3. •Introduction
•Bar Magnet
•Magnetism and Gauss`s law
•The earths magnetism
•Magnetisation and magnetic intensity
•Magnetic properties of material
•Permanent magnets and electromagnets
•Credit

4. Magnetic phenomenon are universal in nature. The word
magnet is derived from the name of an island in Greece called
“MAGNESIA” where magnetic ore deposits were found. The
directional properties of magnets are known since earlier times.
A thin long magnet when suspended freely pointed in the north
south direction. The name LOADSTONE which is given to
magnetite means leading stone.
The science of magnetism indeed blossomed with the
publication of the famous book “DE MAGNETE” in 1600
written by WILLIAM GILLBERT.
* POSTULATES GIVEN BY WILLIAM GILBERT.

5. •The earth is a magnet with the magnetic field pointing from the
geographic south to the north.It probably consist of a “giant bar
magnet” placed approximately along its axis of rotation.
•When a bar magnet is freely suspended or floated in still water, it
points in the north south direction. The tip towards geographic
north is the north pole and that towards geographic south is south
pole.
•There is a repulsive force when the two like poles are bought
together and vice versa.
•We cannot isolate the north and the south pole.
•It is possible to make magnets out of iron and its alloys.
BACK

6. • On examining iron fillings sprinkled on a sheet of glass over a
short bar magnet,the pattern of iron fillings suggests that the
magnet has 2 poles similar to the positive and negative charge of
an electric dipole.
Related topics to bar magnet
•The magnetic field lines
•Bar magnet as an equivalent solenoid
•Dipole in a uniform magnetic field.
•Electrostatic analog
DEF: A uniform cubical piece of magnet is called a bar
magnet. It resembles the shape of a bar

7. • The magnetic field lines are a visual and intuitive
realization of the unseen magnetic field.
Their properties are as follows
• The magnetic field lines of a magnet form
continuous closed loops.This is unlike the electric
dipole where these lines begin on a positive charge
and end on negative charge.
• The tangent to the field line at a given pt.
represents the direction of the net magnetic field.
• Larger the no. of field lines crossing per unit
normal area,larger is the magnitude of magnetic
field.

8. The magnetic lines do not intersect. This is so since the
direction of the magnetic field would not be unique at the point
of intersection.
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9. •The magnetic dipole moment m associated with a current loop is
defined to be m = NiA where N is the no. of turns in a loop, I is
the current and A is the area vector.
•The resemblance of magnetic field lines of a bar magnet and a
solenoid suggests that a bar magnet may be thought of as a large
no. of circulating currents in analogy with solenoid.
•Cutting a bar magnet into half is like cutting a solenoid into two
smaller solenoids with weaker magnetic properties.
•TEST: Move a small compass needle in the neighborhood of a
bar magnet and a current carrying solenoid. Deflections of the
needle will be similar in both the cases.

10. Similarities in Axial fields of bar magnet and a
solenoid.
Let the above solenoid consist of n turns per unit length of
radius a. Let its length be 2l. We can evaluate the axial field
at a distance r from the center of the solenoid to do this
consider a circular element dx of the solenoid at a distance x
from the center. It consists of ndx terms. Let I be the current
in the solenoid. The magnitude of the field at a pt. P due to
circular element is
dB= μondxia2
2{(r-x)2
+a2
}3/2

11. The magnitude of the total field is given by integrating x
from –l to +l which comes out to be
~ μoni 2la2
2 r3
Magnitude of the magnetic moment of the solenoid is
M = n (2l) I(⊼ a2
)
( Total no. of turns *current*cross sectional area)
Thus
B ~ μo 2m
4⊼ r3
BACK

12. The pattern of iron filing and the magnetic field lines give us an
approximate idea of the magnetic moment m and its field B.
Thus, the torque on the needle is
τ = m * B
τ(θ) = mBsinθ
From Newton`s second law
I d2
θ ~ -mBθ
dt2
This represents simple harmonic motion. The sq of angular
frequency w2
= mB/I. The time period is
T = 2 (l/mB)⊼ 1/2
BACK

