MAHARASHTRA STATE BOARD CLASS XI AND XII PHYSICS CHAPTER 11 MAGNETIC MATERIAL

1. Chapter 11
Magnetic Materials
MAHARASHTRA STATE BOARD

2. Can You Recall?
1. What are magnetic lines of force?
Magnetic Lines of Force is a an imaginary line
representing the direction of magnetic field such
that the tangent at any point is the direction of the
field vector at that point.
2. Why magnetic monopoles do not exist?
A magnetic monopole does not exist . Just as the two faces of a current loop
cannot be physically separated, magnetic North pole and the South pole can
never be separated even on breaking a magnet to its atomic size.
3. Which materials are used in making magnetic compass needle?
The needle of magnetic compass is made of steel. This material can be
magnetised for an extended period. On the other hand, plastic, wood and paper
are non-magnetic substances and hence, can not be magnetised in order to
indicate directions.

3. • Toque on a bar magnet in a magnetic field
If a bar magnet placed in uniform magnetic field
𝜏 = 𝑚𝐵 sin 𝜃
Bar magnet will perform rotational motion
Due to any displacement
Work will be done
(Work – Stored in the form of P.E.)
We say magnetic Potential Energy.
𝑈𝑚 =
0
𝜃
𝜏 𝑑𝜃
𝑈𝑚 = 0
𝜃
𝑚𝐵𝑠𝑖𝑛 𝜃 𝑑𝜃 = −𝑚𝐵 sin 𝜃

4. • Toque on a bar magnet in a magnetic field
Case I: At 𝜃 = 00
𝑈𝑚 = −𝑚 𝐵
Case II: At 𝜃 = 1800
𝑈𝑚 = 𝑚 𝐵
Case III: At 𝜃 = 900
𝑈𝑚 = 0
Where, m – Magnetic Moment
B – Magnetic Field
𝜃 − 𝐴𝑛𝑔𝑙𝑒
• Two magnet suspended Freely –
Mutual Perpendicular to each other

5. • Two magnet suspended Freely – Mutual Perpendicular to each other
At equilibrium: 𝜏 = 𝐼 𝛼
𝜏 = 𝐼
𝑑2𝜃
𝑑𝑡2 __________ (i) 𝛼 =
𝑑𝜔
𝑑𝑡
=
𝑑
𝑑𝑡
𝑑𝜃
𝑑𝑡
𝐼 → 𝑀𝑜𝑚𝑒𝑛𝑡 𝑜𝑓 𝑖𝑛𝑒𝑟𝑡𝑖𝑎
𝛼 → 𝐴𝑛𝑔𝑢𝑙𝑎𝑟 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛
𝜃 → 𝐴𝑛𝑔𝑢𝑙𝑎𝑟 𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡
𝜔 → 𝐴𝑛𝑔𝑢𝑙𝑎𝑟 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦
If we rotate magnet in opposite direction:
Torque will be opposite
𝜏 = −𝑚𝐵 sin 𝜃 ______________(ii)
(-ve sign: Bar magnet is rotating in opposite direction)
From equation (i) and (ii)
∴ 𝐼
𝑑2𝜃
𝑑𝑡2 = −𝑚𝐵 sin 𝜃

6. If 𝜃 → 𝑉𝑒𝑟𝑦 𝑠𝑚𝑎𝑙𝑙 𝑡ℎ𝑒𝑛 sin 𝜃 ≈ 𝜃
∴ 𝐼
𝑑2𝜃
𝑑𝑡2 = −𝑚𝐵 𝜃
𝑑2𝜃
𝑑𝑡2 = −
𝑚𝐵
𝐼
𝜃
Here,
𝑚𝐵
𝐼
→ 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡
𝐼 → 𝑀𝑜𝑚𝑒𝑛𝑡 𝑜𝑓 𝐼𝑛𝑒𝑟𝑡𝑖𝑎
𝐵 → 𝑀𝑎𝑔𝑛𝑒𝑡𝑖𝑐 𝐹𝑖𝑒𝑙𝑑
𝑚 → 𝑀𝑎𝑔𝑛𝑒𝑡𝑖𝑐 𝑚𝑜𝑚𝑒𝑛𝑡
As we studied in Simple Harmonic Motion (S.H.M)
𝑑2𝑥
𝑑𝑡2 = −𝜔2𝑥
Where, 𝑥 → 𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡
𝑑2𝑥
𝑑𝑡2 → 𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛
On comparing, 𝜔2
=
𝑚𝐵
𝐼

