NCERT Textbook: Magnetism & Matter | Physics Class 12 - NEET PDF Download

 Page 1


Physics
136
5.1  INTRODUCTION
Magnetic phenomena are universal in nature. Vast, distant galaxies, the
tiny invisible atoms, humans and beasts all are permeated through and
through with a host of magnetic fields from a variety of sources. The earth’s
magnetism predates human evolution. 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.
In the previous chapter we have learned that moving charges or electric
currents produce magnetic fields. This discovery, which was made in the
early part of the nineteenth century is credited to Oersted, Ampere, Biot
and Savart, among others.
In the present chapter, we take a look at magnetism as a subject in its
own right.
Some of the commonly known ideas regarding magnetism are:
(i) The earth behaves as a magnet with the magnetic field pointing
approximately from the geographic south to the north.
(ii) When a bar magnet is freely suspended, it points in  the north-south
direction. The tip which points to the geographic north is called the
north pole and the tip which points to the geographic south is called
the south pole of the magnet.
Chapter Five
MAGNETISM AND
MATTER
2024-25
Page 2


Physics
136
5.1  INTRODUCTION
Magnetic phenomena are universal in nature. Vast, distant galaxies, the
tiny invisible atoms, humans and beasts all are permeated through and
through with a host of magnetic fields from a variety of sources. The earth’s
magnetism predates human evolution. 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.
In the previous chapter we have learned that moving charges or electric
currents produce magnetic fields. This discovery, which was made in the
early part of the nineteenth century is credited to Oersted, Ampere, Biot
and Savart, among others.
In the present chapter, we take a look at magnetism as a subject in its
own right.
Some of the commonly known ideas regarding magnetism are:
(i) The earth behaves as a magnet with the magnetic field pointing
approximately from the geographic south to the north.
(ii) When a bar magnet is freely suspended, it points in  the north-south
direction. The tip which points to the geographic north is called the
north pole and the tip which points to the geographic south is called
the south pole of the magnet.
Chapter Five
MAGNETISM AND
MATTER
2024-25
137
Magnetism and
Matter
(iii) There is a repulsive force when north poles ( or south poles ) of two
magnets are brought close together. Conversely, there is an attractive
force between the north pole of one magnet and the south pole of
the other.
(iv) We cannot isolate the north, or south pole of a magnet. If a bar magnet
is broken into two halves, we get two similar bar magnets with
somewhat weaker properties. Unlike electric charges, isolated magnetic
north and south poles known as magnetic monopoles do not exist.
(v) It is possible to make magnets out of iron and its alloys.
We begin with a description of a bar magnet and its behaviour in an
external magnetic field. We describe Gauss’s law of magnetism. We next
describe how materials can be classified on the basis of their magnetic
properties. We describe para-, dia-, and ferromagnetism.
5.2  T 5.2  T 5.2  T 5.2  T 5.2  THE HE HE HE HE B B B B BAR AR AR AR AR M M M M MAGNET AGNET AGNET AGNET AGNET
We begin our study by examining iron
filings sprinkled on a sheet of glass placed
over a short bar magnet. The arrangement
of iron filings is shown in Fig. 5.1.
     The pattern of iron filings suggests
that the magnet has two poles similar to
the positive and negative charge of an
electric dipole. As mentioned in the
introductory section, one pole is
designated the North pole and the other,
the South pole. When suspended freely,
these poles point approximately towards
the geographic north and south poles,
respectively. A similar pattern of iron
filings is observed around a current
carrying solenoid.
5.2.1  The magnetic field lines 5.2.1  The magnetic field lines 5.2.1  The magnetic field lines 5.2.1  The magnetic field lines 5.2.1  The magnetic field lines
The pattern of iron filings permits us to plot
the magnetic field lines* * * * *. This is shown both
for the bar-magnet and the current-
carrying solenoid in  Fig. 5.2. For
comparison refer to the Chapter 1, Figure 1.14(d). Electric field lines of an
electric dipole are also displayed in Fig. 5.2(c). The magnetic field lines are a
visual and intuitive realisation of the magnetic field. Their properties are:
(i) The magnetic field lines of a magnet (or a solenoid) form continuous
closed loops. This is unlike the electric dipole where these field lines
begin from a positive charge and end on the negative charge or escape
to infinity.
