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Magnetism and Matter
Introduction : As early as 600BC, Greeks knew that pieces of naturally occurring iron ore
magnetite had the property of attracting small pieces of iron. The word magnetism originates
from the place magnesia in Greece. This property of attraction is called magnetism. The iron
ore showing this property was called a magnet.
Later it was discovered by the Chinese that a long piece of magnet, when suspended
freely always points approximately along geographical north-south direction. Thus a natural
magnet has attractive and directive properties. Based on this property, magnetic needles were
used for navigation of ships. Because of this use magnetite was also called leading stone.
Generally the natural magnets are not strong enough magnetically and have irregular
shape. They are not convenient for practical use. Hence artificial magnets are made using a
piece of iron or steel of suitable shapes. Some of the artificial magnets in use are bar magnet,
horse shoe magnet, compass needle and magnetic needle.
The bar magnet :
The bar magnet is generally rectangular shaped small piece of the rod having two poles
of the same strength. The two poles of the magnet are named as N-pole and S-pole. Bar
magnet is also called magnetic dipole.
Properties of a bar magnet :1) Attractive property :- A magnet attracts small pieces of magnetic substances like iron,
steel, cobalt, nickel etc. When a magnet is brought near a heap of iron filings the ends of
the magnet show the greatest attraction. These ends where the attraction is maximum are
called poles of the magnet. These poles are situated near the ends of the magnet and not
exactly at the ends. Thus every magnet has two poles.
2) Directive Property :- When a magnet is suspended freely it aligns itself in the geographic
north-south direction. The poles of the magnet points towards geographic north are called
N-pole and the other pole towards the geographic south is called S-pole.
3) Like poles repel and unlike poles attract : - If the S-pole of a magnet is brought near
the N-pole of another magnet they are found to attract each other. Now N-pole of a magnet
is brought near the N-pole they are found to repeal each other. Two S-poles also repeal
each other. Therefore like poles repel and unlike poles attract each other.
4) Magnetic poles always exists in pairs : If we try to isolate the two poles of a magnet
from each other by breaking the magnet in the middle, each broken part is found to be a
magnet with N-Pole at its ends. If we break these parts further each part again found to be
a magnet. So unlike electric charges, magnetic monopoles do not exist. Every magnet
exists as a dipole.
5) Magnetic induction : When a piece of magnetic substance is placed near a bar magnet, it
acquires magnetism. The magnetism so acquired is called induced magnetism. This
phenomenon is called magnetic induction.
6) Repulsion is the surest test of magnetism : A magnet attracts the magnetic substances as
well as unlike poles of another magnet. Attractive property of a magnet cannot distinguish
a magnetic material and a magnet. But if the polarity of the magnet is reversed then it will
repel the like poles of another magnet but attract the magnetic materials. Thus repulsion is
the surest test for distinguishing between magnet and magnetic materials.
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Coulombs’s law in magnetism :
Statement : “The force of attraction or repulsion between two magnetic poles is directly
proportional to the product of their pole strengths and inversely proportional to the square of
the distance between them.”
If qm1 and qm2 are the polestrengths of the two magnetic poles placed a distance ‘r’
apart, then the force between them is given by.
F
qm1 qm2
r
2
or
F=k
qm1 qm 2
r2
Where k is a constant of proportionality which depends on the nature of the medium and the
system of units used.

In SI and for free space, k = 0  10 7 Wb / A / m
4
Where 0 is called permeability of free space.
 q m1 q m 2
F= 0
4 .
r2
SI unit of magnetic pole strength is ampere metre (Am) If qm1= qm2=qm, r=1m then F=10-7
N.
Thus the strength of the magnetic pole is said to be one ampere metre, if it repels an
equal and similar pole with a force of 10-7N, when placed in free space at a distance of 1m
from it.
Magnetic field lines :
Magnetic field is the space around a magnet within which, its influence can be
experienced by a small magnet. Michael Faraday introduced the concept of magnetic lines of
force to represent the magnetic field. Visually magnetic lines of force do not exist really but
they are drawn to visualize the magnetic field.
Magnetic lines of force :
It is an imaginary curve, the tangent to which at any point gives the direction of
magnetic field at that point.
Properties of magnetic lines of force :
1. The magnetic field lines are continuous closed loops.
2. The tangent at any point on the magnetic field line gives the direction of magnetic field at
that point.
3. No two magnetic field lines can intersect each other.
4. The lines of force have a tendency to contract length wise and expand side wise.
5. Widely spaced field lines represent weak magnetic field and closely spaced field lines
represent strong magnetic field
Magnetic dipole and magnetic dipole moment :
Magnetic dipole : An arrangement of two equal and opposite magnetic poles separated by a
small distance is called a magnetic dipole.
The two poles of a magnet are always of equal strength and opposite in nature. They
are always exists in pairs.
Magnetic length : The distance between the two poles of a bar magnet is called its magnetic
length.