7. ∴ 𝜔 =
𝑚𝐵
𝐼
Time period for Bar Magnet, ∴ 𝑇 =
2𝜋
𝜔
∴ 𝑇 =
2𝜋
𝑚𝐵
𝐼
= 2𝜋 ×
𝐼
𝑚𝐵
∴ 𝑇 = 2𝜋
𝐼
𝑚𝐵
Examples
A bar magnet of moment of inertia of 500 𝑔 𝑐𝑚2 makes 10 oscillations per
minute in a horizontal plane. What is its magnetic moment, if the horizontal
component of earth's magnetic field is 0.36 gauss?
Ans: 𝑇 = 2𝜋
𝐼
𝑚𝐵

8. Examples
A bar magnet of moment of inertia of 500 𝑔 𝑐𝑚2
makes 10 oscillations
per minute in a horizontal plane. What is its magnetic moment, if the
horizontal component of earth's magnetic field is 0.36 gauss?
Given: Moment of Inertia I = 500 𝑔 𝑐𝑚2
Frequency n = 10 oscillation per minute = 10/60 oscillations per
second
Time period T = 6 sec
𝐵𝐻 = 0.36 gauss
𝑇 = 2𝜋
𝐼
𝑚𝐵
𝑚 =
4𝜋2𝐼
𝑇2𝐵
=
4 × (3.14)2 ×500 ×10−7
36 × 0.36 × 10−4
m = 1.524 𝐴 𝑚2

9. 𝑀𝑎𝑔𝑛𝑒𝑡𝑖𝑠𝑚 → 𝐴𝑡𝑜𝑚𝑖𝑐 𝑠𝑡𝑟𝑢𝑐𝑡𝑢𝑟𝑒 → 𝐷𝑒𝑝𝑒𝑛𝑑
Origin of Magnetism in Materials:
Electron Revolving around the nucleus
↓
Magnetic Dipole Moment
(m = IA)
Where, I → Moment of Inertia
𝑚 → 𝑚𝑎𝑔𝑛𝑒𝑡𝑖𝑐 𝑑𝑖𝑝𝑜𝑙𝑒 𝑚𝑜𝑚𝑒𝑛𝑡
A → 𝐴𝑟𝑒𝑎 𝑅𝑜𝑡𝑎𝑡𝑒𝑑 𝑏𝑦 𝑒−
• Magnetism depends upon atom.

10. Magnetic Moment of an Electron Revolving Around the
Nucleus of an Atom:
Intrinsic Angular
Momentum
Magnetic dipole moment due to current loop is,
m = I A
Where, m → magnetic Dipole
(Orbital Magnetic Moment)
I → Current
A → Area enclosed by loop
Consider, An electron moving in an orbit with constant
velocity (v),
Having radius r about nucleus
Electron covers distance of circumference i.e. 2𝜋𝑟 in time
𝑆𝑝𝑒𝑒𝑑 =
𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝑇𝑖𝑚𝑒
=
2𝜋𝑟
𝑇

11. Magnetic Moment of an Electron Revolving Around the
Nucleus of an Atom:
Intrinsic Angular
Momentum
Current associated with charge 𝑒− is,
𝐼 =
𝑒
𝑇
_______(i)
∴ 𝐹𝑜𝑟 𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑠𝑝𝑒𝑒𝑑, 𝑇 =
2𝜋
𝜔
We get from (i), 𝐼 =
𝑒
2𝜋
𝜔
=
𝑒𝜔
2𝜋
𝐼 =
𝑒𝜔
2𝜋
As 𝑣 = 𝜔 𝑟 i.e. 𝜔 =
𝑣
𝑟
∴ 𝐼 =
𝑒𝑣
2𝜋𝑟
Now, For orbital magnetic moment: 𝑚𝑜𝑟𝑏 = 𝐼𝐴
𝑚𝑜𝑟𝑏 =
𝑒𝑣
2𝜋𝑟
𝜋𝑟2 =
1
2
evr ________ (ii)

