagnetic specimen is as

shown in the fig (a) .when the specimen is placed in
the magnetic field the domains the domains parallel
or nearly parallel to the filed direction H, can grow in
size as shown in fig (b).

2. Due to rotation of Domains Fig (a) Fig (b)

The domains rotate until magnetic moments are more or less aligned in the direction of external
magnetic field as shown in the figure.

HYSTERISIS

Hysteresis means Lagging i.e., The Lagging of intensity

intensity of magnetization (I) behind the
intensity of magnetic field (H). The plot of Magnetization M or Magnetic field B as a function of
Magnetic Field Intensity H (i.e. M
M-H or B-H graph) gives the Hysteresis curve.

Consider an unmagnetised ferromagnetic substance (iron bar) is placed in a magnetising field.

When the bar is slowly magnetized the variation in the intensity of magnetization I is shown in
the fig. When the substance is slowly magnetised, then magnetic induction B increases
nonlinearly
inearly along the curve (OACDE) called as the magnetization curve. At point E almost all of
the magnetic domains are aligned parallel with the magnetic field. An additional increase in H
does not produce any increase in B. E is called as the point of magnetic
magne saturation of the
material.
H is decreased till it reduces to zero. B reduces from its saturation value at "E" to that at
point "F". Some of the magnetic domains lose their alignment but some maintain alignment i.e.

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Some magnetic flux density B is still retained in the material. When the field H is switched off
the curve does not retrace in its original path. At zero field there exists a residual field called
remanent flux or retentivity (OF).
To bring back the magnetization zero the magnetic field is applied in reverse direction H
is reversed in this case the curve EFH is obtained which is called coercive field Hc. The amount
of intensity of magnetic field applied in the reverse direction to remove the retentivity is known
as Coercivity or Coercive force. It is represented as OG in the graph. Further repeating the
process the remaining portion [HIJKEA] in the graph is obtained. The closed loop
[OABCDEFGHIJA] is called Hysteresis loop (or) (I - H) curve. For one cycle of magnetization,
now the material is taken out. After a cycle of magnetization, there is some expenditure (loss) of
energy. This loss of energy is radiated in the form of heat energy in the material. This loss of
energy is directly proportional to the area of the loop.

From the hysteresis loop, a number of primary magnetic properties of a material can be
determined.
1. Retentivity - A measure of the residual flux density corresponding to the saturation
induction of a magnetic material. In other words, it is a material's ability to retain a
certain amount of residual magnetic field when the magnetizing force is removed after
achieving saturation. (The value of B at point b on the hysteresis curve.)
2. Residual Magnetism or Residual Flux - the magnetic flux density that remains in a
material when the magnetizing force is zero. Note that residual magnetism and retentivity
are the same when the material has been magnetized to the saturation point. However, the
level of residual magnetism may be lower than the retentivity value when the
magnetizing force did not reach the saturation level.
3. Coercive Force - The amount of reverse magnetic field which must be applied to a
magnetic material to make the magnetic flux return to zero. (The value of H at point c on
the hysteresis curve.)
4. Permeability, m - A property of a material that describes the ease with which a magnetic
flux is established in the component.
5. Reluctance - Is the opposition that a ferromagnetic material shows to the establishment
of a magnetic field. Reluctance is analogous to the resistance in an electrical circuit.

SOFT AND HARD MAGNETIC MATERIALS:

Soft or Type-I Magnetic Materials
Materials which can be easily magnetized and demagnetized are called soft magnetic materials.
Properties:
 The fig. shows the nature of hysteresis loop of soft magnetic material.
 They have small hysteresis loss due to small area of hysteresis loop area.
 These materials having large values of permeability and susceptibility
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 Coercivity and retentivity are small.