It is a vector and directed from S-pole to N-pole of a magnet and denoted by 2l .
Since the magnetic poles are situated within the magnet, then the magnetic length is
always less than its geometric length.
Magnetic dipole moment :
It is defined as the product of the pole strength of either
pole and the magnetic length of the magnet.
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

m  qm  2l
Its direction is from S-pole to N-pole. It is a vector quantity. In SI its unit is Am2.
Magnetic field at a point on the axial line due to a magnetic dipole (bar magnet) :
A line passing through two
poles of a bar magnet is called its
axial line.
Let NS be a bar magnet of
length 2l and of pole strength qm.
Let P be a point on the axial line
of a bar magnet at a distance ‘r’
from its centre.
Then the magnetic moment of the magnet is m = qm  2l .
 Magnetic field at ‘p’ due to the N-pole is B1 =
0
qn
along NP.
.
4 (r  l )2
0
qm
along PS.
.
4 (r  l ) 2
B = B1 – B2.
Magnetic field at p due to the S-pole is B2 =
The resultant magnetic field at ‘p’ is

q

q
B= 0. m 2  0. m 2
4 (r  l )
4 (r  l )
 r  l 2  r  l 2 


2
r2  l2


 4rl 

= 0 .qm  2 2 2 
4
 r  l  

2mr
B= 0 2 2 2
4 r  l
=
0
.qm
4




(m = qm x 2l )
For a short magnet l<<r. Then l2 can be neglected when compared to r2.
 2m
B= 0. 3
4 r
The direction of the resultant magnetic field is along the direction of magnetic dipole moment m .
Magnetic field at a point on the equatorial line due to a magnetic dipole (bar magnet) :A line passing through the mid point and  r to the axis of the
magnet is called equatorial line.
Let P be a point on the equatorial line of a bar magnet at
distance r from the centre of the magnet. Let 2l is the magnetic
length and qm is the pole strength of each pole of magnet.

q
Magnetic field at P due to N-pole is B1  0 . 2 m 2 along NP
4 r  l 
produced

q
Magnet field at P due to S-pole is B2  0 . 2 m 2 along PS
4 r  l 
Clearly B1 and B2 have equal magnitude. The components
of B1 and B2 along the equatorial line B1sin and B2sin are
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equal and opposite hence they cancel each other. The
components of B1 and B2 parallel to the axial line
B1 cos and B2 cos added.
 The resultant field at P on the equatorial line
is B=B1cos + B2 cos

q
= 2 0 2 m 2 . cos 
4 r  l 
From the figure, cos =
B  2
r
0
qm
l
.
.
4 r  l  r  l
2
2
2
l
 l2
2

1
2

1
2
2
0
m
.
qm 2l  m
4 r 2  l 2 3 2
For a short magnet l << r. Then l2 can be neglected compared to r2.
B=
0 m
.
4 r 3
The direction of the resultant magnetic field at a point on the equatorial line is opposite
to the direction of magnetic dipole moment.
Bar magnet as an equivalent solenoid :
We know that a current loop can act like a magnetic dipole. A solenoid can be regarded
as a combination of circular current loops placed side by side. So the magnetic field lines of a
solenoid and a bar magnet are similar. If a magnetic needle is placed near a solenoid and then
near a bar magnet it is observed that the deflection of the needle is similar in both the cases. If
a solenoid is cut into two pieces like a bar magnet we get two small solenoids of weaker
strength. Therefore a bar magnet can be considered to be consisting of large number of
circulating currents like that in a solenoid. Axial field of a solenoid is similar to that of a bar
magnet.
Consider a solenoid of length 2l having n
turns per unit length. Let ‘a’ be the radius of the
solenoid. We calculate the magnetic field at a point
P on the axis of solenoid, at a distance r from the
centre ‘o’. Consider a small circular element of
thickness dx at a distance x from o. Number of turns
in this element is ndx. If I is the current flows through the solenoid then the magnetic field
at P on the axis of the solenoid due to the circular element at P is
 0 2 (ndx) Ia 2
.
dB =
4 a 2  (r  x) 2 3 2
B 
If the point P is at very large distance from ‘o’ ie r >>a and r >>x then a 2  (r  x) 2  2  r 3 .
 2 (ndx) Ia 2
 0 2 nIa 2