13. Magnetic field at large distances due to a bar magnet of magnetic
moment m can be obtained from the equation for electric field due
to an electric dipole of dipole moments by making the following
replacements:
E → B
p → m
1 → μo
4Eo 4⊼ ⊼
In particular we can write down the equatorial field(BE) of a bar
magnet at a distance r for r>>l , where l is the size of the magnet.
B = -μ m /4 ⊼ r3

14. Likewise, the axial field (BA) of a bar magnet for r>>l is
BA= 2μom /4 ⊼ r3
BACK

15. GAUSS LAW is applicable in Electrostatics but in Magnetism
it’s application is different as in case of
magnetism the magnetic field of lines forms closed loops .
Consider a small vector area element Δ S of a closed surface S .
The magnetic flux through Δ S is defined as
Δ ØB = B. Δ S
Where, B is the field at Δ S .
We divide S into many small area elements & calculate flux
through each. Then the net flux ØB is
ØB = Σ Δ ØB = Σ B. Δ S

16. Thus GAUSS LAW for magnetism is :
“ The net magnetic flux through any closed surface is zero.”
Gauss law is the reflection of the fact that isolated magnetic
poles do not exist. There is no source or sink of B.

17. The value of gravitational field on the earth surface is few
tenths of Gauss (1 G = 10-4
T). This magnetic field was
thought of arising of a gigantic bar magnet placed
approximately along the axis of rotation of the earth and
deep in its interior.
Let us denote the geographical north and south poles by Ng
and Sg respectively. The magnetic axis of the earth makes an
angle of approx. 20 degree with the geographic axis. Since
the north pole of the compass needle pts. Approx. to the
geographic north Ng, we designate the earths magnetic pole
close to Ng as Sm ,the south magnetic pole. Similarly Nm the
north magnetic pole of the earth is close to Sg.

18. Sm is located at a pt. In northern canada with latitude at 70.5
degree north and longitude at 96 degree west. Nm is located at
a pt. Diametrically opposite 70.5 degree south and 84 degree
east.
RELATED TOPICS TO EARTH`S MAGNETISM
•Magnetic declination and dip.
•Origin of the earth`s magnetic field
•Global variation in the earth`s magnetic field.
•Temporal variation in the earth`s magnetic field.

19. Consider a pt P on earths surface say Delhi. At this pt.,the
longitude determines the north south direction. The vertical plane
containing the vertical axis is called the geographic meridian. At P
there also exists the earths magnetic field B.The magnetic
meridian is the vertical plane containing B and the vertical axis.
The angle between the geographic and the magnetic meridian
planes is called the magnetic declination.
As we move north from the equator, the magnetic field changes
direction and dips down. The angle that magnetic meridian
makes with the horizontal is called the dip angle. The dip angle
is determined by using a dip circle or a dip meter.
BACK

20. The magnetic field of the earth can be approxim,ated by a gtiant
bar magnet located deep inside the earth. The earth does have large
deposits of iron ore deep inside but it is highly unlikely that any
large solid mass of magnetic material is responsible for earths
magnetism.
The earths core is very hot and molten circulating ions. In the
highly conducting liquid region of the earths core could form
current loops and produce a magnetic field.

