154 U-4 Magnetic Materials

8/7/2019 154 U-4 Magnetic Materials

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Name o the Facult : Mr D Pavan Kumar, Ms B Bhar aviVenkat

UNIT-4

MAGNETIC PROPERTIES

INTRODUCTION:

The magnet attracts iron pieces which in turn, behave like magnets as long as they are

in contact with the magnet.

Magnetic materials can be magnetized by the application of external magnetic fields.

Magnetism arises from the magnetic moment (or) magnetic dipole of the magnetic

materials.

When the electron revolves around the positive nucleus, orbital magnetic moment

arises. Similarly when the electron spins, magnetic moment arises.

Magnetic dipole is a system consisting of 2 equal and opposite poles separated by a

small distance.

Magnetic moment is defined as the product of its pole strength and magnetic length.

i.e. M=m*2l=2lm units: A-m2

where m is pole strength and

2l is distance between 2 poles.

When current iflows round a circular wire of one turn and area a, it is said to have a

magnetic dipole moment M= ia

Under magnetic field of induction B, the force acting on a moving charge q is given by

F=q (v*B)

If the charge moves under both E and B then F=q (E+v*B)

According to Amperes law dlH. = I

H dl = i

H=

r

i

2

MAGNETIC INDUCTION (B):- It is defined as the force experienced by a unit north pole

placed at a point in the magnetic field. It is also defined as number of magnetic lines of

force crossing per unit area normal to the surface. B =A

Units : Tesla (or) Wb/m2

INTENSITY OF MAGNETIZATION (I):-It is defined as the magnetic moment per unit

volume. It is given by I =V

Units : Amp-m-1


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MAGNETIC FIELD INTENSITY (H):-It is defined as the ratio of magnetic induction and

the permeability of the medium. It is given by

BH ( HB ) Units : Amp-m-1

MAGNETIC PERMEABILITY: ( ) - The magnetic field induced at a given point by a

magnet depends on the nature of the medium

The ability of the medium to alter the vacuum field is described by a factor called

permeability of the medium. It is denoted by .

The magnetic induction B due to a magnetic field of intensity H applied in vacuum is

given by B = Ho where o is permeability of free space and its value is 4 mHX /107 .

In a medium this relation can be written as B = H =H

B

Def: It is also defined as the ratio of magnetic induction in the sample to the applied field

intensity.

RELATIVE PERMEABILITY: It is defined as the ratio of permeability of a medium to the

Permeability of free space. It is given byo

r

MAGNETIZATION:

It is the process of converting a non-magnetic material in to a magnetic sample.

The iron rod will be magnetized when it is subjected to a magnetic field H.

It is due to the polarization of magnetic dipoles within the body.

The intensity of magnetization(I) is directly proportional to the applied field intensity(H).

i.e., I H I = HB where B is magnetic susceptibility.

MAGNETIC SUSCEPTIBILITY (B

): we know thatB

=H

I.

Def: It is defined as the ratio of intensity of magnetization to the applied field.

RELATION BETWEEN B, H and I :

If an specomen is placed in an external magnetic field of magnetic flux density B0, the

net magnetic flux density B is given by

B= B0+Bm

Where B0 = o H, lines of force crossing unit area due to external field

Bm = o I, lines of force crossing unit area due to Intensity of Magnetization

B=o

H +o

I =o

(I+H)


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RELATION BETWEENr

andB : We know that B = H

B =r

o

H ( sinceo

r

)

B =r

o

H +o

H -o

H

B = o H + o H ( r -1) ------(1)

And alsoB =o

(I+H) because the magnetic induction at any point is due to H and I.

Bo

H +o

I ---------(2)

Comparing equ(1) and equ---(2), we get I = H(r

-1) H

Ir

-1

r

= 1+H

I

r

= 1+B

ORIGIN OF MAGNETIC MOMENT:

The magnetic moment in a material due to the orbital motion and spinning motion of

electrons in an atom.

when a magnetic moment is obtained through the motion of electrons in various orbits

of an atom, it is called orbital magnetic moment.