.
dx
dB = 0 .
4
4
r3
r3
Total magnetic field at P due to the whole solenoid can be obtained by integrating the
equation between the limits x = -l to x = +l.
 2nIa 2 l
0 2nIa 2 l
B 0 .
dx

 4 . r 3 [ x]l
4
r3
l
3
B
=
 0 2nIa 2
l  (l )
4 r 3
Page : 4
=
 2
0 2nIa 2 2l 
= 0 3 n  2l  I   a 2 
3
4 r
4
r
 2m
B = 0 3 .
4 r
(n 2l)I( 
a2 )  m
magnetic moment of solenoid
This expression is same as the magnetic field on the axial line of a bar magnet. Hence a
finite solenoid carrying current is equivalent to a bar magnet. ˖
Torque on a dipole (bar magnet) in a uniform magnet field :
Consider a bar magnet of length 2l and pole strength qm

placed in a uniform magnetic field B . Let the axis of magnet
makes angle  with the field B.

Force on N-Pole = qm B along B .
These two equal and opposite forces constitute a couple, which tends to rotate the

magnet in the direction of B .
  Force   r dis tan ce
Moment of couple or torque
= qm B  NA
= qm B  2lSin
= (qm  2l )B Sin

= m B Sin
Where m = qm  2l is the magnetic dipole moment.

In vector form


 m B
The direction of the torque  is given by right hand screw rule. The direction of  is


r to the plane containing m and B .
Special Cases :
1. If  = 00 Sin =0  = 0 Thus when the magnet lies along the direction of magnetic field
the torque is minimum or zero.
2. If =900 Sin90=1 then  max  mB ie when the magnet lies  r to the direction of magnetic
field torque acting on it is maximum.
Definition of magnetic dipole moment :
m=

BSin 
if B = 1,  = 900 then m = 
Hence “the magnetic dipole moment can be defined as the torque acting on a magnetic dipole
placed Perpendicular to a uniform magnetic field of unit strength.
Compass needle placed in a magnetic field:
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Expression for time period of oscillation of small compass needle in a uniform magnetic field
T  2
is given by
I
mB
Where I= moment of inertia,
m= magnetic dipole moment, B= uniform magnetic field.
Gauss’s Law in magnetism :
Statement : The net magnetic flux through any closed
surface is always zero.
Consider a closed surface S in a uniform magnetic