* * * * * In some textbooks the magnetic field lines are called magnetic lines of force.
This nomenclature is avoided since it can be confusing. Unlike electrostatics
the field lines in magnetism do not indicate the direction of the force on a
(moving) charge.
FIGURE FIGURE FIGURE FIGURE FIGURE 5.1 5.1 5.1 5.1 5.1 The arrangement
of iron filings surrounding a bar
magnet. The pattern mimics
magnetic field lines. The pattern
suggests that the bar magnet is
a magnetic dipole.
2024-25
Page 3


Physics
136
5.1  INTRODUCTION
Magnetic phenomena are universal in nature. Vast, distant galaxies, the
tiny invisible atoms, humans and beasts all are permeated through and
through with a host of magnetic fields from a variety of sources. The earth’s
magnetism predates human evolution. 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.
In the previous chapter we have learned that moving charges or electric
currents produce magnetic fields. This discovery, which was made in the
early part of the nineteenth century is credited to Oersted, Ampere, Biot
and Savart, among others.
In the present chapter, we take a look at magnetism as a subject in its
own right.
Some of the commonly known ideas regarding magnetism are:
(i) The earth behaves as a magnet with the magnetic field pointing
approximately from the geographic south to the north.
(ii) When a bar magnet is freely suspended, it points in  the north-south
direction. The tip which points to the geographic north is called the
north pole and the tip which points to the geographic south is called
the south pole of the magnet.
Chapter Five
MAGNETISM AND
MATTER
2024-25
137
Magnetism and
Matter
(iii) There is a repulsive force when north poles ( or south poles ) of two
magnets are brought close together. Conversely, there is an attractive
force between the north pole of one magnet and the south pole of
the other.
(iv) We cannot isolate the north, or south pole of a magnet. If a bar magnet
is broken into two halves, we get two similar bar magnets with
somewhat weaker properties. Unlike electric charges, isolated magnetic
north and south poles known as magnetic monopoles do not exist.
(v) It is possible to make magnets out of iron and its alloys.
We begin with a description of a bar magnet and its behaviour in an
external magnetic field. We describe Gauss’s law of magnetism. We next
describe how materials can be classified on the basis of their magnetic
properties. We describe para-, dia-, and ferromagnetism.
5.2  T 5.2  T 5.2  T 5.2  T 5.2  THE HE HE HE HE B B B B BAR AR AR AR AR M M M M MAGNET AGNET AGNET AGNET AGNET
We begin our study by examining iron
filings sprinkled on a sheet of glass placed
over a short bar magnet. The arrangement
of iron filings is shown in Fig. 5.1.
     The pattern of iron filings suggests
that the magnet has two poles similar to
the positive and negative charge of an
electric dipole. As mentioned in the
introductory section, one pole is
designated the North pole and the other,
the South pole. When suspended freely,
these poles point approximately towards
the geographic north and south poles,
respectively. A similar pattern of iron
filings is observed around a current
carrying solenoid.
5.2.1  The magnetic field lines 5.2.1  The magnetic field lines 5.2.1  The magnetic field lines 5.2.1  The magnetic field lines 5.2.1  The magnetic field lines
The pattern of iron filings permits us to plot
the magnetic field lines* * * * *. This is shown both
for the bar-magnet and the current-
carrying solenoid in  Fig. 5.2. For
comparison refer to the Chapter 1, Figure 1.14(d). Electric field lines of an
electric dipole are also displayed in Fig. 5.2(c). The magnetic field lines are a
visual and intuitive realisation of the magnetic field. Their properties are:
(i) The magnetic field lines of a magnet (or a solenoid) form continuous
closed loops. This is unlike the electric dipole where these field lines
begin from a positive charge and end on the negative charge or escape
to infinity.