12. Magnetic Moment of an Electron Revolving Around the
Nucleus of an Atom:
Intrinsic Angular
Momentum
For some electron, orbital angular momentum:
𝐿 = 𝑚𝑒𝑣𝑟
Where, 𝑚𝑒 → 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑒−
From equation (ii), 𝑚𝑜𝑟𝑏 =
1
2
𝑒𝑣𝑟
𝑚𝑜𝑟𝑏 =
1
2
𝑒𝑣𝑟 ×
𝑚𝑒
𝑚𝑒
=
𝑒
2𝑚𝑒
× (𝑚𝑒𝑣𝑟)
𝑚𝑜𝑟𝑏 =
𝑒
2𝑚𝑒
× 𝐿
Where, 𝑚𝑜𝑟𝑏 → 𝑂𝑟𝑏𝑖𝑡𝑎𝑙 𝑚𝑎𝑔𝑛𝑒𝑡𝑖𝑐 𝑚𝑜𝑚𝑒𝑛𝑡
Conclusion: 𝑂𝑟𝑏𝑖𝑡𝑎𝑙 𝑚𝑎𝑔𝑛𝑒𝑡𝑖𝑐 𝑚𝑜𝑚𝑒𝑛𝑡 ∝ 𝐴𝑛𝑔𝑢𝑙𝑎𝑟 𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚
𝑖. 𝑒. 𝑚𝑜𝑟𝑏 ∝ 𝐿
Where,
𝑒
2𝑚𝑒
→ 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝐶𝑎𝑙𝑙𝑒𝑑 𝑎𝑠 𝐺𝑦𝑟𝑜𝑚𝑎𝑔𝑛𝑒𝑡𝑖𝑐 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡

13. 𝑬𝒏𝒆𝒓𝒈𝒚 = 𝒏 ×
𝒉
𝟐𝝅

14. Similarly, From Quantum Mechanics: From 2𝑛𝑑
postulates of Bohr’s theory:
Angular momentum of electron is n multiple of
ℎ
2𝜋
i.e. 𝐿 = 𝑚𝑒𝑣𝑟 = 𝑛
ℎ
2𝜋
We know that, 𝑚𝑜𝑟𝑏 =
𝑒
2𝑚𝑒
𝐿
∴ 𝑚𝑜𝑟𝑏 =
𝑒
2𝑚𝑒
.
𝑛ℎ
2𝜋
=
𝑒𝑛ℎ
4𝜋𝑚𝑒
For 1𝑠𝑡 orbit, n = 1
∴ 𝑚𝑜𝑟𝑏 =
𝑒ℎ
4𝜋𝑚𝑒
The Value
𝑒ℎ
4𝜋𝑚𝑒
→ 𝐵ℎ𝑜𝑟 𝑀𝑎𝑔𝑛𝑒𝑡𝑜𝑛 → 9.274 × 10−24 𝐴/𝑚2
Example
Calculate the gyromagnetic ratio of electron
(given 𝑒 = 1.6 × 10−19 𝐶, 𝑚𝑒 = 9.1 × 10−31 𝑘𝑔)

15. Example
Calculate the gyromagnetic ratio of electron
(given 𝑒 = 1.6 × 10−19
𝐶, 𝑚𝑒 = 9.1 × 10−31
𝑘𝑔)
Ans: Gyromagnetic Ratio =
𝑒
2 𝑚𝑒
Gyromagnetic Ratio =
1.6 × 10−19
2 × 9.1 × 10−31
𝐺𝑦𝑟𝑜𝑚𝑎𝑔𝑛𝑒𝑡𝑖𝑐 𝑟𝑎𝑡𝑖𝑜 = 8.8 × 1010
𝐶/𝑘𝑔

16. Magnetization
• Unpaired electron having magnetic dipole moment
• 𝑀𝑎𝑔𝑛𝑒𝑡𝑖𝑧𝑎𝑡𝑖𝑜𝑛 =
𝑀𝑎𝑔𝑛𝑒𝑡𝑖𝑐 𝑀𝑜𝑚𝑒𝑛𝑡
𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙
• 𝑀 =
𝑀𝑛𝑒𝑡
𝑉𝑜𝑙𝑢𝑚𝑒
• M is vector quantity
• Unit -
𝐴
𝑚
• Dimension - [𝐿−1𝐴]

