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

1/15/2017 1Dr A K Mishra, Academic Coordinator, JIT Jahangirabad

Engineering Physics II

Presentation by

Dr.A K Mishra

Associate Professor

Jahangirabad Institute of Technology, Barabanki

Email: [email protected]

[email protected]

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

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.


0C

rr0

CC

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


dC 00

A

0

0K

r

d AC

continued

From equation (2) & (4)…………………..(5)


00 C

Cr

K

d

A 0

KC

dC rA 0

• 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 areelectrical insulators and they are mainly used to store electrical energy.

• All dielectrics are electrical insulators and they are mainly used to storeelectrical energy.

Ex: Mica, glass, plastic, water & polar molecules


+q -qX

Dielectric polarizationDielectric 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, CO 2



Unpolarized

Polarized by an applied electric field

+ + + + + + + + + + +

- - - - - - - - - - - - -

• Unpolarized and Polarized


++

+

+

++++

++

+

+++++

--

-

-----

--

-

-----

- + - + - + - +- + - + - + - +

- + - + - + - +

- + - + - + - +

- + - + - + - +

- + - + - + - +

- + - + - + - +

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

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


ipPP P -

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, CO 2


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


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 .


AP

Q

QA

Q

P

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 .


1q

1q 2 4 r

D

1q r

P

Line of forces from 1q

A

qD

q 12

4

r1

1q

q2

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/


q2 F

q 2

F

E

1

4

4 F

rqq

q 21

22

21

2

rq

qE

Er

E

0 D

E D D

rE 0

D

M 2

r

Relation between , ,


ED

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

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 permitivityof the material.

• The 3 vectors D,E and P are related by the equation D= є0 E+PP= є0 (єr -1)E


Various polarization processes:

When the specimen is placed inside a d.c. electric field, polarization is due to four types of processes.1.Electronic polarization2.Ionic polarization3.Orientation polarization4.Space charge polarization


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.


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

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 thenPolarization can be given as


E

E

iip

p i

E N ip i

Na Cl

No Field E= 0

r 0

(a)

Na Cl

Field E(b)

r0 xx

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.


Epp

o

o

o

E

o

ab

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.


No FieldE=0

Field E

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


oei

i & e i & e

d

od

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


pi pi pi pi pi

dd d

A B C D E

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)


Epi

dECB 2

0

i

4

2

p

dp

dp

3

0

i3

0

i

4

2

)(- 4

2

E CD

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 wilbe given as

- ………………(6)


dp

E 3

0

iCD

E CB

(2d)p

E 3

0

iCE

4

2

ECA (-2d)

p3

0

i

4

2

(2d)p

E 3

0

iCE

ECA

(d)p

3

0

i

E

E i (2d)

p3

0

i

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


(d)p

3

0

i

E

E i (2d)p

3

0

i

(3d)p

3

0

i

(d)p

3

0

i

E

E i

................................. 1 1 1

(3)(2) 33

1 33

0

i 1

E

(d)p

ni nE

1 31

n n

(d)p

3

0

i

2 x 1 E

E i

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 ,


d 31

0

i

N 2 x 1 E

p E i

2 x 1

p piN

p E 0

E i

0l 3

p E E

E i

31

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


pi

E l

E L p i

p

Ep Li N N

p

E LNp

0l 3

p E E

E i

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


03

p EN

p

E 1 - r0

p

1 - p

r0

E

E

0r0 3p

1 - pN

p

31

1 - 1

1

r

0

N

1 - 32

1

r

r0

N 2

1 - r

03

r

N

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.


r0

0

00 1

1

mediumin waveofVelocity

in vaccume waveofVelocity n

1 v

0

1 0

v m

2

1 -

3 nn

2

2

0

N

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.


ppp eio

p

Pola

rizat

ion

FrequencyVariation of dielectric constant with frequency

pe

pe pi

pp oe pi

Microwave Infrared Ultraviolet

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.