* * * * * In some textbooks the magnetic field lines are called magnetic lines of force.
This nomenclature is avoided since it can be confusing. Unlike electrostatics
the field lines in magnetism do not indicate the direction of the force on a
(moving) charge.
FIGURE FIGURE FIGURE FIGURE FIGURE 5.1 5.1 5.1 5.1 5.1 The arrangement
of iron filings surrounding a bar
magnet. The pattern mimics
magnetic field lines. The pattern
suggests that the bar magnet is
a magnetic dipole.
2024-25
Physics
138
(ii) The tangent to the field line at a given
point represents the direction of the net
magnetic field B at that point.
(iii) The larger the number of field lines
crossing per unit area, the stronger is
the magnitude of the magnetic field B.
In Fig. 5.2(a), B is larger around
region  ii  than in region  i  .
(iv) The magnetic field lines do not
intersect, for if they did, the direction
of the magnetic field would not be
unique at the point of intersection.
One can plot the magnetic field lines
in a variety of ways. One way is to place a
small magnetic compass needle at various
positions and note its orientation. This
gives us an idea of the magnetic field
direction at various points in space.
5.2.2  Bar magnet as an
equivalent solenoid
In the previous chapter, we have
explained how a current loop acts as a
magnetic dipole (Section 4.9). We
mentioned Ampere’s hypothesis that all
magnetic phenomena can be explained in
terms of circulating currents.
FIGURE 5.3 Calculation of (a) The axial field of a
finite solenoid in order to demonstrate its
similarity to that of a bar magnet. (b) A magnetic
needle in a uniform magnetic field B. The
arrangement may be used to determine either B
or the magnetic moment m of the needle.
FIGURE 5.2 The field lines of (a) a bar magnet, (b) a current-carrying finite solenoid and
(c) electric dipole. At large distances, the field lines are very similar. The curves
labelled  i  and ii are closed Gaussian surfaces.
2024-25
Page 4


Physics
136
5.1  INTRODUCTION
Magnetic phenomena are universal in nature. Vast, distant galaxies, the
tiny invisible atoms, humans and beasts all are permeated through and
through with a host of magnetic fields from a variety of sources. The earth’s
magnetism predates human evolution. 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.
In the previous chapter we have learned that moving charges or electric
currents produce magnetic fields. This discovery, which was made in the
early part of the nineteenth century is credited to Oersted, Ampere, Biot
and Savart, among others.
In the present chapter, we take a look at magnetism as a subject in its
own right.
Some of the commonly known ideas regarding magnetism are:
(i) The earth behaves as a magnet with the magnetic field pointing
approximately from the geographic south to the north.
(ii) When a bar magnet is freely suspended, it points in  the north-south
direction. The tip which points to the geographic north is called the
north pole and the tip which points to the geographic south is called
the south pole of the magnet.
Chapter Five
MAGNETISM AND
MATTER
2024-25
137
Magnetism and
Matter
(iii) There is a repulsive force when north poles ( or south poles ) of two
magnets are brought close together. Conversely, there is an attractive
force between the north pole of one magnet and the south pole of
the other.
(iv) We cannot isolate the north, or south pole of a magnet. If a bar magnet
is broken into two halves, we get two similar bar magnets with
somewhat weaker properties. Unlike electric charges, isolated magnetic
north and south poles known as magnetic monopoles do not exist.
(v) It is possible to make magnets out of iron and its alloys.
We begin with a description of a bar magnet and its behaviour in an
external magnetic field. We describe Gauss’s law of magnetism. We next
describe how materials can be classified on the basis of their magnetic
properties. We describe para-, dia-, and ferromagnetism.