In an atom, every two electrons will form a pair

and they have opposite spins. Thus resultant

spin magnetic moment is zero.

But in magnetic materials like iron, cobalt, nickel,

there are unpaired electrons.

This unpaired electrons contributes spin magnetic moment.

These unpaired electron spins are responsible for ferro and paramagnetic behavior of

materials.

The value of spin magnetic moment is larger than orbital magnetic moment.

Note: Magnetic moment arises due to

1) Magnetic moment due to orbital motion of the electron: The revolving and rotating electrons constitute current loops.

Each loop is like a magnet with one face as a north pole and

Other face as a south pole.

consider an electron moving in a circular orbit of radius r

With angular velocity . Current produced due to this


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Motion is given by I =T

e

t

q where T is the time taken to complete one revolution.

The magnetic moment associated with this electron is 2rT

eiA . Where 2r is area

of the circular orbit.

we know that = 2 n =T

2 T =

2.

=

2

2re

= rer

2=

2

erv------ (1)( )rcityvlinearvelo

In case of circular motion, Angular momentum L = mvr vr = L/m.

From equa-----(1),m

eLl

2

m

e

L

l

2

The ratio of orbital magnetic moment l to the angular momentum L is known as

Gyro magnetic ratio.

Lm

el

2 ------ (2)

According to quantum theory, the angular momentum is given by L = l2

h----- (3)

From (2) and (3). We get

22

lh

m

el = l

m

eh

4------- (4) (l is orbital quantum number).

Here

m

eh

4is known as Bohr magneton.

lBl

Its value is given by B

m

eh

4= 9.27X10-24 A-m2

Bohr magneton:The magnetic moment contributed by a single electron is known as

Bohr Magneton. It is represented by B

m

eh4

Note: Bohr magneton is the fundamental unit for magnetic moment.

2) MAGNETIC MOMENT DUE TO SPIN MOTION: An electron spins around itself which produces spin magnetic moment. According to

quantum theory, the spin angular momentum is +4

hor -

4

h.

The relation between spin angular momentum S and spin magnetic moments

is given

bys

= Sm

e

,=

m

eh

4= B Bs


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Thus spin magnetic moment is Bohr magneton.

3) MAGNETIC MOMENT DUE TO SPIN OF PROTON:

Magnetic moment due to nucleus spin is given byn

=

pm

eh

4

Where mp is the mass of proton.

n = 5.05X10-27A-m2

The valuen

is small compare toB

. So this contribution can be neglected.

CLASSIFICATION OF MAGNETIC MATERIALS:

Magnetic materials are classified on the basis of magnetic properties of the atomic

dipoles and the interaction between them.

If the atoms of an element possess net moment, they act as magnetic dipoles.

Based on the nature and degree of response to the external magnetic fields, materials

are classified into different magnetic materials.

Based on the values of relative permeability and magnetic susceptibilityB

the

materials are classified into Dia, Para and Ferro magnetic materials.

Materials which lack permanent dipoles are called diamagnetic.

If the permanent dipoles do not interact among themselves, the material is

paramagnetic.

If the interaction among permanent dipoles is strong then the material is

Ferromagnetic material.

If the permanent dipoles line up in anti parallel the material is anti-ferromagnetic.

Based on the nature of magnetization curve ( Hysterisis), ferromagnetics are divided

into soft and hard magnetic materials.

DIAMAGNETIC MATERIALS:

The substances which are repelled by magnetics are called diamagnetic materials.

Ex :- Antimony, Bismuth, Copper, etc.,

The atoms in the diamagnetic material contains as many electrons orbiting in

clockwise as in anticlockwise direction.

Thus net magnetic moment is zero in these materials.

PROPERTIES:

The induced magnetic moment is always in the opposite direction of the applied

magnetic field.

Permanent dipoles are absent.

When placed in a magnetic field, the magnetic lines of force are repelled.


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In the non uniform magnetic field they move from

stronger part to weaker part of the field.

If it is suspended freely it comes to rest perpendicular

to the direction of field.