field B . Let S be a small area element of this surface

with n along its normal. The magnetic flux through this
area S is


 B   B . s  0
S
The total flux through the closed surface is given by


 B   B . ds  0
S
In other words, magnetic field lines entering a surface are equal to the field lines leaving it. If
monopoles existed magnetic flux has certain non zero value. According to Gauss law
monopoles do not exist.
The Earth’s magnetism :
The study of magnetism of the earth is called terrestrial magnetism. It is found that the
strength of earths magnetic field varies from place to place on the earths surface and its value
is of the order of 10-5T . Various theories have been proposed about the cause of earths
magnetism from time to time. What causes the magnetic field of the earth is not clear. But it is
now believed that there are large deposits of ferromagnetic materials like iron, nickel etc. in
the core of the earth. The core of the earth is very hot and molten. The circulating ions in the
highly conducting liquid region of the earth core form current loops and hence produce
magnetic field. At present this hypothesis seems most probable because our moon which has
no molten core has no magnetic field.
The earths magnetic field is assumed to be like
that of huge magnetic dipole whose axis makes an
angle of about 200 with the axis of rotation of the
earth. The magnetic north pole(Nm) of the earth lies
some where near the geographic south pole (SG).
While the magnetic south pole (Sm) lies some where
near the geographic north pole(NG).
Some definitions in connection with earths
magnetism :
1. Geographic axis : A Straight line passing through
the geographic north and south poles of the earth is called its geographic axis. It is the axis
of rotation of the earth.
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2. Magnetic axis : A straight line passing through the magnetic north and south poles of the
earth is called its magnetic axis.
3. Magnetic meridian : It is a vertical plane passing through the magnetic axis.
4. Geographic meridian : It is a vertical plane passing through the geographic axis.
5. Magnetic equator : It is the great circle on the earth perpendicular to the geographic axis.
Magnetic elements of the earth :
The earths magnetic field at a place can be completely described by three quantities
known as magnetic elements. They are 1) declination 2) inclination or dip and 3) horizontal
component of earths field.
1. Magnetic declination (  ) : The angle between the magnetic meridian and geographic
meridian at a place is called magnetic declination at that place.
2. Magnetic inclination or dip :
If the magnetic needle is pivoted at its centre of
gravity and free to rotate in the magnetic meridian about
vertical axis, the needle comes to rest with its axis
inclined to the horizontal. This shows that the earths total
magnetic field is inclined to the horizontal in the magnetic
meridian.
“The angle made by the earth’s total magnetic field with the horizontal in the magnetic
meridian is called dip at a place”.
The dip is zero at the magnetic equator and at poles it is 900. It is about 420 at Delhi.
3. Horizontal component of earths magnetic field ( BH) :
It is the component of the earths total magnetic field along the horizontal in the magnetic
meridian.
In the figure BH = Bcos is the horizontal component and Bv = Bsin is the vertical
component.

Bv
BSin 

 tan 
BH B cos 
or tan  
Bv
BH
Also B2H + B2v = B2(cos2 + sin2 ) = B2
or B =
B 2 H  Bv
2
Some important terms :
1. Magnetising field :
When a magnetic material is placed in a magnetic field magnetism is induced in it.
“The magnetic field that exists in vacuum and induces magnetism is called magnetizing
field.”
B0 =  0 nI
2. Magnetic induction or magnetic flux density (B) :
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When a ferromagnetic substance like soft iron is placed in a uniform magnetic field B0, it
gets magnetized. Because of the induced magnetism, it produces its own magnetic field
and the resultant field inside the substance is increased.
“The total magnetic field inside a magnetic material is the sum of the external magnetic
field and the additional magnetic field produced due to the magnetization of the material is
called magnetic induction.”
OR It can also be defined as “The total number of magnetic lines of force crossing per unit
area normally through a material.”
In SI, its unit is tesla(T) or weber mtre-2(Wb /m2)
3. Intensity of magnetizing field (H) (magnetic intensity ) :The ability of the magnetizing field to magnetise a material medium is called intensity
of magnetizing field.
The magnitude of the intensity of magnetizing field is equal to the number of ampere
turns (nI) per unit length of the solenoid to produce the magnetic field B.
H = nI
 B0   0 nI   0 H
H 
B0
0
In SI, its unit is A/m.
4. Intensity of magnetization (M) :
When a magnetic material is placed in a magnetizing field it gets magnetized.
It is defined as “The magnetic moment developed per unit volume of a material when it
is placed in a magnetizing field.”
M =
m
V
In SI, its unit is A m
But m = qm  2l,
M 
V = A  2l
qm  2l qm

A  2l
A
Hence, intensity of magnetization can also be defined as pole strength developed per
unit cross sectional area of the material.
5. Magnetic permeability () : The ability of the material to conduct the magnetic field
lines through it is called magnetic permeability
It is defined as the ratio of its magnetic induction (B) to the magnetizing field(H).
i.e  
B
H
Magnetic susceptibility (  ) :
It is the property of the substance which shows how easily the substance can be
magnetized when it is placed in magnetising field.
It is defined as the ratio of intensity of magnetization to the magnetising field. It is denoted by  .
Page : 8
 =
M
H
It is the ratio of two quantities having the same units so it has no unit.
Relation between magnetic permeability and susceptibility :
Consider a long solenoid of ‘n’ turns per unit length and
carrying current I. The magnetic field in the interior of the
solenoid, when it is filled with vacuum is given by
B0 =  0 nI   0 H .
If the interior of the solenoid is filled with a material
which gets magnetized, the magnetic field inside the
solenoid will be greater than B0.
The net magnetic field B in the interior of the solenoid is given by B = B0 + Bm
Where ‘B’ is the contribution to the magnetic field due to magnetisation of the material. If M
is the magnetisation of the material. It can be shown that Bm =  0 M .
B  B0  Bm  0 H  M 
But B = H