5.2  T 5.2  T 5.2  T 5.2  T 5.2  THE HE HE HE HE B B B B BAR AR AR AR AR M M M M MAGNET AGNET AGNET AGNET AGNET
We begin our study by examining iron
filings sprinkled on a sheet of glass placed
over a short bar magnet. The arrangement
of iron filings is shown in Fig. 5.1.
     The pattern of iron filings suggests
that the magnet has two poles similar to
the positive and negative charge of an
electric dipole. As mentioned in the
introductory section, one pole is
designated the North pole and the other,
the South pole. When suspended freely,
these poles point approximately towards
the geographic north and south poles,
respectively. A similar pattern of iron
filings is observed around a current
carrying solenoid.
5.2.1  The magnetic field lines 5.2.1  The magnetic field lines 5.2.1  The magnetic field lines 5.2.1  The magnetic field lines 5.2.1  The magnetic field lines
The pattern of iron filings permits us to plot
the magnetic field lines* * * * *. This is shown both
for the bar-magnet and the current-
carrying solenoid in  Fig. 5.2. For
comparison refer to the Chapter 1, Figure 1.14(d). Electric field lines of an
electric dipole are also displayed in Fig. 5.2(c). The magnetic field lines are a
visual and intuitive realisation of the magnetic field. Their properties are:
(i) The magnetic field lines of a magnet (or a solenoid) form continuous
closed loops. This is unlike the electric dipole where these field lines
begin from a positive charge and end on the negative charge or escape
to infinity.
* * * * * In some textbooks the magnetic field lines are called magnetic lines of force.
This nomenclature is avoided since it can be confusing. Unlike electrostatics
the field lines in magnetism do not indicate the direction of the force on a
(moving) charge.
FIGURE FIGURE FIGURE FIGURE FIGURE 5.1 5.1 5.1 5.1 5.1 The arrangement
of iron filings surrounding a bar
magnet. The pattern mimics
magnetic field lines. The pattern
suggests that the bar magnet is
a magnetic dipole.
2024-25
Physics
138
(ii) The tangent to the field line at a given
point represents the direction of the net
magnetic field B at that point.
(iii) The larger the number of field lines
crossing per unit area, the stronger is
the magnitude of the magnetic field B.
In Fig. 5.2(a), B is larger around
region  ii  than in region  i  .
(iv) The magnetic field lines do not
intersect, for if they did, the direction
of the magnetic field would not be
unique at the point of intersection.
One can plot the magnetic field lines
in a variety of ways. One way is to place a
small magnetic compass needle at various
positions and note its orientation. This
gives us an idea of the magnetic field
direction at various points in space.
5.2.2  Bar magnet as an
equivalent solenoid
In the previous chapter, we have
explained how a current loop acts as a
magnetic dipole (Section 4.9). We
mentioned Ampere’s hypothesis that all
magnetic phenomena can be explained in
terms of circulating currents.
FIGURE 5.3 Calculation of (a) The axial field of a
finite solenoid in order to demonstrate its
similarity to that of a bar magnet. (b) A magnetic
needle in a uniform magnetic field B. The
arrangement may be used to determine either B
or the magnetic moment m of the needle.
FIGURE 5.2 The field lines of (a) a bar magnet, (b) a current-carrying finite solenoid and
(c) electric dipole. At large distances, the field lines are very similar. The curves
labelled  i  and ii are closed Gaussian surfaces.
2024-25
139
Magnetism and
Matter
The resemblance of magnetic field lines for a bar magnet and a solenoid
suggest that a bar magnet may be thought of as a large number of
circulating currents in analogy with a solenoid. Cutting a bar magnet in
half is like cutting a solenoid. We get two smaller solenoids with weaker
magnetic properties. The field lines remain continuous, emerging from
one face of the solenoid and entering into the other face. One can test this
analogy by moving a small compass needle in the neighbourhood of a
bar magnet and a current-carrying finite solenoid and noting that the
deflections of the needle are similar in both cases.
