PHY PUC 2 NOTES:- MAGNETISM AND MATTER

5. Magnetism and matter
Page 90
The property of any object by virtue of which naturally attract piece of
iron ,steel is called as magnetism.
The word magnet is derived from the name of an island in Greece called
magnesia where magnetic ore deposits were found, as early as 600 BC.
Types of magnets:
1)NATURAL MAGNETS: The naturally occurring material like Iron ore or lodestone
which has naturally attractive property are known as natural magnets.
Natural magnets are not strong and have uneven shapes.
Exa: Iron ore, lodestone(Magnetite), Iron Oxide
2)ARTIFICIAL MAGNETS: The magnets made of using naturally occurring magnets
are known as artificial magnets.
Artificial magnets are strong and have different shape and size.
Exa: Bar magnets
Properties of magnets:
1) Attractive Property: Every magnet attract small pieces of Iron , cobalt, nickel etc.
2) Directive Property: When a magnet suspended freely it align itself in the direction of
geographical north-south direction.
3) Like pole repel, and unlike poles attract.
4) Magnetic poles always exist in pair.
5) Magnetic induction .

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THE BAR MAGNET
A bar magnet is the simplest form of magnets which is rectangular in shape
and has a magnetic field around it. It is usually made of ferromagnetic materials
(elements that have naturally magnetic fields like cobalt, iron and nickel)
Properties of Bar Magnet
 It has a north pole and a south pole at two ends.
 The magnetic force of it is the strongest at the pole.
 If this magnet is suspended freely in the air with a thread, it will come to rest until
the poles are aligned in a north-south position.
 If two bar magnets are placed close to each other, their unlike poles will attract
and like poles will repel each other.
 A bar magnet will attract all ferromagnetic materials such as iron, nickel and
cobalt.
The magnetic field lines
The magnetic field is the area around a magnet in which there is magnetic force
can be experienced by electric charge or other magnetic material.
Properties of magnetic field lines
1) The lines start from North pole and end on south pole.
2) The lines always make a complete closed loop.
3) The lines never cross over each other.
4) The tangent to the field line at a given point represents the direction of the net
magnetic field ‘B’ at that point.

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Bar magnet as an equivalent solenoid( 5 M)
Let the solenoid of consists of ‘n’ turns per unit length. Let its length be 2l and
radius ‘a’ . Let the axial field at a point P, at a distance ‘r’ from the centre O of the
solenoid.
Consider a circular element of thickness ‘dx’ of the solenoid at a distance ‘x’
from its centre. It consists of ndx turns. Let ‘I’ be the current in the solenoid.
We know the expression of magnetic field on the axis of a circular current
loop. Hence the magnitude of the field at point P due to the circular element ‘dx’ is
𝑑𝐵 =
μ0(𝑛𝑑𝑥)𝐼𝑎2
2[ (𝑟−𝑥)2+𝑎2]
3
2
⁄
But for magnetic dipole r>>a and r>>l hence above equation reduces to
𝑑𝐵 =
μ0(𝑛𝑑𝑥)𝐼𝑎2
2𝑟3

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The magnitude of the total field is obtained by integrating from x = – l to x = + l
Thus we have
∫ 𝑑𝐵 =
μ0𝑛𝐼𝑎2
2𝑟3
∫ 𝑑𝑥
𝑙
−𝑙
= 𝐵 =
μ0𝑛𝐼𝑎2
2𝑟3
[𝑥 − (−𝑥)]
By placing upper limit and lower limit instead of x=l we get
𝐵 =
μ0𝑛𝐼𝑎2
2𝑟3
2𝑙 =
μ0𝑛𝐼𝑎2
2𝑙
2𝑟3
×
2𝜋
2𝜋
Multiplying and divide above eqn. by 2𝜋 and magnetic moment of dipole is
𝑚 = 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑢𝑟𝑛𝑠 × 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 × 𝑐𝑟𝑜𝑠𝑠 𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑙𝑜𝑜𝑝
𝑚 = 2𝑛𝑙 × 𝐼 × 𝜋𝑟2 = 2𝜋𝑛𝑙𝐼𝑎2 hence above equation become
𝐵 =
μ0
4𝜋
2(2𝜋𝑛𝑙𝐼𝑎2
)
𝑟3
Substituting the value of ‘m’ we get
𝑩 =
𝛍𝟎
𝟒𝝅
𝟐𝒎
𝒓𝟑
The above equation exactly same that of bar magnet. Hence the solenoid behave as
bar magnet by showing the same behavior and properties.