17. Magnetization
Consider, a rod placed in solenoid
∴ Magnetic field inside solenoid 𝐵𝑂 = 𝜇0𝑛𝐼
Where, n = No. of turns on solenoid
I = Current Passing
∴ Magnetic field due to material kept inside solenoid (𝐵𝑚)
Here, Net Magnetic Field 𝐵 = 𝐵𝑂 + 𝐵𝑚
We know that, 𝐵𝑚 ∝ 𝑚𝑎𝑔𝑛𝑒𝑡𝑖𝑧𝑎𝑡𝑖𝑜𝑛
∴ 𝐵𝑚 = 𝜇𝑜𝑀
Where, 𝜇𝑜 → 𝑃𝑒𝑟𝑚𝑒𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑓𝑟𝑒𝑒 𝑠𝑝𝑎𝑐𝑒
∴ 𝐵 = 𝜇𝑂𝑛𝐼 + 𝜇𝑂𝑀
Here, new quantity called as magnetic field intensity ‘H’
∴ 𝐻 = 𝑛 𝐼
Does not depend upon on material rod.

18. Magnetization
Hence, 𝐵 = 𝜇𝑂𝐻 + 𝜇𝑂𝑀
𝐵 = 𝜇𝑂(𝐻 + 𝑀) ………..(1)
∴ 𝐻 + 𝑀 =
𝐵
𝜇0
∴ 𝐻 =
𝐵
𝜇0
− 𝑀
Unit of H and M is same – A/m
If H is not too strong, So
Magnetization induced in material ∝ Magnetic Intensity
∴ 𝑀 ∝ 𝐻
𝑀 = 𝜒𝐻
Where, 𝜒 → 𝑀𝑎𝑔𝑛𝑒𝑡𝑖𝑐 𝑆𝑢𝑠𝑐𝑒𝑝𝑡𝑎𝑏𝑖𝑙𝑖𝑡𝑦

19. Magnetization
From equation no. (1)
𝐵 = 𝜇𝑂(𝐻 + 𝑀)
∴ 𝐵 = 𝜇𝑂 𝐻 + 𝜒𝐻
𝐵 = 𝜇𝑂 1 + 𝜒 𝐻
∴ 𝐵 = 𝜇0𝜇𝑟𝐻
𝐵 = 𝜇𝐻
Where, 𝜇𝑟 = 1 + 𝜒
𝜇 = 𝜇𝑜𝜇𝑟
∴ 𝜇 = 𝜇0(1 + 𝜒)
Where, 𝜇 → 𝑀𝑎𝑔𝑛𝑒𝑡𝑖𝑐 𝑃𝑒𝑟𝑚𝑒𝑎𝑏𝑖𝑙𝑖𝑡𝑦
𝜇𝑟 → 𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑚𝑎𝑔𝑛𝑒𝑡𝑖𝑐 𝑝𝑒𝑟𝑚𝑒𝑎𝑏𝑖𝑙𝑖𝑡𝑦
𝜇𝑜 → 𝑃𝑒𝑟𝑚𝑒𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑓𝑟𝑒𝑒 𝑠𝑝𝑎𝑐𝑒

20. Magnetic Permeability in Different Materials

21. • Magnetic permeability and susceptibility are quantitative measures of
magnetic properties of materials.
• The key difference between magnetic permeability and susceptibility
is that magnetic permeability describes the ability of a material to
support the formation of a magnetic field inside itself whereas
susceptibility describes whether a material is attracted to a magnetic
field or is repelled from it.
• Magnetic susceptibility is a dimensionless measure.
Summary – Magnetic Permeability vs Susceptibility
• Magnetic permeability is given by the units Henries per meter, and magnetic
susceptibility is a dimensionless property of materials.
• The key difference between magnetic permeability and susceptibility is that
magnetic permeability describes the ability of a material to support the
formation of a magnetic field inside itself whereas susceptibility describes
whether a material is attracted to a magnetic field or is repelled from it.