To make this analogy more firm we may calculate the axial field of a
finite solenoid depicted in Fig. 5.3 (a). We can demonstrate that at large
distances this axial field resembles that of a bar magnet.
The magnitude of the field at point P due to the solenoid is
0
3
2
4
m
B
r
µ
p
=
(5.1)
This is also the far axial magnetic field of a bar magnet which one may
obtain experimentally. Thus, a bar magnet and a solenoid produce similar
magnetic fields. The magnetic moment of a bar magnet is thus equal to
the magnetic moment of an equivalent solenoid that produces the same
magnetic field.
5.2.3  The dipole in a uniform magnetic field
Let’s place a small compass needle of known magnetic moment m allowing
it to oscillate in the magnetic field. This arrangement is shown in
Fig. 5.3(b).
The torque on the needle is [see Eq. (4.23)],
t t t t t = m × B (5.2)
In magnitude t = mB sin?
Here t t t t t  is restoring torque and ? is the angle between m and B.
An expression for magnetic potential energy can be obtained on lines
similar to  electrostatic potential energy.
The magnetic potential energy U
m
 is given by
U d
m
=
?
t ? ? ( )
      
= = - ?
mB d mB sin cos ? ? ?
      = –m.B (5.3)
We have emphasised in Chapter 2 that the zero of potential energy
can be fixed at one’s convenience. Taking the constant of integration to be
zero means fixing the zero of potential energy at ? = 90°, i.e., when the
needle is perpendicular to the field. Equation (5.3) shows that potential
energy is minimum (= –mB) at ? = 0° (most stable position) and maximum
(= +mB) at ? = 180° (most unstable position).
Example 5.1
(a) What happens if a bar magnet is cut into two pieces: (i) transverse
to its length, (ii) along its length?
(b) A magnetised needle in a uniform magnetic field experiences a
torque but no net force. An iron nail near a bar magnet, however,
experiences a force of attraction in addition to a torque. Why?
 EXAMPLE 5.1
2024-25
Page 5


Physics
136
5.1  INTRODUCTION
Magnetic phenomena are universal in nature. Vast, distant galaxies, the
tiny invisible atoms, humans and beasts all are permeated through and
through with a host of magnetic fields from a variety of sources. The earth’s
magnetism predates human evolution. 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.
In the previous chapter we have learned that moving charges or electric
currents produce magnetic fields. This discovery, which was made in the
early part of the nineteenth century is credited to Oersted, Ampere, Biot
and Savart, among others.
In the present chapter, we take a look at magnetism as a subject in its
own right.
Some of the commonly known ideas regarding magnetism are:
(i) The earth behaves as a magnet with the magnetic field pointing
approximately from the geographic south to the north.
(ii) When a bar magnet is freely suspended, it points in  the north-south
direction. The tip which points to the geographic north is called the
north pole and the tip which points to the geographic south is called
the south pole of the magnet.
Chapter Five
MAGNETISM AND
MATTER
2024-25
137
Magnetism and
Matter
(iii) There is a repulsive force when north poles ( or south poles ) of two
magnets are brought close together. Conversely, there is an attractive
force between the north pole of one magnet and the south pole of
the other.
(iv) We cannot isolate the north, or south pole of a magnet. If a bar magnet
is broken into two halves, we get two similar bar magnets with
somewhat weaker properties. Unlike electric charges, isolated magnetic
north and south poles known as magnetic monopoles do not exist.
(v) It is possible to make magnets out of iron and its alloys.
We begin with a description of a bar magnet and its behaviour in an
external magnetic field. We describe Gauss’s law of magnetism. We next
describe how materials can be classified on the basis of their magnetic
properties. We describe para-, dia-, and ferromagnetism.
5.2  T 5.2  T 5.2  T 5.2  T 5.2  THE HE HE HE HE B B B B BAR AR AR AR AR M M M M MAGNET AGNET AGNET AGNET AGNET
We begin our study by examining iron
filings sprinkled on a sheet of glass placed
over a short bar magnet. The arrangement
of iron filings is shown in Fig. 5.1.