The magnetic lines of force shows less performanceto pass through the substance than through the air,

so relative permeability r is less than 1.

The susceptibility B is small and negative.

The diamagnetic susceptibility is independent of temperature.

PARA MAGNETIC MATERIALS:

The substances which are attracted by the magnet are called paramagnetic.

The induced magnetism is the source of Para magnetism.

Ex :- Aluminum, Platinum, Tungsten, Nitrogen, Mn, CuCl2, etc.,

PROPERTIES:

The spin of unpaired electrons is responsible for paramagnetic behavior of materials.

The induced magnetism is in the direction of applied magnetic field.

In each atom there is a resultant magnetic moment even in the absence of magnetic

field. Spin alignment is as shown in the figure.

But due to thermal agitations,orientation is random.

Thus the material is unmagnified.

When placed in a non-uniform magnetic field, they

move from weaker part to stronger part of the field.

If it is suspended freely it comes to rest in the field

direction. The magnetic lines of force shows little more

performance to pass through the substance than

through air. So r is greater than 1.

Susceptibility B is small and positive.

The paramagnetic susceptibility is inversely

proportional to temperature.i.e., Tm

1


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EXPRESSION FOR PARAMAGNETIC SUSCEPTIBILITY:

Paramagnetic materials possess permanent magnetic dipoles.

But the dipoles are randomly oriented.

Consider a magnetic dipole which is oriented with an angle with the field direction.

The work done in rotating the dipole through an angle will be W= -Bcos ------ (1)

According to statistical mechanics, the no.of molecules whose axes makes with the

field direction is proportional to KTW

e

The no of atoms with in the solid angle 2sind per unit volume is given by

dn = c KTW

e

2sind

n = c

0

cos

KT

B

e 2sind

n = 2c

0

cos

KT

B

e sind

The total magnetic moment is cos N

Total magnetic moment = 2c

0

cos

KT

B

e dsincos

The average magnetic moment is given bysnoofdipole

ticmomenttotalmagne

=

dec

d

KT

B

sin2

sin2ecosc

0

cos

0

KT

Bcos

Put a =KT

Band cos = x -sind=dx and limits are changed from 1 to -1.

Now the above integration becomes =

a

a1

coth = )(aL ---- (2)

Where L(a) is Langevins function. Its value is aa

aa

ee

ee

CASE (1)For larger values of a i.e. for high field strengththe function approaches to saturation value unityThus a >>1, L(a)1CASE (2)

if a


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Intensity of magnetization I = N = NKT

B

3

2=

KT

HN

3

0

2

SusceptibilityB

=H

I=

KT

N

3

0

2=

T

Cwhere C is called curies constant.

B T

1

This is called curies law.

Note: Weissformulated the following relation from the Curies law as

B =

T

Cwhere is Curie temperature.

If T>1.

Spin alignment is parallel in the same direction.


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SusceptibilityB is large and positive.

SusceptibilityB

depends on temperature in the following mannercTT

T

When heated these materials turn into paramagnetic materials above a temperature

known as CURIE TEMPERATURE.

The stronger effect of ferromagnetism is explained on the basis of magnetic dipole

domains.

DOMAIN THEORY OF FERROMAGNETISM:

Weiss proposed the concept of domains in 1907 to explain the hysterisis effect of

ferromagnetic.

A region of ferromagnetic material where all the magnetic moments are aligned in the

same direction is called domain.

These domains are oriented randomly so that

the net magnetic moment is always zero.

Each domain posses dipoles aligned in the

same direction. Fig

When magnetic field is applied the domains may

tend to rotate in the direction of B

Thus magnetic material will be strongly magnetized

by the external magnetic field induction B.

In ferromagnetism the adjacent atomic dipoles are

interact with exchange coupling.

HYSTERISIS CURVE: (OR) Behavior of ferromagnetic material below Curie

Temperature:

Below the Ferro magnetic Curie temperature ferromagnetic materials exhibit thehysteresis in B verses H curve as shown in figure.

Hysterisis refers to the lag of magnetization (I) or (B) behind the magnetizing field (H).