22. Magnetic Permeability vs Susceptibility
Magnetic permeability of a material is the ability of
a material to support the formation of a magnetic
field inside itself.
Magnetic susceptibility is the measure of magnetic
properties of a material which indicates whether
the material is attracted or repelled from an
external magnetic field.
Units of Measurement
Magnetic permeability is measured by the SI unit
Henries per meter (H/m or H·m−1) which is
equivalent to Newtons per ampere squared (N·A−2).
The magnetic susceptibility is a dimensionless
property.
Value for Diamagnetic Materials
The value of magnetic permeability for diamagnetic
materials is less than 1.
The value of magnetic susceptibility for diamagnetic
materials is less than zero.
Value for Paramagnetic Materials
The value of magnetic permeability for
paramagnetic materials is greater than 1.
The value of magnetic susceptibility for
paramagnetic materials is greater than zero.

23. Example: The region inside a current carrying toroid winding is filled with Aluminium
having susceptibility 𝜒 = 2.3 × 10−5. What is the percentage increase in the
magnetic field in the presence of Aluminium over that without it?
Solution: The magnetic field inside the solenoid without Aluminium
𝐵𝑂 = 𝜇𝑂𝐻
The magnetic field inside the solenoid with Aluminium B = µ H
𝐵−𝐵0
𝐵0
=
𝜇−𝜇𝑜
𝜇𝑜
𝜇 = 𝜇𝑜(1 + 𝜒)
𝜇
𝜇𝑜
− 1 = 𝜒
𝜇−𝜇𝑜
𝜇𝑜
= 𝜒
therefore
𝐵−𝐵0
𝐵0
=
𝜇−𝜇𝑜
𝜇𝑜
= 𝜒
Percentage increase in the magnetic field after inserting Aluminium is
𝐵−𝐵0
𝐵0
× 100 = 2.3 × 10−5 × 100 = 0.0023 %

24. Magnetic susceptibility of some material

25. Magnetic properties of material
• Diamagnetic: Susceptibility is Negative
• Paramagnetic: Susceptibility is Positive but small
• Ferromagnetic: Susceptibility is Positive but large

26. Diamagnetism
• Repels magnetic line of forces
• These material having completely filled electron
• Having no net magnetic dipole moment
• When these material placed in magnetic field, then they move from
stronger to weaker
• These material are repelled by a magnet
• Eg. – Copper, gold, metal etc

27. Diamagnetic Substances
• Diamagnetic substances are those which are repelled by magnets and
when placed in a magnetic field move from the stronger to the
weaker part of the field.
• Diamagnetic materials examples
• Bismuth
• Phosphorus
• Antimony
• Copper
• Water
• Alcohol
• hydrogen

28. Properties of Diamagnetic materials
• When a diamagnetic substance is placed in a magnetic field it sets
itself at right angles to the direction of the lines of force.
• When diamagnetic material is placed within a magnetic field the lines
of force tend to go away from the material.

29. Paramagnetism
• Those substances which are weekly magnetized when placed in an external magnetic
field in the same direction as the applied field are called paramagnetic substances.
• They tend to move from weaker to the stronger part of the field.
• According to Piere Curie (Applied for paramagnetic material)
• 𝑀𝑎𝑔𝑛𝑒𝑡𝑖𝑧𝑎𝑡𝑖𝑜𝑛 𝑀 ∝ 𝑀𝑎𝑔𝑛𝑒𝑡𝑖𝑐 𝐹𝑖𝑒𝑙𝑑 ……………….(1)
• 𝑀𝑎𝑔𝑛𝑒𝑡𝑖𝑧𝑎𝑡𝑖𝑜𝑛 𝑀 ∝
1
𝐴𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝑇𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒
… … … … . . 2
• i.e. M ∝
𝐵
𝑇
……From eq. (1) and (2)
• ∴ 𝑀 = 𝐶
𝐵
𝑇
• Where, 𝐶 → 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡 …..(3)
We know that, 𝐵 = 𝜇𝑂𝐻
From equation (3), 𝑀 =
𝐶𝜇𝑂𝐻
𝑇
∴
𝑀
𝐻
= 𝜒 = 𝐶
𝜇0
𝑇
∴ 𝜒 = 𝜇𝑟 − 1 = 𝐶
𝜇0
𝑇
(a) No (b) Weak (c) Strong
External Magnetic Field

30. Paramagnetism
Paramagnetic substances are those which are attracted by magnets and when
placed in a magnetic field move from weaker to stronger parts of the field.
Paramagnetic materials examples
Aluminum
Manganese
platinum,
crown glass
the solution of salts of iron and oxygen
Properties of paramagnetic materials
If a bar of paramagnetic material is suspended in between the pole pieces of
an electromagnet, it sets itself parallel to the lines of force.
When a bar of paramagnetic material is placed in a magnetic field the lines of
force tend to accumulate in it.