21. That is why moon do not have any magnetic field as it does not
possess any molten core.Venus which has slower rate of rotation
has a weaker magnetic field. On the other hand, Jupiter has a
faster rotation rate and hence a stronger magnetic field.
•But no one knows what is the precise mode of action and the
energy needed to sustain such circulating currents!!
BACK

22. The dipole approximation suggests that the earths magnetic field
falls below a micro tesla at a distance of five times the earths
radius i.e. at about 30 thousand km.
Beyond this the solar wind disturbs the dipole pattern. The solar
wind consist of screen of charged particles that emerges
continuously from the sum. The charged particles of the solar
wind get trapped near the magnetic pole of the earth. They ionize
the atmosphere above these poles which in turn causes a
spectacular display of light in the shape of giant curtains high up
in the atmosphere./
In the arctic region it is called the “aurora borealis” or northern
lights and in the south it is called “aurora australis”.
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23. The earths magnetic field is found to change with time. These
changes can be characterized into short term and long term. In
short term,magnetic poles of earth S and N keep shifting their
positions.
Changes in the earth’s magnetic field over long term or geological
time scales are quite interesting. It appears that earths field has
reversed itself every million year or so. The evidence of the same
come from basalt which contain iron and it is emitted during
volcanic activity on ocean floor. opposite direction.

24. As basalt cools, it solidifies and provides a picture earths
magnetic field and direction. The basalt can be dated by other
means and thus clear picture of reversal of earths magnetic
field over reversal time scales has emerged. These reversal
means that one in million years or so, the current in the earths
core slow down, come to halt, and then pick up the
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25. The Earth abounds with a bewildering variety of elments and
compounds. In addition we have been synthesising new alloys,
compounds and even elements.
Consider a solenoid of n turns per unit length and carrying a current
I. The magnetic field in the interior of the solenoid is,
B0 = µ0 n I
The magnetic intensity H is a quantity related to current in coils 7
conductors. In this case it is defined as
H = B0 / µ0
H = n I
The magnetic intensity is a vector with dimension of L-1
A. Its S.I

26. We will next fill the solenoid with a magnetic material keeping the
current I constant. The total field B inside will be different from B0.
The additional field will be due to magnetic material under the
influence of B0. Let this magnetic material posses a dipole moment
m.
We define the relevant quantity called Magnetisation M which is
equal to the magnetic moment per unit volume(V).
M = m / V
M is a vector with dimension L –1
A and unit A m –1
.
Thus additional magnetic field inside is µ0 M & the total field is
B = B0 + µ0 M
= µ0 ( H + M)

27. The magnetic field due to specific nature of the magnetic material M
can be influenced by external factors which is expressed
M = χ H
Where χ , a dimensionless quantity is approximately called the
Magnetic Susceptibility. It is a measure of how a magnetic material
respond to an external field.
• χ is small & positive for materials which are called Paramagnets.
χ is small & negative for materials which are called Diamagnets.
Thus
B = µ0 (1+ χ) H
= µ0 µr H
= µ H

28. Here µr = 1 + χ is a dimensionless quantity called the relative
magnetic permeability of the substance.
The magnetic permeability of the substance is µ & it has the same
units as µ0.

29. Materials are classified on the basis of susceptibility χ as
• Diamagnetic if χ is negative
• Paramagnetic if χ is positive & small
• Ferromagnetic if χ is positive & large
Detailed Information regarding different types of material :
• DIAMAGNETISM
• PARAMAGNETISM
• FERROMAGNETISM

30. The individual atoms,or ions or molecules do not possess a
permanent dipole moment of their own. The application of an
external magnetic field B induces in each atom, a small dipole
moment proportional to B but in opposite direction. The field
lines are expelled or repelled and field intensity is reduced.
When placed in a uniform magnetic field, the bar will tern d to
move from high to low.
Some diamagnetic materials are bisumith, copper lead, nitrogen
at STP etc.
The most exotic diamagnetic materials are Type-I super
conductors. These are metals cooled to very low temperatures
which exhibit both perfect conductivity and perfect
diamagnetism.

31. The phenomenon of perfect diamagnetism is called MEISSNER
EFFECT.It can be gain fully exploited in variety of situations. E.g.
for running magnetic leviated super fast trains.
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32. The individual atom of paramagnetic material posess the
permanent dipole moment of its own.
On the account of ceaseless random motion of the atoms, no net
magnetization is seen. In the presence of external field B which is
strong enough ,and at low temperatures, the individual atomic
dipole moments can be made to align and point ion the sanme
direction as B. The field line gets concentrated inside the material
and field intensity is enhanced inside. When placed in non
uniform magnetic field, bar will move from low to high.
Some paramagnetic materials are aluminum,sodium
calcium,oxygen at STP and copper chloride.