µH = 0(H+M) = 0 H 1 


or  = 0 1 
M

H
M

H
But  = M H
  = 0 ( 1 +  )
This is the relation between permeability and susceptibility.
or

1  
0
r = 1+ 
When r =

is the relative permeability of the medium.
0
Magnetic properties of materials :
On the basis of their behavior in external magnetic field Faraday classified the various
substances into three categories namely.
1) Diamagnetic substances
2) Paramagnetic substances
3) Ferromagnetic substances
Diamagnetic substances :
The substances which are weakly magnetized in a direction opposite to the direction of
applied magnetic field are called diamagnetic substances. They are weakly repelled by magnet
and tend to move from stronger to weaker region of external magnetic field.
Ex: copper, gold, silver, lead, mercury, Zinc, bismuth, nitrogen, hydrogen, water, sodium
chloride etc.
Page : 9
Properties :
1) When a bar of diamagnetic material is placed in an
external magnetic field, the field lines are repelled by
the material and the magnetic field inside the
material is slightly reduces.
2) When a piece of diamagnetic material is placed near the pole of magnet it tends to move
away from the magnet ie it tends to move from stronger to weaker field.
3) In a diamagnetic substance the net magnetic dipole moment of the atom is zero. When a
magnetic field is applied, a small value of magnetic dipole moment is induced in a
direction opposite to the magnetic field. Hence the material is repelled by the magnet.
4) The susceptibility of diamagnetic substances has a small negative value. Hence the relative
permeability is slightly less than 1.
5) They do not obey Curie’s law. Normally their magnetic properties do not change with
temperature.
Paramagnetic Substances :
The substances which are weakly magnetized in the direction of the applied magnetic
field are called paramagnetic substances. They are weakly attracted by magnets and tend to
move from weaker region to stronger region in the magnetic field.
Ex : Aluminum, chromium, manganese, antimony, lithium, platinum, tungsten, sodium,
calcium, oxygen etc.
Properties :
1) When a bar of paramagnetic material is placed in a
magnetic field, the field lines get concentrated inside
the material and the field inside the material is slightly
increased. So the magnetic induction ‘B’ becomes
slightly grater than the magnetic field.
2) When a small piece of paramagnetic substance is placed near the pole of a magnet, it tends
to move towards the pole ie it tends to move from weaker to stronger field.
3) The atoms of paramagnetic substance possess a small value of permanent magnetic dipole
moment. When it is placed in a strong magnetic field, the atomic dipole moments align
parallel to the direction of magnetic field. Hence it is weakly magnetized in the direction of
the field.
4) The susceptibility of paramagnetic substance has small positive value i.e.  is positive.
5) The relative permeability of paramagnetic substance has a value slightly greater than 1 ie.
r > 1.
6) The susceptibility of paramagnetic substance varies inversely as the absolute temperature.
 
