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A NAME IN CONCEPTS OF PHYSICS

9027187359, 7351266266 XI &XII (CBSE & ICSE BOARD)

IIT-JEE / NEET /AIIMS / JIPMER / uptU

MAGNETIC MATERIALS 1.

Important definitions and Relations

(i) Magnetising field or Magnetic intensity ( H ) Field in which a material is placed for magnetisation, called as magnetising field. Magnetising field = H =

Magneticfield B0 = 0 permeabiltyoffreespace

Unit of : Ampere/meter

(ii) Intensity of magnetisation ( I ) When a magnetic material is placed in magnetising field then induced dipole moment per unit volume of that material is known as intensity of magnetisation ( I ) I = Unit of I : Ampere/meter

[

M V

Ampere meter 2 M IA = = ] meter 3 V V

(iii) Magnetic susceptibility ( m) m =

I [It is a scalar with no units & dimensions] H

Physically it represent the ease with which a magnetic material can be magnetised Note :- A material with more m , can be change into magnet easily. (iv) Magnetic permeability µ µ=

Bm TotalMagneticfield inside thematerial = H Magneticfield

It measures the degree to which a magnetic material can be penetrated (or permeated) by the magnetic field line Weber HA H Wb / m2 = Am Am m A/m Relative permeability µr = (It has no units and dimensions.) 0

Unit of µ : µ =

Bm H

[ = LI Weber Henry – Ampere]

(v) Relation between permeability & susceptibility When a magnetic material is placed in magnetic field B 0 for magnetisation then total magnetic field in material B m B0 B i ,

B 0 = µ0 H ;

where B i = induced field. B i = µ0 I B m = µ0 H + µ0 I B m = µ0( H + I ) = µ0 H (1+I/H)

B I 0 1 = µ0 µ = µ0 (1 + m ) H H

µr = (1 + m )

for vacuum m = 0,

( µr = 1)

at STP for Air m = 0.04

( at S.T.P. for Air µr = 1.04)

THEORY NOTES FOR IIT - PMT

MAGNETISM

P.L. SHARMA ROAD, center

SHASTRI NAGAR center CENTRAL MARKET,

Opp. Sagar Complex Meerut

OPP. SUMIT NURSING HOME, 1ST FLOOR AIM INTERNATIONAL Page 1

A NAME IN CONCEPTS OF PHYSICS

9027187359, 7351266266 XI &XII (CBSE & ICSE BOARD)

IIT-JEE / NEET /AIIMS / JIPMER / uptU

Bar Magnet

2R

A bar magnet consist of two equal and opposite magnetic

S

pole separated by a small distance. Poles are not exactly at

N

Le = 2l

Lg

the ends. The shortest distance between two poles is called

(A) Bar magnet

effective length (Le) and is less than its geometric length (Lg). for bar magnet Le = 2l and

S

N

(B) Semicircular magnet

Le = (5/6) Lg.

for semi circular magnet Lg R and Le 2R Magnetic axis

(1) Directive properties : When a magnet suspended freely

N

S

Magnetic meridian

it stays in the earth’s N-S direction (in magnetic meridian). (2) Monopole concept : If a magnet is Broken into number of

S

N

pieces, each piece becomes a magnet. This in turn implies that S

monopoles do not exist. (i.e., ultimate individual unit of magnetism

N

S

N

S

N

in any magnet is called dipole). Q

P

(3) For two rods as shown, if both the rods attract in figure (A) and doesn’t attract in figure (B) then, Q is a magnetic and P is simple iron rod.