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Torque on the magnetic dipole in a uniform magnetic field
Consider a magnetic dipole of length 2𝑙 and pole strength ‘𝒒𝒎’ is placed in a uniform
magnetic field strength ‘B’ with an angle 𝜃 with m and B. The bar magnet will
𝑀 = 𝑞𝑚 × 2𝑙
𝒒𝒎

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experience a force equal but opposite to each other which constitute a torque and
magnet will rotates. The torque is given by
𝜏 = 𝑚𝑎𝑔𝑛𝑒𝑡𝑖𝑐 𝑓𝑜𝑟𝑐𝑒 × 𝑝𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑓𝑜𝑟𝑐𝑒𝑠
𝜏 = 𝑞𝑚𝐵 × 𝐴𝑁
From diagram, 𝐴𝑁 = 2𝑙𝑠𝑖𝑛𝜃 and 𝑚 = 𝑚𝑎𝑔𝑛𝑒𝑡𝑖𝑐 𝑑𝑖𝑝𝑜𝑙𝑒 𝑚𝑜𝑚𝑒𝑛𝑡 = 𝑞𝑚 × 2𝑙
𝜏 = 2𝑙𝑞𝑚𝐵𝑠𝑖𝑛𝜃
𝝉 = 𝒎𝑩𝒔𝒊𝒏𝜽
1)Torque is maximum when 𝜽 = 𝟗𝟎𝒐
2)Torque is minimum when 𝜽 = 𝟎𝒐
POTENTIAL ENERGY OF A MAGNETIC DIPOLE
Potential energy of a magnetic dipole, in a magnetic field, is defined as the
amount of work done in rotating the dipole from zero potential energy position to any
desired position.
When 𝜃1 = 900
and 𝜃2 = 00
→ most stable position
→ most unstable position

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Note: The suspended bar magnet OR magnetic needle can execute an SHM with Time
period(T)
𝑻 = 𝟐𝝅√
𝑰
𝑴𝑩
Where, T= Time period , I= moment of inertia, 𝑰 =
𝒎𝒍𝟐
𝟏𝟐
M= Magnetic dipole moment , B = Uniform magnetic field in Tesla
Numerical:
1)The magnetic needle has magnetic moment 6.7 × 10–2 Am2 and moment of inertia
I = 7.5 × 10–6 kg m2 . It performs 10 complete oscillations in 6.70 s. What is the magnitude
of the magnetic field?(Ans-0.01T)
2) A short bar magnet placed with its axis at 30° with an external field of 800 G
experiences a torque of 0.016 Nm. (a) What is the magnetic moment of the magnet? (b)
What is the work done in moving it from its most stable to most unstable position? (c) The
bar magnet is replaced by a solenoid of cross-sectional area 2 × 10–4 m2 and 1000 turns,
but of the same magnetic moment. Determine the current flowing through the solenoid.
THE DIPOLE ANALOGY (Comparism)
ANALOGY BETWEEN ELECTRIC AND MAGNETIC DIPOLES.
PHYSICAL QUANTITY ELECTROSTATIC MAGNETISM
Free space constant
1
𝜀𝑜
𝜇𝑜
Dipole moment 𝑃
⃗ = 2𝑞𝑎 𝑚
⃗⃗ = 2𝑞𝑚𝑙
Axial Field
1
4𝜋𝜀𝑜
2𝑃
𝑟3
𝜇𝑜
4𝜋
2𝑚
𝑟3
Equatorial Field −
1
4𝜋𝜀𝑜
𝑃
𝑟3 −
𝜇𝑜
4𝜋
𝑚
𝑟3
Torque in external field 𝑃
⃗ × 𝐸
⃗ 𝑚
⃗⃗ × 𝐵
⃗
P.E. in external field −𝑃
⃗ ∙ 𝐸
⃗ −𝑚
⃗⃗ ∙ 𝐵
⃗