31. Ferromagnetism
Ferromagnetic materials are those materials which exhibit a spontaneous net
magnetization at the atomic level, even in the absence of an external
magnetic field.
When placed in an external magnetic field, ferromagnetic materials are
strongly magnetized in he direction of the field.
Having strong magnetic property, they become permanent magnet.
Domain Theory: In ferromagnetic material
There is strong exchange of magnetic dipole moment
Due to this exchange, small area formed in which all atoms are present.
Small area (domain) Line which separate it called as domain axis.
(a) Unmagnetised and (b) Magnetised
Ferromagnetic material with domain

32. Ferromagnetic Substances
Ferromagnetic substances are those which are attracted by the
magnets and can also be magnetized.
Ferromagnetic materials examples
• Iron
• Nickel
• cobalt and their alloys
Properties of Ferromagnetic Substances
The ferromagnetic substance shows the properties of the paramagnetic
substance to a much greater degree.
The susceptibility has a positive value and the permeability is also very large.
The intensity of magnetization I is proportional to the magnetizing field H for
a small value.

33. Example: A domain in ferromagnetic iron is in the form of cube of side 1 µm.
Estimate the number of iron atoms in the domain, maximum possible dipole
moment and magnetisation of the domain. The molecular mass of iron is 55
g/mole and density is 7.9 𝑔/𝑐𝑚3. Assume that each iron atom has a dipole
moment of 9.27 × 10−24
𝐴𝑚2
.
Solution: The volume of the cubic domain (10−6)3 = 10−18 𝑚3 = 10−12𝑐𝑚3
mass = volume × density = 7.9 × 10−12 𝑔
An Avogadro number (6.023 x 1023) of iron atoms has mass 55 g.
The number of atoms in the domain N =
7.9 ×10−12 × 6.023 x 1023
55
= 8.56 × 1010
The maximum possible dipole moment 𝑚𝑚𝑎𝑥 is achieved for the case when all
the atomic moments are perfectly aligned (though this will not be possible in
reality).
𝑚𝑚𝑎𝑥 = 8.65 × 1010 × 9.27 × 10−24 = 8 × 10−13 𝐴𝑚2
Magnetisation M =
𝑚𝑚𝑎𝑥
domain volume
= 8 × 105 𝐴/𝑚

34. Effect of Temperature
• Ferromagnetic material depends upon temperature.
• Temperature → Increased → Domain Distorted → Dipole moment weaker →
It becomes paramagnetic material
• The temperature at which a ferromagnetic material transforms into a
paramagnetic substance is called Curie temperature (𝑇𝐶) of that material.
• Curie Temperature → Temperature at which ferromagnetic material →
paramagnetic material
• Magnetic Susceptibility, 𝜒 =
𝐶
𝑇 − 𝑇𝐶
for 𝑇 > 𝑇𝐶
• Where, C is a constant
Fig.: Curie Temperature of
some Ferromagnetic material.
Curie Temperature of
some materials

35. Hysteresis
• The behaviour of ferromagnetic material when placed in external magnetic
field is quite interesting and informative.
• It is nonlinear and provides information of magnetic history of the sample.
• Consider an unmagnetized ferromagnetic material in the form of a rod
placed inside a solenoid.
• On passing the current through solenoid,
magnetic field is generated which
magnetises the rod.
• Knowing the value of χ of the material of the
rod, M (magnetization) = χ H. From Eq. (1)
• 𝐻 =
𝐵
𝜇0
− 𝑀
Fig.: Hysteresis cycle (loop)

36. Hysteresis
• Knowing the value of H (= 𝑛𝑙) and M, one can calculate the corresponding
magnetic field B.
• Figure shows the behaviour of the material as we take it through one cycle
of magnetisation.
• At point O in the graph the material is in nonmagnetised state.
Fig.: Hysteresis cycle (loop)
• As the strength of external magnetic intensity
H is increased, B also increases.
• But the increase is non linear.
• Near point a, the magnetic field is at its
maximum value which is the saturation
magnetization condition of the rod.
• This represents the complete alignment and
merger of domains.