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The variation of flux density B with magnetic field intensity H is not linear. But it

performs a closed loop is known as hysteresis loop.

Take a magnetic material completely in the unmagnified state.

If we increase the applied magnetic field

the magnetization of the material first increasesrapidly and then slowly until it attains a

saturation value.

Now the magnetic field is decreasing the rate

of decrease of magnetization is less.

Thus some amount of magnetism is present

in the material even at H=0

This is known as residual magnetism (or)remanant magnetism (Br).

For certain values of negative magnetizing force, Hysterisis curve of Ferromagnetic

Magnetic induction B becomes zero.

The amount of negative field which is used to destroy the residual magnetism is known

as coercivity or coercive field Hc.

Further increasing the magnetic field in the same direction we attain negative

saturation value.Finally the field once again reversed to get complete close loop.

Thus B is lagging behind H. This is known as hysteresis.

APPLICATIONS OF DIFFERENT MAGNETIC MATERIALS:

Magnetic Recording: Magnetic recording heads are the miniaturized hearts of disk

drives and other magnetic storage devices.

Magnetic Memories: For Random Access storage in Computers, Ferrite-Core

memories are used. Permanent Magnets: Barium Ferrite and Strontium Ferrites are the materials used

for these applications.

Soft Ferrites used in Inductor cores, transformer Cores.

Ferrimagnetic Materials can be manufactured in the form of Pressed and Sintered

Ceramic powders.


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SOFT AND HARD MAGNETIC MATERIALS:

Hysteresis is the loss of energy in taking a ferromagnetic body through a complete

cycle of magnetization and this loss is represented by the area.

Based on the area of hysteresis magnetic materials are classified into hard and soft

materials.Their properties are given below

SOFT MAGNETIC MATERIALS

1.The figure shows nature of hysteresis

loop of soft materials.

2. These materials can be easilymagnetized and demagnetized.

3.They have small hysteresis loss due

to small area of loop.

4.In these materials the domain wall

movement is easier. Even for a small

change in applied field there is a

large change in the magnetization.5.The coercivity and retentivity are

small.

6.They have high value of

susceptibility and permeability.

7. The magnetostatic energy is very

small since these are free from

irregularities.

HARD MAGNETIC MATERIALS

1.The figure shows nature of hysteresis

Loop of hard materials.

2.These materials can not be easily

magnetized and demagnetized.

3.They have large hysteresis loss due

to large area of loop.

4.In these materials the domain wall

movement is difficult because of

presence of impurity and defects.

5.The coercivity and retentivity are

large.

6.They have small value of

susceptibility and permeability.

7. Because of presence of impurities

and defects the mechanical strain is

more. The magneto static energy is

more.


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8. Ex:-Iron-Silicon alloys, Fe-Ni,

Ferrites and Fe-Co alloys.

APPLICATIONS:

1. These are used as magnetic cores

for direct current applications.2. They are also used in switching

circuits.

3. Iron-Nickel alloys are used for

audio frequency applications

8. Ex:- Al-Ni-Co alloys, Cu-Ni-Co

alloys and Cu-Ni-Fe alloys.

APPLICATIONS:

1. These are used to prepare

Permanent magnets.2. Permanent magnets are used in

magnetic detectors , micro phones,

flux meters and voltage regulators.

Uses of Hysterisis Curve to select the material:

The properties of Hysterisis curve i.e., saturation, Retentivity and Coercivity helps to

choose the material

(1). Permanent magnets: The permanent magnetic material must retain large residual

magnetism. Thus it must have large coercivity. Permanent magnets are used in galvanometers, Voltmeters, Ammeters,

Microphones, Loud Speakers , telephones, etc.,

(2). An electromagnetic core: The electromagnetic core material should have maximum

flux density B even with small fields H, low hysterisis loss and high permeability.

(3). Transformer cores, Dynamo Core, Chokes, Telephone Diaphragms, etc.,: The

core material should have high permeability, low hysterisis loss and high specific

resistance. Soft iron is suited material.


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