(A)

P

Q

(B)

Repulsion is sure test of magnetism. (4) Pole strength (m) : The strength of a magnetic pole to attract magnetic materials towards itself is known as pole strength. (i) It is a scalar quantity. (ii) Pole strength of N and S pole of a magnet is conventionally represented by +m and –m respectively. (iii) It's SI unit is amp × m or N/Tesla and dimensions are [LA]. (iv) Pole strength of the magnet depends on the nature of material of magnet and area of cross section. It doesn't depends upon length. S S S S S S S

N N N N N N N

A – more m – more

S SS SS SS

A – less m – less (B)

(A)

(5) Magnetic moment or magnetic dipole moment

(M )

:

It represents the strength of magnet. Mathematically it is defined as the product of the strength of either pole and effective length. i.e. M m(2 l ) –m

N

S L = 2l

+m

M

(i) It is a vector quantity directed from south to north. (ii) It's S.I. unit amp×m2 or N-m / Tesla and dimensions [AL2]

THEORY NOTES FOR IIT - PMT

MAGNETISM

P.L. SHARMA ROAD, center

SHASTRI NAGAR center CENTRAL MARKET,

Opp. Sagar Complex Meerut

OPP. SUMIT NURSING HOME, 1ST FLOOR AIM INTERNATIONAL Page 2

A NAME IN CONCEPTS OF PHYSICS

9027187359, 7351266266 XI &XII (CBSE & ICSE BOARD)

IIT-JEE / NEET /AIIMS / JIPMER / uptU

(6) Cutting of a rectangular bar magnet : Suppose we have a rectangular bar magnet having length, breadth and mass are L, b and w respectively if it is cut in n equal parts along the length as well as perpendicular to the length simultaneously as shown in the figure then L

Length of each part L' Mass of each part w'

w n

n

, breadth of each part b'

b n

,

,

b

pole strength of each part m'

m n

b

,

Magnetic moment of each part M ' m' L'

m

L

L

L

M n n n

If initially moment of inertia of bar magnet about the axes passing from centre and perpendicular to it’s length is L2 b 2 I w 12

then moment of inertia of each part I '

I n2

(7) Cutting of a thin bar magnet : For thin magnet b = 0 so L'

L n

, w'

w n

, m'

m n

, I'

I n3

Force and Field (1) Coulombs law in magnetism : The force between two magnetic poles of strength m1 and m2 lying at a distance r is given by F k.

m1m2 r

2

. In S.I. units k

0 10 7 wb / Amp m , In CGS units k 1 4

(2) Magnetic field (i) Magnetic field due to an imaginary magnetic pole (Pole strength m) : Is given by B

F m0

also B

0 m . 4 d 2

(ii) Magnetic field due to a bar magnet : At a distance r from the centre of magnet (a) On axial position :

Ba

0 2Mr 4 (r 2 l 2 ) 2

(b) On equatorial position : Be then Be

; If l 1

r >> 1r = 102

Intensity of magnetisation (I)

I is in a direction opposite to that of H and its value is very low

I is in the direction of H but value is low

I is in the direction of H and value is very high.

I-H curves

+I

Is

H

–I

H

Hs

H

Magnetic moment (M)

Very low ( 0)

Very low

Very high

Examples

Cu, Ag, Au, Zn, Bi, Sb, NaCl, H2O air and diamond etc.

Al, Mn, Pt, Na, CuCl2, O2 and crown glass

Fe, Co, Ni, Cd, Fe3O4 etc.

THEORY NOTES FOR IIT - PMT

MAGNETISM

P.L. SHARMA ROAD, center

SHASTRI NAGAR center CENTRAL MARKET,

Opp. Sagar Complex Meerut

OPP. SUMIT NURSING HOME, 1ST FLOOR AIM INTERNATIONAL Page 9

9027187359, 7351266266

A NAME IN CONCEPTS OF PHYSICS

XI &XII (CBSE & ICSE BOARD)

IIT-JEE / NEET /AIIMS / JIPMER / uptU

IMPORTANT: Bohr magneton B

eh 9.27×10–24 A/m2 . It serves as 4m

At the poles and equator of earth the values of total intensity are 0.66 and 0.33 Oersted respectively.

natural unit of magnetic moment.

Magnetic moment of straight current carrying wire is zero. Magnetic moment of toroid is zero Atoms which have paired electron have the magnetic moment zero.

Remember time period of oscillation in difference position is greater than that in sum position Td > Ts .