 These materials are free from irregularities
 Its magneto static energy is small.
 They are used in Electromagnetic machinery and in transformer’s cores, switching
circuits, Microwave isolators, shift registers and to produce electromagnets
Examples: Fe-NiNi alloy, Fe-Si
Fe alloy

Hard or Type-II
II Magnetic Materials
Materials which are hardly magnetized and demagnetized are called hard magnetic materials.
The fig. shows the nature of hysteresis loop of hard magnetic materials.
Properties:
 They have large hysteresis loss due to large h
hysteresis loop area.
 These materials have small values of permeability and susceptibility.
 Coercivity and retentivity are high.
 In these materials the irregularities in the structure are more.
 Its magneto static energy is more
 They are used to produce permanent
permanent magnets which are used in magnetic detectors,
microphones, flux meters, voltage regulators, damping devices etc.,
Examples: Al-Ni-Co
Co alloy, Cu-Ni-Co
Cu alloy.

FERRO ELECTRICITY:
Certain crystals exhibit spontaneous polarization in the absence of electric field is called ferro
electrics and this phenomenon is called ferro electricity. In ferro electric crystals the centers of
positive and negative charges do not coincide with each other even in the absence of the field,
thus producing non zero valuee of dipole moment.

Examples:: Rochellle salt ( NaK.C4H4O6.4H2O), Barium Titanate (BaTiO3),

Di HydrogenPotassium Phosphate (KH2PO4), Potassium Niobate etc.

Properties:

1. The ferro electricity disappears above a certain temperature called transition temperature or
the Curie point Tc, material transforms into Para electric state by rapid decrease in the dielectric
constant with increase in temperature.

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2. In ferro electrics, polarization P varies nonlinearly with the applied field E. where as in
ordinary
ry dielectrics P varies nonlinearly with the applied field E. So ferro electrics are called non
linear dielectrics and ordinary dielectrics are linear dielectrics.

3. Ferro electrics exhibit hysteresis. When a virgin ferro electric crystal is subjecte
subjected to an
alternating electric field the polarization P increases nonlinearly with the applied field E and
reaches saturation at a certain value of polarization. The polarization does not change even if E is
further increases. If the field is switched off, p
polarization
olarization does not tends to zero and having some
residual polarization.. This is also called remanent flux.

To bring back this polarization to zero value, electric field must be applied in opposite direction,
called coercive field Ec. Further increase in the field, saturation value of polarization also occurs
in negative direction also. Further increase in field, a closed loop is obtained as shown in fig.
called hysteresis loop. Above transition temperature hysteresis loop disappears and the crystal
behaves like ordinary dielectric.

4. All ferro electrics exhibit pyro electricity and piezo electricity but all pyro and piezo electrics
need not to be ferro electric. For example tourmaline is pyro electric and not ferro electric.
Quartz is piezo electric but not ferro electric.

5. Ferro electric crystals exhibit birefringence, i.e. double refraction when a plane polarized light
is passed through them.
Note: Certain crystals exhibit polarization when they are subjected to heat are called pyro
electric.

Applications:
1. Ferro electric materials possess high value of dielectric constant, so they are used to produce
small sized and high capacitance capacitors.
2. Ferro electric materials show piezo electricity, so they are used to produce and detect sound
waves.
3.. Ferro electric materials also show pyro electricity, so they are used to detect infrared radiation.
4. Ferro electrics show hysteresis property, so they are used to construct memory devices in
computers.

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DIELECTRICS
Dielectrics are nothing but insulators in which there are no free electrons for conduction. In
dielectrics forbidden energy is greater than 6ev.

Electric Dipole

The arrangement of equal and opposite charges separated by a distance is called electric dipole
or dipole.

Dipole Moment

Electric dipole moment is product of magnitude of charge and distance of separation between the
two charges. If q is the magnitude of the charge and r is the distance of separation, the dipole
moment is given by
µe = q x r coulomb-meter

Nonpolar Dielectrics

In an atom or molecule, if the center of gravity of positive charge coincides with the center of
gravity of negative charge, the distance of separation between two charges is zero. The net dipole
moment is zero (µe = q x 0 = 0). Such a molecule is called nonpolar molecule and medium
formed by these molecules is called nonpolar dielectric.
Ex. H2, N2, Co2, CH4, C6H6 etc.