1
T
or  =
C
which is known as Curie’s law
T
7) For a given temperature, the intensity of magnetization is proportional to the magnetizing
field so the susceptibility and permeability do not show any variation with the field.
8) As soon as the magnetizing field is removed paramagnetic substance loses its magnetism.
Ferromagnetic substances :
Page : 10
The substances which are strongly magnetized in the direction of the applied magnetic
field are called ferromagnetic substances. They are strongly attracted by magnets and tend to
move strongly from weaker to stronger region in the magnetic field.
Ex : Iron, steel, nickel, cobalt etc.
Properties :
Ferromagnetic substances exhibit all the properties of paramagnetic substances but to a larger
extent.
1. When a ferromagnetic substance is placed in a magnetic
field the field lines concentrated greatly into the material,
so that magnetic induction B becomes much more than the
magnetizing field.
2. When a piece of ferromagnetic substance is placed in a non
uniform magnetic field, it moves from weaker to stronger region in the magnetic field.
3. The susceptibility of ferromagnetic substance has a large positive value.  M >>H
4. The relative permeability of a ferromagnetic substance has large positive value. It is of the
order of several thousands for iron r = 1000.
5. The susceptibility of ferromagnetic substance decreases with temperature in accordance
with Curie-Weiss law.
 =
C
T  Tc
6. At a certain temperature called the Curie temperature, the susceptibility suddenly falls and
the ferromagnetic substance becomes paramagnetic.
7. A ferromagnetic substance retains magnetism even after the magnetizing field is removed.
Types of ferromagnetic materials :
There are two types of ferromagnetic materials.
1. Soft ferromagnetic materials : Materials which can be demagnetized easily are called
soft ferromagnetic materials. These are the materials in which the magnetisation
disappears on the removal of external magnetic field.
For example: Iron is a soft ferromagnetic material which is used to make the cores of
transformers, electromagnets, computer discs etc.
2. Hard ferromagnetic materials : Materials which can not be demagnetized easily are
called hard ferromagnetic materials. These are the materials which retain magnetisation
even after the removal of the external magnetic field.
ex : Steel, alnico, ticonol etc. are hard ferromagnetic materials
Hysterisis :
Hysterisis curve is a graph between the magnetic
induction B and the magnetising field H.
When a ferromagnetic substance is placed in a
magnetising field it gets magnetized by induction. As
H increases B also increases but not linearly. Consider
an unmagnetised ferromagnetic substance and it is
placed in a solenoid and increase the current through it.
As H increases B also increases gradually and then
attains a saturation value at H = Hmax. This is
represented by the curve OA and is called initial
Page : 11
magnetization curve. Now if H is decreased gradually to zero, B decreases but along the
new path AB. It is found that B does not become zero even when the magnetizing field H
is zero. The value of B at H=0 is called residual magnetism (retentivity). If the current in
the solenoid is reversed and slowly increased, B decreases and becomes zero at a value of
H=OC. The value of reverse magnetising field required to demagnetise the substance
completely is called coercive field (coercivity). On further increasing H in the reverse
direction to a value – Hmax we reach the saturation point D. Now if H is decreased
gradually the point A is reached after going through the path DEFA. The closed path
ABCDEFA represents the cycle of magnetisation of the sample called hysterisis loop.
Throughout the cycle, B is always lagging behind the H. The phenomenon of lagging
behind the magnetic induction (B) w.r.t the magnetising field (H) is called hysterisis.
During the cycle of operation some energy is spent in magnetising and
demagnetizing the substance. This energy appears in the form of heat in the substance.
This loss of energy is called hysterisis loss. The loss of energy per unit volume of the
specimen is equal to the area of hysterisis loop.
The study of hysterisis loop provides information about retentivity, coercivity and
hysterisis loss of the magnetic materials. This helps in selecting the magnetic materials for
different purposes.
Retentivity: The property of the magnetic material to retain magnetism even when the
magnetizing field is reduced to zero is known as retentivity.
Coercivity: The value of reverse magnetizing field required to demagnetize the substance
completely is called coercivity of the substance.
Permanent magnets and electromagnets :
Permanent magnets :
At room temperature the substances which retain their ferromagnetic property for a
long period of time are called permanent magnets.
Methods for making permanent magnets :
1. By holding the steel rod in north south direction and hammering it repeatedly.
2. Hold a steel rod and stroke it with one end of a bar magnet a number of times always
in the same sense to make a permanent magnet.
3. The most efficient way of making a permanent magnet is to place a steel rod in a
solenoid and pass a strong current. The rod gets magnetized due to the magnetic field
of the solenoid.
The materials used for making permanent magnets must have the following
characteristics.
1,. The materials used should have high retentivity so that it produces a strong field.
2. The material should have high coercivity.
3. The material should have high permeability.
Electro magnets :
The material used for making cores of electromagnets must have high permeability and
low retentivity. Soft iron is suitable material for electromagnets.
Uses of electromagnets :
1. Electromagnets are used in electric bells, loud speakers, telephone diaphragms
2. Large electro magnets are used in cranes to lift heavy machinery and bulk quantities of
iron and steel.
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