If a rectangular bar magnet is cut in n equal parts then time period of each part will be

Magnetostriction : The length of an iron bar changes when it is magnetised, when an iron bar magnetised it's length increases due to alignment of spins parallel to the field. This increase is in the direction of magnetisation. This effect is known as magnetostriction.

When a magnetic dipole of moment M moves from unstable equilibrium to stable equilibrium position in a magnetic field B, the kinetic energy will decrease by 2 MB.

Intensity of magnetisation (I) is produced in materials due to spin motion of electrons.

For protecting a sensitive equipment from the external magnetic field it should be placed inside an iron cane. (magnetic shielding)

complete magnet (i.e. T '

T n

1 n

times that of

) while for short magnet

T . If nothing is said then bar magnet is treated as n short magnet. T'

Suppose a magnetic needle is vibrating in earth’s magnetic field. With temperature rise M decreases hence time period (T) increases but at 770oC (Curie temperature) it stops vibrating.

An iron cored coil and a bulb are connected in series with an ac generator. If an iron rod is introduced inside a coil, then the intensity of bulb will decrease, because some energy lost in magnetising the rod.

Hysteresis energy loss = Area bound by the hysteresis loop = VAnt Joule;

B=0

Where , V = Volume of ferromagnetic sample, A = Area of B – H loop P, n = Frequency of alternating magnetic field and t = Time

Apparent dip : In a vertical plane inclined at an angle to the magnetic meridian, vertical component of earth's magnetic field remains unchanged while in the new inclined plane horizontal component B' H BH cos

' apparent angle of dip and tan ' tan '

tan cos

Magnetic meridian

BH

BV

BV BV BH cos BH'

BH cos

B Inclined plane

If at any place the angle of dip is and magnetic latitude is then tan = 2tan

THEORY NOTES FOR IIT - PMT

MAGNETISM

P.L. SHARMA ROAD, center

SHASTRI NAGAR center CENTRAL MARKET,

Opp. Sagar Complex Meerut

OPP. SUMIT NURSING HOME, 1ST FLOOR AIM INTERNATIONAL Page 10

View more...
9027187359, 7351266266 XI &XII (CBSE & ICSE BOARD)

IIT-JEE / NEET /AIIMS / JIPMER / uptU

MAGNETIC MATERIALS 1.

Important definitions and Relations

(i) Magnetising field or Magnetic intensity ( H ) Field in which a material is placed for magnetisation, called as magnetising field. Magnetising field = H =

Magneticfield B0 = 0 permeabiltyoffreespace

Unit of : Ampere/meter

(ii) Intensity of magnetisation ( I ) When a magnetic material is placed in magnetising field then induced dipole moment per unit volume of that material is known as intensity of magnetisation ( I ) I = Unit of I : Ampere/meter

[

M V

Ampere meter 2 M IA = = ] meter 3 V V

(iii) Magnetic susceptibility ( m) m =

I [It is a scalar with no units & dimensions] H

Physically it represent the ease with which a magnetic material can be magnetised Note :- A material with more m , can be change into magnet easily. (iv) Magnetic permeability µ µ=

Bm TotalMagneticfield inside thematerial = H Magneticfield

It measures the degree to which a magnetic material can be penetrated (or permeated) by the magnetic field line Weber HA H Wb / m2 = Am Am m A/m Relative permeability µr = (It has no units and dimensions.) 0

Unit of µ : µ =

Bm H

[ = LI Weber Henry – Ampere]

(v) Relation between permeability & susceptibility When a magnetic material is placed in magnetic field B 0 for magnetisation then total magnetic field in material B m B0 B i ,

B 0 = µ0 H ;

where B i = induced field. B i = µ0 I B m = µ0 H + µ0 I B m = µ0( H + I ) = µ0 H (1+I/H)

B I 0 1 = µ0 µ = µ0 (1 + m ) H H

µr = (1 + m )

for vacuum m = 0,

( µr = 1)

at STP for Air m = 0.04

( at S.T.P. for Air µr = 1.04)