Polar Dielectrics

When two or more atoms form a molecule and if the center of gravity of positive charge do not
coincide with that of negative charge, molecule possess some permanent dipolemoment such
molecule is said to be polar molecule. The medium formed by these molecules is called polar
dielectric.
Example: H2O, HCl, N2O, NH3……

DIELECTRIC CONSTANT OR RELATIVE PERMITTIVITY r

Let us consider a parallel plate capacitor connected to voltage source V0. Let the charges on the
plates be +Q0 and –Q0.
The capacitance of the capacitor when no medium is placed between the plates is

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0A
C0 = ------- (1) where‘d’ is distance of separation between the plates and ‘A’ is area
d
of the plate.

When the plates of the condenser are disconnected from the voltage source, the magnitude of
charge Q0 on either plate must remain constant. When the dielectric is placed between the plates
of the condenser, the potential difference decreases to a value V and capacitance of the
condenser increases to ‘C’.
A
C= where  is permittivity of the medium.
d
  A
C= 0 r = rC0
d
C
Dielectric Constant or relative permittivity r =
C0
So dielectric constant is defined as the ratio of the capacity of the condenser with
dielectric between the plates to the capacity of the condenser with air or vaccum in between the
plates. It is also defined as the ratio of permittivity of the medium to the permittivity of the air or
free space.

r = where 0 = 8.854 x 10-12 F/m or C2/N-m2 is permittivity of air or free space.
0

FIELD VECTORS IN DIELECTRICS

ELECTRIC FIELD INTENSITY (E)

Electric field intensity at any point in the electric field is defined as the force experience by unit
positive charge placed at that point. Let ‘F’ be the force acting on a charge ‘q’ then according to
definition,


 F
E = N/coulomb
q

The direction of ‘E’ is same as direction of F


DIELECTRIC POLARIZATION ( P )

The induced dipole moment per unit volume of the dielectric medium placed in the external field

is called dielectric polarization P

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 
i.e. P = --------- (1) where V is the volume of dielectric
V
It is vector quantity whose direction is induced negative charge to induced positive charge.
But induced dipole moment is the product of induced charge and distance of separation between
the charges.
If q1 and l are the induced charge and length of the dielectric (distance of separation),

 q1 x l q1
P = = C/m2 (V = area x length)
A xl A
Thus electric polarization is also equal to the induced charge per unit area

_
ELECTRIC DISPLACEMENT ( D ) :

Electric displacement is nothing but electric flux density. i.e. electric lines of force per unit area.
Mathematically it can be written as real charge per unit area of the conducting surface. Let a
charge ‘q’ be uniformly distributed on a conducting surface of area ‘A’,
_
_
q
D= C/m2 or q = D A. In integral form q =  D. ds
A
The electric displacement is also equal to the product of absolute permittivity of the medium ()
and resultant electric field intensity E
_
i.e. D =  E

ELECTRIC SUSCEPTIBILITY  e 

The electric polarization P is proportional to the electric field intensity E P  E or P =

0eE where e is proportionality constant called electric susceptibility
P
e =
0E

RELATION BETWEEN E AND R

Consider a parallel plate condenser of plate area ‘A’. let it be completely filled with a
dielectric. Let the magnitude of the real charge on either plate is ‘q’ coulombs. Let a charge of
magnitude ‘q1’ is induced on the dielectric faces as shown in figure.

Let ‘E’ be the electric field intensity. According to Gauss law in electrostatics,

UNIT V Page 18
 MAGNETISM AND DIELECTRICS

_
q  q1
 E. ds =
S
0
or

q  q1
E.A =
0
q q1
 0E =  or 0E = D – P
A A

_ _
D = 0E + P ----------- (1) This is the relation between D, E and P

Dividing the above equation by 0E, we get

_ _
D P
_ = 1+
0E
0 E

 1+ or  D  E 
0
r = 1+ or

 = r – 1 --------- (2)

POLARIZABILITY ()

Dipole moment is directly proportional to the electric field intensity.