33. M = C B0 / T
Or equivalent to
χ =Cμo / T
The constant C is called curies constant.Thus, for a
paramagnetic material, both χ and μr. Depends not only on the
material but also on the sample temperature. At very high fields
or at very low temp., the magnetization approaches its max.
value when all atomic dipole moments are aligned. This is
called the saturation magnetization value. Ms… Beyond this,
curies law is no longer valid.
Experimentally one finds that the magnetisation of paramagnetic
material is directly proportional to the absolute temperature T.
BACK

34. The individual atoms in a ferromagnetic material possess a dipole
moment.
However, they interact with one another in such a way that they
spontaneously align themselves in a common direction over a
microscopic volume called domain.
Each domain has a net magnetization. Typical domain sizes 1 mm
and the domain contain about 100,000,000,000 atoms.
In the first instance, the magnetization varies randomly from
domain to domain and there is no bulk magnetization.
When we apply an external magnetic field B0,the domain orient
themselves in the direction of B0. And simultaneously they grow in
size.

35. In a ferromagnetic material, the magnetic field lines are highly
concentrated.
In some Ferro magnets, magnetic materials even after removing
the external field, the magnetization persists. Such materials are
called “Hard magnetic materials or hard Ferro magnets” .
ALNICO an alloy of aluminum, iron ,nickel ,cobalt and copper is
one such material.
There is a class of ferromagnetic materials in which the
magnetization disappears on removal of the external field. Soft
iron is one such material. Such materials are called soft
ferromagnetic materials.
The ferromagnetic property depends upon temperature.At high
enough temperatures, a ferromagnet becomes a paramagnet. The
domain structure disintegrates with temperature.
BACK

36. Substances which at room Temperature retain their magnetic
properties for a long period of time are called Permanent Magnets.
There are no. of ways of making permanent magnets :
• One can hold an iron rod in the north & south direction and
hammer it repeatedly.
• One can hold a steel rod and stroke it with one end of the bar
magnet a large no. of times , always in the same sense to make
permanent magnets.
•An efficient way to make permanent magnet is to place a
ferromagnetic rod in a solenoid & pass the current. The magnetic
field magnetises the rod .

37. Characteristics of the material for making Permanent Magnets :
• The material should have high retentivity so that the magnet is
strong .
• The material should have high coercivity so that the
magnetisation is not erased by stray magnetic field , temperature
fluctuations & minor mechanical damage .
• Further the material should have a high permeability.
• Suitable material material for making permanent magnets are :
Steel , Alnico , Cobalt steel & Ticonal .

38. ELECTROMAGNETS are made of ferromagnetic material
which have high permeability & low retentivity .
Soft Iron is a suitable material for electromagnets .
On placing the soft iron in a solenoid by a thousands of fold.
When we switch off the solenoid curent , the magnetism is
effectively switched off since the soft iron core has low
retentivity.
In certain cases , the material goes through an ac cycle of
magnetisation for a long period .This is a case in Transformers
& Telephone diaphragms .
Electromagnets are used in electric bells , loudspeakers and
telephone diaphragms. Giant electromagnets are used in cranes .

39. The temperature of transition from ferromagnetism to para
magnetism is called curie temperature Tc.
The susceptibility above the curie temperature, I.e. in the para
magnetic phase is described by
χ = C / (T- Tc.) {T > Tc} where C is constant.

40. Our sincere thanks to:
Our Physics Teacher Mrs. Yashu Kumar
Source : Physics NCERT textbook for class XII
Project Prepared by :
Nitish Goel of class XII - D
Varun Dutt of class XII - D