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MAGNETISM AND GAUSS’S LAW:
The net magnetic flux through any closed surface is zero.
∮ 𝑩. 𝒅𝒔 = 𝟎
THE EARTH’S MAGNETISM
Earth is a giant natural magnet. The strength of the earth’s magnetic field varies
from place to place on the earth’s surface; its value being of the order of 10–5 T.
The magnetic field is arise due to electrical currents produced by convective
motion of metallic fluids (consisting mostly of molten iron and nickel ions) in the outer
core of the earth. This is known as the dynamo effect.
The magnetic field around the earth also very similar to that of the Bar magnet.
But Earths geographic poles do not coincide with Earths magnetic poles. The magnetic
axis and axis of rotation of the earth are titled by 11.3°.
The location of the north magnetic pole is at a latitude of 79.74° N and a longitude
of 71.8° W, a place somewhere in north Canada.
The magnetic south pole is at 79.74° S, 108.22° E in the Antarctica.
The pole near the geographic north pole of the earth is called the south magnetic
pole. Likewise, the pole near the geographic south pole is called the north magnetic pole.

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COMPONENTS OF EARTH’S MAGNETIC FIELD
There are three components that are responsible for the magnitude as well as
the direction of the earth’s magnetic field:
 Magnetic declination
 Magnetic inclination or the angle of dip
 Horizontal component of the earth’s magnetic field
Magnetic Declination
The magnetic declination is defined as the angle between the true north and the
magnetic north.
Magnetic Inclination(Angle of dip), 𝜹
The magnetic inclination is also known as the angle of dip. It is the angle made the
horizontal plane on the earth’s surface.
At the magnetic equator, the angle of dip is 𝛿 =0°.
At the magnetic poles, the angle of dip is 𝛿 = 90°.
Horizontal Component of the Earth’s Magnetic Field
There are two components to explain the intensity of the earth’s magnetic field:

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 Horizontal component (H)
 Vertical component (v)
Horizontal component (H): It is the component of the Earths total magnetic field in
the horizontal direction in the magnetic meridian.
Relation between Vertical and Horizontal Component of the Earth’s Magnetic
Field
From figure 𝐵𝐻 = 𝐵 cos 𝛿
and 𝐵𝑉 = 𝐵 sin 𝛿
𝐵𝑉
𝐵𝐻
=
𝐵 sin 𝛿
𝐵 cos 𝛿
𝐵𝑉
𝐵𝐻
= 𝑡𝑎𝑛 𝛿
𝐵 = √ 𝐵𝐻
2
+ 𝐵𝑉
2

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MAGNETISATION AND MAGNETIC INTENSITY
In a bulk material, these moments add up vectorially and they can give a net
magnetic moment which is non-zero.
MAGNETISATION: The net magnetic moment per unit volume of sample. It is also
called as intensity of magnetization.
𝑀 =
𝑚𝑛𝑒𝑡
𝑉
It is an vector quantity and has Unit- Am-1 ,dimension[L-1A].
Consider a long solenoid of ‘n’ turns per unit length and carrying a current I.
The magnetic field in the interior of the solenoid was shown to be given by
B0 = µ0 nI
If the interior of the solenoid is filled with a material with non-zero
magnetisation, the field inside the solenoid will be greater than B0 . The net ‘B’ field in
the interior of the solenoid may be expressed as
B = B0 + Bm
where Bm is the field contributed by the material core. It turns out that this additional
field Bm is proportional to the magnetisation M of the material and is expressed as
Bm = µ0M
where µ0 is the same constant (permittivity of vacuum) that appears in Biot-Savart’s
law.
MAGNETIC INTENSITY(H):It is defined as the ratio of the magnetizing field (B0) to the
permeability of free space(µ0)
𝐻 =
B0
𝜇0
where H has the same dimensions as M and is measured in units of A m–1 .
Thus, the total magnetic field B is written as B = µ0 (H + M)
Note:-For Solenoid H=nI