  E or  = E where ‘’ is polarizability of the medium

If medium possess ‘N’ molecules per unit volume, polarization
P = NE

INTERNAL FIELD OR LOCAL FIELD OF THE CUBIC DIELECTRICS

The electric field experienced by a dipole inside the dielectric medium is called local field or
internal field Ein. It is different from the externally applied field.

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 MAGNETISM AND DIELECTRICS

Body of the dielectric between the condenser plates is shown in figure. We have to calculate the
electric field experienced by a dipole at the center of the dielectric. Let us consider a spherical
cavity with in the dielectric as shown in the figure. Polarized charges also appear on the surface
of the sphere.
Consider a molecule of dielectric at the center ‘C’of the dielectric. The dipole
experiences the following fields in addition to the applied field.
Ein = E1 + E2 + E3 + E4

Where E1 is electric field at center ‘C’ due to the charges on the surface of condenser plates.
E2 is electric field at center ‘C’ due to the charges on the surface of the dielectric
E3 is electric field at center ‘C’ due to the charges on the surface of the sphere
E4 is electric field at center ‘C’ due to the permanent dipoles inside the sphere.

But in our present case, nonpolar, isotropic dielectric, it is zero. i.e. E4 = 0

 Ein = E + E3 --------- (1) (E1 + E2 = E, externally applied field)

Consider a small element of area ‘ds’ on the surface of the sphere making an angle ‘d’
with the center and ‘’ with the field direction. The polarization will be parallel to the electric
field E.
q1
The charge on the surface element is q1 = Pcos ds ( p= , pcos is parallel component of
A
polarization)
1 q1
Electric field intensity at center ‘C’ due to this charge is dE3 =
4 0 r2
1 p cos  ds
= -------- (2)
4 0 r2

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 MAGNETISM AND DIELECTRICS

Where ‘r’ is radius of the sphere. This field intensity is along ‘r’. Therefore parallel component
of the electric field E will be dE3 cos
1 p cos  ds
dE3 = cos --------- (3)
4 0 r2
The area of the small surface element is ds = 2r(AB x BM)
BM AB AB
From fig. sin = or BM = r sin, sin d = or d  or AB = r d
r r r
ds = 2 r2 sin d
Substitute this value in equation (3), we get

P
dE3 = cos2 sin d ----------- (4)
2 0
Electric field intensity at ‘C’ due to the charges on whole sphere will be


P
E3 =  cos 2  sin  d
2 0 0
P 2
= .  put cos   t , dz   sin  d 
2 0 3
P
=
3 0

P
 Total internal field Ein = E + --------- (5)
3 0

CLAUSIUS-MOSSOTTI EQUATION:

This equation gives the relation between the dielectric constant r and polarizability 
We know  = r – 1 or
P
= –1
0E r
P = 0(r – 1) E ----------- (1)
P
Internal field Ein = E +
3 0
Substitute the ‘P’ value from equ.(1) in equ.(2)

 0 ( r  1)
Ein = E + E
3 0

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 MAGNETISM AND DIELECTRICS

  r  1
= E + 1 
 3 
r  2
=E --------- (2)
3
Polarization is also proportional to the internal field Ein.
P = N Ein -------- (3)
Where N is total no. of molecules in the dielectric,  is polarizability
r  2
0(r – 1) E = N E (from equ. (1) and (2))
3
 r  1 N
= -------- (4) is called Clausius-Mossotti equation.
 r  2 3 0
M
Multiplying the above equation by , where M is molecular weight and  is density.

 r 1 M N M
=
r  2  3 0 
 r 1 M  NA  N A x density 
= ------- (5)  number of molecules  
r  2  3 0  Molecular Weight 

Where NA is Avogadro’s number = 6.023 x 1026/kmol

 1 M
The quantity r is called molar polarization of a dielectric.
r  2 

TYPES OF POLARIZATION:

Electronic Polarization

When an electric field is applied to the atom, electrons in the atom are displaced relative to the
nucleus and produce dipole moment. Polarization arises due to the displacement of electron
cloud relative to the nucleus, with in the same atom is called electronic polarization.