THEORY NOTES FOR IIT - PMT

MAGNETISM

P.L. SHARMA ROAD, center

SHASTRI NAGAR center CENTRAL MARKET,

Opp. Sagar Complex Meerut

OPP. SUMIT NURSING HOME, 1ST FLOOR AIM INTERNATIONAL Page 1

A NAME IN CONCEPTS OF PHYSICS

9027187359, 7351266266 XI &XII (CBSE & ICSE BOARD)

IIT-JEE / NEET /AIIMS / JIPMER / uptU

Bar Magnet

2R

A bar magnet consist of two equal and opposite magnetic

S

pole separated by a small distance. Poles are not exactly at

N

Le = 2l

Lg

the ends. The shortest distance between two poles is called

(A) Bar magnet

effective length (Le) and is less than its geometric length (Lg). for bar magnet Le = 2l and

S

N

(B) Semicircular magnet

Le = (5/6) Lg.

for semi circular magnet Lg R and Le 2R Magnetic axis

(1) Directive properties : When a magnet suspended freely

N

S

Magnetic meridian

it stays in the earth’s N-S direction (in magnetic meridian). (2) Monopole concept : If a magnet is Broken into number of

S

N

pieces, each piece becomes a magnet. This in turn implies that S

monopoles do not exist. (i.e., ultimate individual unit of magnetism

N

S

N

S

N

in any magnet is called dipole). Q

P

(3) For two rods as shown, if both the rods attract in figure (A) and doesn’t attract in figure (B) then, Q is a magnetic and P is simple iron rod.

(A)

P

Q

(B)

Repulsion is sure test of magnetism. (4) Pole strength (m) : The strength of a magnetic pole to attract magnetic materials towards itself is known as pole strength. (i) It is a scalar quantity. (ii) Pole strength of N and S pole of a magnet is conventionally represented by +m and –m respectively. (iii) It's SI unit is amp × m or N/Tesla and dimensions are [LA]. (iv) Pole strength of the magnet depends on the nature of material of magnet and area of cross section. It doesn't depends upon length. S S S S S S S

N N N N N N N

A – more m – more

S SS SS SS

A – less m – less (B)

(A)

(5) Magnetic moment or magnetic dipole moment

(M )

:

It represents the strength of magnet. Mathematically it is defined as the product of the strength of either pole and effective length. i.e. M m(2 l ) –m

N

S L = 2l

+m

M

(i) It is a vector quantity directed from south to north. (ii) It's S.I. unit amp×m2 or N-m / Tesla and dimensions [AL2]

THEORY NOTES FOR IIT - PMT

MAGNETISM

P.L. SHARMA ROAD, center

SHASTRI NAGAR center CENTRAL MARKET,

Opp. Sagar Complex Meerut

OPP. SUMIT NURSING HOME, 1ST FLOOR AIM INTERNATIONAL Page 2

A NAME IN CONCEPTS OF PHYSICS

9027187359, 7351266266 XI &XII (CBSE & ICSE BOARD)

IIT-JEE / NEET /AIIMS / JIPMER / uptU

(6) Cutting of a rectangular bar magnet : Suppose we have a rectangular bar magnet having length, breadth and mass are L, b and w respectively if it is cut in n equal parts along the length as well as perpendicular to the length simultaneously as shown in the figure then L

Length of each part L' Mass of each part w'

w n

n

, breadth of each part b'

b n

,

,

b

pole strength of each part m'

m n

b

,

Magnetic moment of each part M ' m' L'

m

L

L

L

M n n n

If initially moment of inertia of bar magnet about the axes passing from centre and perpendicular to it’s length is L2 b 2 I w 12

then moment of inertia of each part I '

I n2

(7) Cutting of a thin bar magnet : For thin magnet b = 0 so L'

L n

, w'

w n

, m'

m n

, I'

I n3

Force and Field (1) Coulombs law in magnetism : The force between two magnetic poles of strength m1 and m2 lying at a distance r is given by F k.

m1m2 r

2

. In S.I. units k

0 10 7 wb / Amp m , In CGS units k 1 4

(2) Magnetic field (i) Magnetic field due to an imaginary magnetic pole (Pole strength m) : Is given by B

F m0

also B

0 m . 4 d 2

(ii) Magnetic field due to a bar magnet : At a distance r from the centre of magnet (a) On axial position :

Ba

0 2Mr 4 (r 2 l 2 ) 2

(b) On equatorial position : Be then Be

; If l 1

r >> 1r = 102

Intensity of magnetisation (I)

I is in a direction opposite to that of H and its value is very low

I is in the direction of H but value is low

I is in the direction of H and value is very high.