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From above detail we can write as Magnetisation(M) is directly proportional to the
magnetic intensity(H).
𝑀 ∝ 𝐻
𝑀 = 𝝌𝐻
Where 𝝌 is known as Magnetic susceptibility and it is dimensionless.
Magnetic susceptibility (𝝌):It is the property of material which shows how easily it
can be magnetized.
𝝌 =
M
𝐻
It is small and positive for materials, which are called paramagnetic.
It is small and negative for materials, which are termed diamagnetic.
It is large and positive for materials, which are termed ferromagnetic.
Magnetic susceptibility is given by , 𝝌 = 𝟏 − 𝝁𝒓
Relative Permeability(𝝁𝒓):It is the ratio of permeability of the medium (𝝁) to the
permeability of the free space(𝝁𝒐).
𝝁𝒓 =
𝝁
𝝁𝟎
Relation between H, B and M
B = 𝝁𝒐(𝟏 + 𝝌)𝑯
Numerical:
1) A solenoid has a core of a material with relative permeability 400. The windings of
the solenoid are insulated from the core and carry a current of 2A. If the number of
turns is 1000 per metre, calculate (a) H, (b) M, (c) B
2) In the magnetic meridian of a certain place, the horizontal component of the earth’s
magnetic field is 0.26G and the dip angle is 60°. What is the magnetic field of the
earth at this location?

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Page 103
MAGNETIC MATERIALS
The origin of magnetism lies in the orbital and spin motions of electrons and
how the electrons interact with one another. The best way to introduce the different
types of magnetism is to describe how materials respond to magnetic fields.
The magnetic behavior of materials can be classified into the following
three major groups:
1. Diamagnetism
2. Paramagnetism
3. Ferromagnetism
Diamagnetism
Thus, the substance develops a net magnetic moment in direction opposite to
that of the applied field and hence repulsion. In other words, unlike the way a magnet
attracts metals like iron, it would repel a diamagnetic substance.
Orgin of the Diamagnetism is Orbital magnetic moment of electron. Diamagnetic
substances are the ones in which resultant magnetic moment in an atom is zero.
A bar of diamagnetic material placed in an external magnetic field. The field lines
are repelled or expelled and the field inside the material is reduced. When placed in a
non-uniform magnetic field, the bar will tend to move from high to low field.
Diamagnetic materials are bismuth, copper, lead, silicon, nitrogen (at STP), water and
sodium chloride. Diamagnetism is present in all the substances.
Paramagnetism: Paramagnetic substances are those which get weakly magnetised
when placed in an external magnetic field. They have tendency to move from a region of
weak magnetic field to strong magnetic field, i.e., they get weakly attracted to a magnet.
The source of paramagnetism is the individual atoms (or ions or molecules)
possess a permanent magnetic dipole moment.
A bar of paramagnetic material placed in an external field. The field lines gets
concentrated inside the material, and the field inside is enhanced. When placed in a non-
uniform magnetic field, the bar will tend to move from weak field to strong.
Some paramagnetic materials are aluminium, sodium, calcium, oxygen (at STP) and copper
chloride.