Electronic polarizability (e)

As shown in the figure +ze is charge of nucleus is surrounded by an electronic cloud of charge –
ze distributed in a sphere of radius ‘R’. Thus charge density of the electrons is charge/volume,

ze  3  ze
=- =   -------- (1)
4 4   R3
 R3 
3

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 MAGNETISM AND DIELECTRICS

When this system is subjected to an external field of intensity E, the nucleus and electron
experiences a lorentz force of magnitude ZeE. Therefore electron and nucleus pulled apart
opposite direction and a coulomb attraction force is developed between them. Let the
displacement of electrons be ‘x’.
Thus Lorentz force = -ZeE
ZeE and
1  ch arg e enclosed in the sphere of radius x 
Coulomb force = Ze x
4 0  x2 

The charge enclosed in the sphere of radius ‘x’ = charge densi
density
ty x volume (with radius x)
 3  ze 4
=   3 x
 x3
 4 R 3
Zex 3
=- 3
R
3
1 Zex ( ze) ( ze) x
Hence coulomb force = Ze x 2 x - 3  = -
4 0 x R 4 0 R 3
At thermal equilibrium the two forces are equal
(ze) ( ze) x Ze x
i.e. –ze E = - 3 or E =
4 0 R 4 0 R 3
4 0 R 3 E
x= This is expression for distance of separation between the two
ze
charges when electric field is applied.
 Dipole moment e = charge x displacement
4 0 R 3 E
= ze x
ze
3
= 40R E
= e E
3
Where e = 40R is called electronic polarizability

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 MAGNETISM AND DIELECTRICS

Ionic Polarization:

This polarization occurs in ionic bonding compounds. When an electric field is applied positive
and negative ions displace in opposite directions causing a change in length of ionic bond. This
effect of change in length causes to dipole moment. So polarization arises due to relative
displacement of ions is called ionic polarization.

Let us consider m and M are the masses of the positive and negative ions respectively.
When electric field E is applied on an ionic dielectric then positive ions displace in the direction
of the applied field through x1 units of distance and negative ions displaced in opposite direction
to the field through x2 units of distance as shown fig.b

Hence net distance between two opposite ions x = x1 + x2 ---- (1)

Lorentz force acting on the positive ion = eE ---- (2)
Lorentz force acting on the negative ion = eE ---- (3)

When ions are displaced in their respective directions from the mean positions, then the restoring
force appears on the ions which tend to move the ions back to the mean positions.
 Restoring force acting on the positive ion = k1 x1 ---- (4) where k1 force constant = mω02
Restoring force acting on the negative ion = k2 x2 ---- (5) where k1 force constant = Mω02

At equilibrium position Lorentz force is equal and opposite to restoring force

Ee Ee
Hence eE = k1 x1 or x1 = and x2 =
m 02
M 02
From equation (1)
x = x 1 + x2

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 MAGNETISM AND DIELECTRICS

Ee Ee
 x= +
m 02 M 02
Ee 1 1
= [ + ]
 02 m M
But dipole moment µ = charge x displacement
Ee 1 1
=e [ + ]
 02 m M
Ee 2
1 1
= [ + ]
 02 m M

We know that ionic polarizability αi =
E
e 2
1 1
= [ + ]
 02 m M
Hence we can say that ionic polarizability is inversely proportional to square of the angular
mM
velocity ω0 and reduced mass ( ).
mM
Dipolar or Orientation Polarization:

This type of polarization only occurs in polar substances. In the absence of an external field the
orientation of these dipoles is random. So that the net polarization is zero. When applied field is
very strong these dipoles come to align. For ordinary fields these dipoles not

come to align completely because the orientation of dipoles is continuously disturbed by

temperature.
Anyway the dipole moment is induced when electric field is applied to polar molecules. This
polarization is known as dipolar polarization. This polarization is strongly temperature
dependent.
2
Polarizability 0 =
3K B T

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 MAGNETISM AND DIELECTRICS

where µ is the average dipole moment of all molecules.