106

106 1011

1011 1014

1015

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:

.


Curr

ent

Voltage

I c

I RO

I

(a)

cDielectric

cI R

I c

R

(b)

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. cLet 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)


I RI C

900 I C I RI C I

I R 900 I C I

cosI cI

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.


sin cos

I c

V

tan cIVX c

c f 21

X c

X cI c

c f 2 V V Xc

I c

c f 2 V V c f 2 2 V

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.


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.


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


VI M

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.


H I

H mI

HI

m

m

Relative permeability ( )


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 BH B

H 00 B 0

Relative between and


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

)HIH(1

0 H

) (1 m0

m0

1

m 1

r

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


Te i

Magneton.Bohr clled is and ofmoment magnetic theshows this)m 4

eh(n

m 22e M thus

m 2nh r v

2

r vm

iselectron ofmomentun angular postulate,Bohr 2

evr . r 2

evA i M

by given ismoment magneic now r 2

ev

)speed

distance Time ( v

r 2

r 2

M

nh

nhfrom

i

T

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.


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 r

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.gAlluminiun , Platinum, chromium , magnese, copper sulphate ,oxygen.


1 r

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 r

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)


21 - and

21

0

o0

2

02

0r re whe

rm

r m vv f e

F m

) B x v ( e F m

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)


veF m

F e F e

F m

e

v

(a) (b)

dtd -



(6).................... dtd

r 2e -

dtdv

dtd - .

r 2e

dtdvm

Hence )5.(....................r 2

E

electron for the usecan weere

V Ecapaitor plate parallelin know we.......(4).......... E e dtdvm

i.eelectron theaccelarate f m e

m

Hd

This

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.


2meBr -

r 2e - dv

d .r 2

e - dv m

get we, 6 eqfron henceA) B ( 0 -

r

rr

2

22

B

BBd

)8.....(..........2

e x e x

2 M

area x chargex Frequency A i Mbygiven ismoment magnetic Then the

moment magneticin change a producesit andfrequency Larmor called isfrequency in change

)7.......(..........2meB -

rdv

r r2

2 B

This

d

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


)........(9.......... m 2B e -

2 e

2

e M rr 22

Hence

smean value showing arey &on x bars wheresay) ( 3

aton symmetricy sphericallfor and

can write then weaxis-z along is field theif

r) of projection thebe ( ......(10).......... 4meB -

ryx

yxr

r

222

2221

121

rM



strength. field as wellas e tempraturoft independen and ve- is substance diamagneic ofity suceptibil shows (12)equation

..(12).......... m 6 n

- H m 6H n

- HI

bygiven isity suceptibil thehence m 6

Bn I

is eunit volumper

molecules ofnumber n afor ion magnetizat ofintensity theH B and VM I

thatknow but we 11).........(.......... 32

m 4B

- M

gives (9)equation there therefo3

2

reere

re

ryx

22

22

m

22

22

2222

1

r

r


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

ab

C

d

ef

g

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).................... cos m M

Continued……………….Now, the torque acting on dipole is


m

cosm

sin m

.....(4).................... d sin m - dM(1) eq using in increase toduemoment magneticin Change

)........(3..........d Sin H m - dW

d - dW is d to from rotatingin done work theTherfore

H B

..(2).................... sin H M

sin B m

0

0

0

Continued……..

From eq (3) and (4)

Now


.....(6)dM........ H dM H W

is cycle complete afor material theof eunit volumper field gmagnetizin heby done work theThus

.(5).................... dM H

00

0

dW

dH H - dB H dM H

dM H dH H dB H

dM dH dB

) M (H B

know wenow

.(7)..........loop...... H-M of area x

00

00

00

0

0

W


• 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.


curve. H-B of area toequal is eunit volumper ion magnetizat ofcycle complete a during discipatedenergy or done work theThus

Curve HB of Area

0 dH H Since dH H - W

) dH H - dB H (

0

0

W

HdB

W

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.