Coaching for 8-10th Page 104
For a paramagnetic material both χ and µr depend not only on the material, but also (in a
simple fashion) on the sample temperature.
Ferromagnetism: Ferromagnetic substances are those which gets strongly
magnetised when placed in an external magnetic field. They have strong tendency to
move from a region of weak magnetic field to strong magnetic field, i.e., they get
strongly attracted to a magnet.
The individual atoms (or ions or molecules) in a ferromagnetic material
possess a dipole moment and interact with one another in such a way that they
spontaneously align themselves in a common direction a macroscopic volume called
domain. Hence Domain are the source of ferromagnetism in material.
Typical domain size is 1mm and the domain contains about 1011 atoms.
In a ferromagnetic material the field lines are highly concentrated. In non-uniform
magnetic field, the sample tends to move towards the region of high field
There is a class of ferromagnetic materials in which the magnetisation
disappears on removal of the external field. Soft iron is one such material, such
materials are called soft ferromagnetic materials.
, 8

Page 105
When the external field is removed. In some ferromagnetic materials the
magnetisation persists. Such materials are called hard magnetic materials or hard
ferromagnets. Alnico, an alloy of iron, aluminium, nickel, cobalt and copper, is one
such material.
There are a number of elements, which are ferromagnetic: iron, cobalt, nickel,
gadolinium, etc.
The ferromagnetic property depends on temperature. At high enough
temperature, a ferromagnet becomes a paramagnet.
The temperature of transition from ferromagnetic to paramagnetism is called
the Curie temperature Tc .

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HYSTERESIS
All ferromagnetic materials exhibit the phenomena of hysteresis. When the
ferromagnetic material placed in a magnetizing filed, the sample get magnetized by
induction. As magnetizing field intensity (H) increases the magnetic induction(B)
does not very linearly . By plotting a graph between H and B we get a smooth close
loop. This loop is called as hysteresis loop.
“The phenomenon of the lagging of magnetic induction behind magnetizing
field is called as Hysteresis.”
Hysteresis loop
Retentivity
The amount of magnetization present when the external magnetizing field is
removed is known as retentivity. OR
It is a material’s ability to retain a certain amount of magnetic property while an
external magnetizing field is removed.
The value of B at point b in the hysteresis loop.

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Coercivity
The amount of reverse(-ve -H) external magnetizing field required to completely
demagnetize the substance is known as coercivity of substance. OR
The value of reverse magnetizing field required at which retentivity becomes Zero.
The value of H at point ‘c’ in the hysteresis loop.
PERMANENT MAGNETS
Substances which at room temperature retain their ferromagnetic property for
a long period of time are called permanent magnets.
The material should have high retentivity and high coercivity. Further, the
material should have a high permeability
Materials for permanent magnets are alnico, cobalt steel and ticonal
ELECTROMAGNETS.
Substances which at room temperature do not retain their ferromagnetic
property for a long period of time are called electromagnets magnets.
Core of electromagnets are made of ferromagnetic materials which have high
permeability and low retentivity.
Soft iron is a suitable material for electromagnets.
Applications: Electromagnets are used in electric bells, loudspeakers and telephone
diaphragms. Giant electromagnets are used in cranes to lift machinery, and bulk
quantities of iron and steel.

Page 108

Page 109
ONE MARKS QUESTION
1. Define magnetic dipole moment of a bar magnet.
2. What is the direction of dipole moment of a bar magnet?
3. What happens when a bar magnet is suspended freely?
4. What are the magnetic field lines?
5. Is magnetic field lines form continuous closed loops.
6. State Gauss’s law in magnetism.
7. Define magnetic meridian.
8. Define geographic meridian.
9. Define magnetic declination.
10. Define inclination or magnetic dip.
11. What is the value of dip at the equator?
12. What is the value of magnetic dip at the poles?
13. If the value of horizontal component of the earth BH is equal to vertical component
BV, then what is the value of dip at that place?
14. How does the value of magnetic inclination/dip vary from equator to the poles?
15. How does the value of magnetic declination vary with the latitudes?
16. Write the relation connecting the angle of dip, horizontal and vertical components
of magnetic field of the earth at a place.
17. Define magnetization of a magnetic material.
18. Mention the S.I unit of magnetization of a magnetic material.
19. Define magnetic susceptibility of a magnetic material.
20. Define relative permeability of a material.
21. How the relative permeability is related to its magnetic susceptibility?
22. Give the relation between magnetic flux density B, magnetization of the material M
and magnetic intensity H.
23. What happens when diamagnetic material is placed in varying magnetic field?
24. How does magnetic susceptibility of diamagnetic material depend on temperature?
25. What does negative susceptibility signify in diamagnetic material?
26. What is the net orbital magnetic moment of an atom of a diamagnetic material?
27. For which material susceptibility low and negative?
28. What are paramagnetic materials?
29. Give an example for paramagnetic material.
30. How does magnetic susceptibility of paramagnetic material depend on
temperature?
31. For which material susceptibility is low and positive?
32. State Curie’s law in magnetism.
33. What is Curie temperature?