FREQUENCY DEPENDENCE OF DIELECTRIC CONSTANT OR POLARIZABILITY:

Generally dielectrics are operated in alternating fields. When a dielectric is subjected to an

alternating field, the components of polarizations (dipoles or electrons or ions) must follow the
field reversals.

In audio frequency range i.e <106 Hz, all types of polarization are possible. The total
polarizability α = αo + αi + αe. (all types of polarizations are not exist in one material. This is for
general case only for explanation).

Below this frequency the dipoles will get sufficient time to follow the field changes.
Usually in the radio frequency region i.e. 106 – 1011 Hz, the permanent dipoles fail to follow the
field reversals so dipolar or orientation polarization ceases in this region. As a result εr decreases
considerably. The total polarizability is α = αi + αe .
Usually in the infra-red region, i.e. 1011-1014 Hz the positive and negative ions
cannot follow the field variations. So εr decreases, ionic polarization ceases in this region. In this
region only electronic polarization contributes to the total polarization. In the optical region the
relative permittivity will be equal to square of the refractive index of dielectric i.e. εr = n2.
In ultraviolet region, i.e. 1016-1018 Hz the electron cloud also fails to follow the field
alternations and electronic polarization ceases. Consequently the total polarization zero. Beyond
the UV region, i.e. in x-ray frequency region, the relative permittivity of the medium tends to
unity,εr = 1.

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 MAGNETISM AND DIELECTRICS

APPLICATIONS OF DIELECTRIC MATERIAL

Some of the applications of dielectrics are as follows-

 These are used for energy storage in capacitors.

 To enhance the performance of a semiconductor device, high permittivity dielectric materials
are used.
 Dielectrics are used in Liquid Crystal Displays.
 Ceramic dielectric is used in Dielectric Resonator Oscillator.
 Barium Strontium Titanate thin films are dielectric which are used in microwave tunable
devices providing high tunability and low leakage current.
 Parylene is used in industrial coatings acts as a barrier between the substrate and the external
environment.
 In electrical transformers, mineral oils are used as a liquid dielectric and they assist in the
cooling process.
 Castor oil is used in high-voltage capacitors to increase its capacitance value.
 Electrets, a specially processed dielectric material acts as electrostatic equivalent to magnets.

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 MAGNETISM AND DIELECTRICS

QUESTIONS
CHAPTER I

1. Define the terms permeability, susceptibility, magnetic flux density?

2. Define magnetic moment. Explain the origin of magnetic moment at the atomic level
3. Define magnetization and derive the relation between B,H and I
4. Explain the Classification of magnetic materials (Dia,Para ,Ferro,Anti ferro and Ferri)
5. Explain the Hysterisis loop ( B or I-H Curve) observed in ferromagnetic materials ? What are
hysteresis losses
6. Define Hard and soft magnetic materials
7. Discuss temperature dependence of susceptibility of para and ferromagnetic materials

CHAPTER II

1. What is meant by dielectrics? explain polar and non polar dieletrics

2. Define dielectric constant, electric polarization,electric susceptibility,Electric dipole, dipole
moment ?
3. Define dielectric displacement and derive the relation between D, E and P
4. Define Clausius - Mosotti Relation in dieletrics
5. Explain electronic,ionic and orientational polarization and their dependence on temperature?
6. Define Dieletric loss and dielectric strength
7. Explain the hysteresis observed in ferroelectric materials?

UNIT V Page 28