37. Hysteresis
• If H is increased, (by increasing the current flowing through the solenoid)
there is no increase in B. This process is not reversible.
• At this stage if the current in the solenoid is reduced, the earlier path of the
graph is not retraced. (Earlier domain structure is not recovered).
• When H = 0 (current through the solenoid is made zero, point b in the
figure) we do not get B = 0.
Fig.: Hysteresis cycle (loop)
• The value of B when H = 0 is called retentivity or
remanence.
• This means some domain alignment is still retained
even when H = 0.
• Next, when the current in the solenoid is increased
in the reverse direction, point c in the graph is
reached, where B = 0 at a certain value of H.
• This value of H is called coercivity.

38. Hysteresis
• At this point the domain axes are randomly oriented with respect to each other.
• If the current is further increased, in the reverse direction, B increases and again
reaches a saturation state (point d).
• Here if H is increase further, B does not increase.
• From this point d onwards, when H is reduced, B also reduces along the path de.
Fig.: Hysteresis cycle (loop)
• At this point e, again H = 0 but B is not zero.
• It means domain structure is present but
the direction of magnetisation is reversed.
• Further increase in the current, gives the
curve efa.
• On reaching point a, one loop is complete.
• This loop is called hysteresis loop and the
process of taking magnetic material through
the loop once is called hysteresis cycle.

41. Permanent Magnet and Electromagnet:
• Soft iron having large permeability (>1000) and small amount of retaining
magnetization, is used to make electromagnets.
• For this purpose, a soft iron rod (or that of a soft ferromagnetic material) is
placed in a solenoid core.
• On passing current through the solenoid, the magnetic field associated with
solenoid increases thousand folds.
• When the current through the
solenoid is switched off, the
associated magnetic field
effectively becomes zero.
• These electromagnets are used in
electric bells, loud speakers,
circuit breakers, and also in
research laboratories.

42. Permanent Magnet and Electromagnet:
• Giant electromagnets are used in cranes to lift heavy loads made of iron.
• Superconducting magnets are used to prepare very high magnetic fields of
the order of a few tesla.
• Such magnets are used in NMR (Nuclear Magnetic Resonance) spectroscopy.
• Permanent magnets are prepared by using a hard ferromagnetic rod instead
of soft used in earlier case.
• When the current is switched on, magnetic
field of solenoid magnetises the rod.
• As the hard ferromagnetic material has a
property to retain the magnetization to
larger extent, the material remains
magnetised even after switching off the
current through the solenoid.

43. Do you know?
• Soft ferromagntic materials can be easily magnetized and
demagnetized.
• Hysteresis loop for hard and soft ferramagnetic materials

44. Magnetic Shielding:
Fig. Magnetic Shielding.
• When a soft ferromagnetic material is kept in a uniform magnetic field, large
number of magnetic lines crowd up inside the material leaving a few outside.
• If we have a closed structure of this material, say a spherical shell of iron kept in
magnetic field, very few lines of force pass through the enclosed space.
• Most of the lines will be crowded into the iron shell. This effect is known as
magnetic shielding.
• The instrument which need to be protected from magnetic field is completely
surrounded by a soft ferromagnetic substance.
• This technique is being used in space ships.
• Some scientific experiments require the experiment
to be protected from magnetic field in the
laboratory.
• There, high magnetic fields of magnets need to be
shielded by providing a case made up of soft
ferromagnetic material.

45. Do you know?
• There are different types of shielding available like electrical
and accoustic shielding apart from magnetic shielding.
• Electrical insulator functions as an electrical barrier or shield
and comes in a wide array of materials.
• Normally the electrical wires used in our households are also
shielded.
• In case of audio recording it is necessary to reduce other stray
sound which may interfere with the sound to be recorded.
• So the recording studios are sound insulated using acoustic
material.