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34. What happens to the property of a ferromagnetic substance when it is heated?
35. How does the ferromagnetism change with temperature?
36. What is retentivity?
37. What is coercivity?
38. Why electromagnets are made of soft iron?
TWO MARK QUESTIONS:
1. When is the potential energy of a dipole in magnetic field (i) minimum (ii)
maximum?
2. When is the torque acting on a magnetic needle/bar magnet/magnetic dipole in a
uniform magnetic field (a) maximum and (b) minimum?
3. Write the expression for potential energy of a magnetic dipole in a uniform
magnetic field and explain the terms.
4. Write the expression for the time period of oscillation of small magnetic needle in a
uniform magnetic field and explain the terms.
5. State and explain Gauss’s law in magnetism.
6. At what place on the earth the dip is (i) maximum and (ii) minimum?
7. Define magnetization of a magnetic material. Mention its S.I unit
8. Define magnetic intensity. Give its S.I unit.
9. What is diamagnetism? Give an example of a diamagnetic material.
10. What is paramagnetism? Give an example of a paramagnetic material.
11. State and explain Curie’s law in magnetism.
39. Draw the behavior of magnetic field lines near a (i) diamagnetic (ii) paramagnetic
substance.
12. What is ferromagnetism? Give an example of a ferro magnetic material.
13. How does susceptibility of ferromagnetic vary with temperature? Explain.
14. What is soft ferromagnetic material? Give an example.
15. What is hard ferromagnetic material? Give an example.
16. What is hysteresis curve? Mention the significance of hysteresis curve.
17. Mention any two applications of hysteresis curve.
18. What is a permanent magnet? Name the material used for making permanent
magnet.
19. Give any two uses of permanent magnets.
20. Mention any two methods to destroy magnetism of a magnet.
THREE MARK QUESTIONS:
1. Give any three properties of a bar magnet.
2.

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3. Sketch the magnetic field lines of (a) a bar magnet (b) a current carrying finite
solenoid
4. Arrive at the expression for magnetic potential energy of a dipole in a magnetic
field.
5. Name the elements of earth’s magnetic field.
6. Define the terms: (1) Declination, (2) Inclination or Dip and (3) Horizontal
component of earth’s magnetic field at a given place.
7. Define the terms: (1) magnetization of a magnetic material, (2) magnetic intensity
and (3) magnetic susceptibility.
8. Define magnetic permeability and magnetic susceptibility. Write a relation between
them.
9. Obtain the relation between relative magnetic permeability magnetic susceptibility.
10. Mention any three properties of diamagnetic material.
11. Explain the cause for the diamagnetic behavior of materials.
12. Mention any three properties of paramagnetic material.
13. Mention any three properties of ferromagnetic material.
14. Explain magnetic hysteresis by drawing hysteresis loop.
15. Write the applications of electromagnets.
16. Give the characteristics of magnetic materials used for making permanent magnets.
FIVE MARK QUESTIONS:
1. Show that a current carrying solenoid is equivalent to a bar magnet.
2. Compare diamagnetic, paramagnetic and ferromagnetic material on the basis of
their properties.

PHY PUC 2 NOTES:- MAGNETISM AND MATTER

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PHY PUC 2 NOTES:- MAGNETISM AND MATTER