I-H curves

+I

Is

H

–I

H

Hs

H

Magnetic moment (M)

Very low ( 0)

Very low

Very high

Examples

Cu, Ag, Au, Zn, Bi, Sb, NaCl, H2O air and diamond etc.

Al, Mn, Pt, Na, CuCl2, O2 and crown glass

Fe, Co, Ni, Cd, Fe3O4 etc.

THEORY NOTES FOR IIT - PMT

MAGNETISM

P.L. SHARMA ROAD, center

SHASTRI NAGAR center CENTRAL MARKET,

Opp. Sagar Complex Meerut

OPP. SUMIT NURSING HOME, 1ST FLOOR AIM INTERNATIONAL Page 9

9027187359, 7351266266

A NAME IN CONCEPTS OF PHYSICS

XI &XII (CBSE & ICSE BOARD)

IIT-JEE / NEET /AIIMS / JIPMER / uptU

IMPORTANT: Bohr magneton B

eh 9.27×10–24 A/m2 . It serves as 4m

At the poles and equator of earth the values of total intensity are 0.66 and 0.33 Oersted respectively.

natural unit of magnetic moment.

Magnetic moment of straight current carrying wire is zero. Magnetic moment of toroid is zero Atoms which have paired electron have the magnetic moment zero.

Remember time period of oscillation in difference position is greater than that in sum position Td > Ts .

If a rectangular bar magnet is cut in n equal parts then time period of each part will be

Magnetostriction : The length of an iron bar changes when it is magnetised, when an iron bar magnetised it's length increases due to alignment of spins parallel to the field. This increase is in the direction of magnetisation. This effect is known as magnetostriction.

When a magnetic dipole of moment M moves from unstable equilibrium to stable equilibrium position in a magnetic field B, the kinetic energy will decrease by 2 MB.

Intensity of magnetisation (I) is produced in materials due to spin motion of electrons.

For protecting a sensitive equipment from the external magnetic field it should be placed inside an iron cane. (magnetic shielding)

complete magnet (i.e. T '

T n

1 n

times that of

) while for short magnet

T . If nothing is said then bar magnet is treated as n short magnet. T'

Suppose a magnetic needle is vibrating in earth’s magnetic field. With temperature rise M decreases hence time period (T) increases but at 770oC (Curie temperature) it stops vibrating.

An iron cored coil and a bulb are connected in series with an ac generator. If an iron rod is introduced inside a coil, then the intensity of bulb will decrease, because some energy lost in magnetising the rod.

Hysteresis energy loss = Area bound by the hysteresis loop = VAnt Joule;

B=0

Where , V = Volume of ferromagnetic sample, A = Area of B – H loop P, n = Frequency of alternating magnetic field and t = Time

Apparent dip : In a vertical plane inclined at an angle to the magnetic meridian, vertical component of earth's magnetic field remains unchanged while in the new inclined plane horizontal component B' H BH cos

' apparent angle of dip and tan ' tan '

tan cos

Magnetic meridian

BH

BV

BV BV BH cos BH'

BH cos

B Inclined plane

If at any place the angle of dip is and magnetic latitude is then tan = 2tan

THEORY NOTES FOR IIT - PMT

MAGNETISM

P.L. SHARMA ROAD, center

SHASTRI NAGAR center CENTRAL MARKET,

Opp. Sagar Complex Meerut

OPP. SUMIT NURSING HOME, 1ST FLOOR AIM INTERNATIONAL Page 10

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