     The pattern of iron filings suggests
that the magnet has two poles similar to
the positive and negative charge of an
electric dipole. As mentioned in the
introductory section, one pole is
designated the North pole and the other,
the South pole. When suspended freely,
these poles point approximately towards
the geographic north and south poles,
respectively. A similar pattern of iron
filings is observed around a current
carrying solenoid.
5.2.1  The magnetic field lines 5.2.1  The magnetic field lines 5.2.1  The magnetic field lines 5.2.1  The magnetic field lines 5.2.1  The magnetic field lines
The pattern of iron filings permits us to plot
the magnetic field lines* * * * *. This is shown both
for the bar-magnet and the current-
carrying solenoid in  Fig. 5.2. For
comparison refer to the Chapter 1, Figure 1.14(d). Electric field lines of an
electric dipole are also displayed in Fig. 5.2(c). The magnetic field lines are a
visual and intuitive realisation of the magnetic field. Their properties are:
(i) The magnetic field lines of a magnet (or a solenoid) form continuous
closed loops. This is unlike the electric dipole where these field lines
begin from a positive charge and end on the negative charge or escape
to infinity.
* * * * * In some textbooks the magnetic field lines are called magnetic lines of force.
This nomenclature is avoided since it can be confusing. Unlike electrostatics
the field lines in magnetism do not indicate the direction of the force on a
(moving) charge.
FIGURE FIGURE FIGURE FIGURE FIGURE 5.1 5.1 5.1 5.1 5.1 The arrangement
of iron filings surrounding a bar
magnet. The pattern mimics
magnetic field lines. The pattern
suggests that the bar magnet is
a magnetic dipole.
2024-25
Physics
138
(ii) The tangent to the field line at a given
point represents the direction of the net
magnetic field B at that point.
(iii) The larger the number of field lines
crossing per unit area, the stronger is
the magnitude of the magnetic field B.
In Fig. 5.2(a), B is larger around
region  ii  than in region  i  .
(iv) The magnetic field lines do not
intersect, for if they did, the direction
of the magnetic field would not be
unique at the point of intersection.
One can plot the magnetic field lines
in a variety of ways. One way is to place a
small magnetic compass needle at various
positions and note its orientation. This
gives us an idea of the magnetic field
direction at various points in space.
5.2.2  Bar magnet as an
equivalent solenoid
In the previous chapter, we have
explained how a current loop acts as a
magnetic dipole (Section 4.9). We
mentioned Ampere’s hypothesis that all
magnetic phenomena can be explained in
terms of circulating currents.
FIGURE 5.3 Calculation of (a) The axial field of a
finite solenoid in order to demonstrate its
similarity to that of a bar magnet. (b) A magnetic
needle in a uniform magnetic field B. The
arrangement may be used to determine either B
or the magnetic moment m of the needle.
FIGURE 5.2 The field lines of (a) a bar magnet, (b) a current-carrying finite solenoid and
(c) electric dipole. At large distances, the field lines are very similar. The curves
labelled  i  and ii are closed Gaussian surfaces.
2024-25
139
Magnetism and
Matter
The resemblance of magnetic field lines for a bar magnet and a solenoid
suggest that a bar magnet may be thought of as a large number of
circulating currents in analogy with a solenoid. Cutting a bar magnet in
half is like cutting a solenoid. We get two smaller solenoids with weaker
magnetic properties. The field lines remain continuous, emerging from
one face of the solenoid and entering into the other face. One can test this
analogy by moving a small compass needle in the neighbourhood of a
bar magnet and a current-carrying finite solenoid and noting that the
deflections of the needle are similar in both cases.
To make this analogy more firm we may calculate the axial field of a
finite solenoid depicted in Fig. 5.3 (a). We can demonstrate that at large
distances this axial field resembles that of a bar magnet.
The magnitude of the field at point P due to the solenoid is
0
3
2
4
m
B
r
µ
p
=
(5.1)
This is also the far axial magnetic field of a bar magnet which one may
obtain experimentally. Thus, a bar magnet and a solenoid produce similar
magnetic fields. The magnetic moment of a bar magnet is thus equal to
the magnetic moment of an equivalent solenoid that produces the same
magnetic field.
5.2.3  The dipole in a uniform magnetic field
Let’s place a small compass needle of known magnetic moment m allowing
it to oscillate in the magnetic field. This arrangement is shown in
Fig. 5.3(b).
The torque on the needle is [see Eq. (4.23)],
t t t t t = m × B (5.2)
In magnitude t = mB sin?
Here t t t t t  is restoring torque and ? is the angle between m and B.
An expression for magnetic potential energy can be obtained on lines
similar to  electrostatic potential energy.
The magnetic potential energy U
m
 is given by
U d
m
=
?
t ? ? ( )
      
= = - ?
mB d mB sin cos ? ? ?
      = –m.B (5.3)
We have emphasised in Chapter 2 that the zero of potential energy
can be fixed at one’s convenience. Taking the constant of integration to be
zero means fixing the zero of potential energy at ? = 90°, i.e., when the
needle is perpendicular to the field. Equation (5.3) shows that potential
energy is minimum (= –mB) at ? = 0° (most stable position) and maximum
(= +mB) at ? = 180° (most unstable position).
Example 5.1
(a) What happens if a bar magnet is cut into two pieces: (i) transverse
to its length, (ii) along its length?
(b) A magnetised needle in a uniform magnetic field experiences a
torque but no net force. An iron nail near a bar magnet, however,
experiences a force of attraction in addition to a torque. Why?
 EXAMPLE 5.1
2024-25
Physics
140
 EXAMPLE 5.1
(c) Must every magnetic configuration have a north pole and a south
pole? What about the field due to a toroid?
(d) Two identical looking iron bars A and B are given, one of which
is definitely known to be magnetised. (We do not know which
one.) How would one ascertain whether or not both are
magnetised? If only one is magnetised, how does one ascertain
which one?  [Use nothing else but the bars A and B.]
Solution
(a) In either case, one gets two magnets, each with a north and
south pole.
(b) No force if the field is uniform. The iron nail experiences a non-
uniform field due to the bar magnet. There is induced magnetic
moment in the nail, therefore, it experiences both force and
torque. The net force is attractive because the induced south
pole (say) in the nail is closer to the north pole of magnet than
induced north pole.
(c) Not necessarily. True only if the source of the field has a net
non-zero magnetic moment. This is not so for a toroid or even for
a straight infinite conductor.
(d) Try to bring different ends of the bars closer. A repulsive force in
some situation establishes that both are magnetised. If it is
always attractive, then one of them is not magnetised. In a bar
magnet the intensity of the magnetic field is the strongest at the
two ends (poles) and weakest at the central region. This fact
may be used to  determine whether A or B is the magnet. In this
case, to see which one of the two bars is a magnet, pick up one,
(say, A) and lower one of its ends; first on one of the ends of the
other (say, B), and then on the middle of B. If you notice that in
the middle of B, A experiences no force, then B is magnetised. If
you do not notice any change from the end to the middle of B,
then A is magnetised.
5.2.4  The electrostatic analog
Comparison of Eqs. (5.1), (5.2) and (5.3) with the corresponding equations
for electric dipole (Chapter 1), suggests that 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 moment
p, by making the following replacements:
? E B , ? p m , 
0
0
1
4 4
µ
e
?
p p
In particular, we can write down the equatorial field (B
E
) of a bar magnet
at a distance r, for r >> l, where l is the size of the magnet:
0
3
4
E
r
µ
= - p
m
B
(5.4)
Likewise, the axial field (B
A
) of a bar magnet for r >> l is:
0
3
2
4
A
r
µ
=
p
m
B
(5.5)
2024-25