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Magnetism Circular Current loop as a magnetic dipole
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…….(1)
For x >>> a, we may neglect the term a2. We have
……..(2)
But the area of the loop A = πa2 .…….(3)
………(4)
M = IA
…….(5)
…….(6)
Electric field of a dipole is
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……….(7)
From equations (6) and (7),
μ0 is analogous to
Magnetic dipole moment M is analogous to
electrostatic dipole moment P and magnetic field is
analogous to electrostatic field.
A planar current loop is equivalent to a magnetic
dipole of dipole moment M = IA which is analogous to
electric dipole moment P.
Thus we have shown that a current loop produces a
magnetic field and behaves like a magnetic dipole. It
experiences a torque given by, when
placed in external magnetic field and also it
generates its own magnetic field.
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Magnetic dipole moment of a revolving electron
……(8)
Circulating current …….(9)
…….(10)
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Magnitude of magnetic moment associated with
circular current is
…..(11)
…….(12)
The direction of this magnetic moment is into the
plane of paper. Negatively charged electron is
moving in anticlockwise direction, leading to a
clockwise current.
Multiplying and dividing the right hand side of
equation (12) by the mass of electron, me then
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…….(13)
……..(14)
Here L0 = me Vr = angular momentum of the
electron revolving round the nucleus.
……(15)
The negative sign indicates that the orbital angular
momentum of electron is opposite in the direction to
the orbital magnetic moment.
The ratio of magnetic dipole moment with angular
momentum of revolving electron is called the
gyromagnetic ratio.
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The circular orbit of electrons produce an orbital
magnetic moment. In addition to the orbital magnetic
moment, the electron has an intrinsic magnetic
moment called the spin magnetic moment.
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Magnetization and magnetic intensity The net magnetic dipole moment per unit volume is
called as the magnetization of the sample.
Magnetization is the vector quantity having unit A/ m
and dimensions [L-1 M0 T0 I1].
magnetization of a paramagnetic sample is directly
proportional to the external magnetic field and
inversely proportional to the absolute temperature.
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…….(18)
Equation (18) is known as Curie’s Law and C is
called Curie constant.
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The magnetization of a ferromagnetic material such
as iron can be studied with an arrangement called
Toroid with an iron core as shown in fig.
The material is formed into a thin toroidal core of
circular crossection. A toroidal coil having n turns per
unit length is wrapped around the core and carries
current I. The coil is long solenoid bent into a circle.
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If iron core were not present, the magnitude of the
magnetic field inside the coil would be
B0 = μ0nI …….(19)
Where μ0 is the permeability of vacuum
However, if iron core were present, the magnetic field
inside the coil is greater than . We can write
magnitude of this field as
B = B0 + BM …….(20)
Where BM is the magnetic field contributed by the iron
core. It turns out that this additional field BM is directly
proportional to the magnetization MZ of the iron.
BM = μ0 MZ ……(21)
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Magnetic intensity is a quantity used in describing
magnetic phenomenon in terms of their magnetic
fields.
The strength of magnetic field at a point can be given
in terms of vector quantity called as magnetic
intensity (H).
Magnetic intensity ‘B0’ is given by the relation,
B0 = μ0H …….(22)
where H = nI has the same dimensions and unit as
MZ. Magnetic intensity has unit A / m and dimensions
[L-1 M0 T0 I1].
Total magnetic field B is written as
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B = μ0 (H + MZ) …..…(23)
Magnetization and magnetic intensity is
mathematically expressed as,
MZ = XH …….(24)
where X is called the magnetic susceptibility.
Magnetic susceptibility is small and positive for
paramagnetic materials. Magnetic susceptibility is
small and negative for diamagnetic materials.
From equations (23) and (24) we obtain
B = μ0 (1 + X) H ………(25)
∴ B = μ0 μr H ………(26)
∴ B = μH ………(27)
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where μr = 1 + X, is a dimensionless quantity called
the relative magnetic permeability of the substance.
μ = μ0 μr = μ0 (1 + X) ……..(28)
Diamagnetic Substances The substances which are weakly repelled by the
magnetic field are called diamagnetic substances.
Origin1. For diamagnetic substances, the dipole moments
of electrons in an atom cancel each other. Hence,
the resultant magnetic moment of an atom is
zero.
2. When an external magnetic field is applied, the
induced magnetic moments oppose the applied
magnetic field. Therefore, the diamagnetic
substances are repelled by the magnet.
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Properties1. If a rod made-up of diamagnetic substance is
placed in a non uniform magnetic field, it moves
from stronger part of the field to the weaker part
of the field.
2. If a rod made-up of a diamagnetic substance is
placed in a uniform magnetic field, it comes to
rest with its length perpendicular to the direction
of the magnetic field.
3. When a solution of a diamagnetic substance is
taken in a watch glass and is kept between two
dissimilar poles of the magnets, there is a small
depression at the middle.
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4. When a diamagnetic liquid is taken in a U shaped
glass tube and one of its arms is held in between
two dissimilar poles of the magnets, liquid level in
that arm is lowered.
5. When a diamagnetic gas is passed through two
poles of the magnets, it spreads at right angles to
the direction of the magnetic field.
Examples : Antimony, gold, bismuth, mercury,
water, air, hydrogen are diamagnetic in nature.
Paramagnetic Substances The substances which are weakly attracted by the
magnetic field are called paramagnetic substances.
Origin1. For paramagnetic substances, the dipole
moments of electrons in an atom do not cancel
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each other. Hence, each atom has a resultant
magnetic moment.
2. Each atom in a paramagnetic substance acts as a
small magnetic dipole, called “ atomic magnet”
3. In the absence of magnetic field, atomic magnets
are randomly oriented; hence, paramagnetic
substances have zero resultant magnetic
moment.
4. When an external magnetic field is applied, the
atomic magnets are oriented so that their
moments are in the direction of the magnetic field.
Hence, the paramagnetic substances are
magnetized in the external field.
5. When the external magnetic field is removed, the
alignment of the atomic magnets is disturbed and
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the paramagnetic substances loose their
magnetism.
Properties1. If a rod made-up of paramagnetic substance is
placed in a non uniform magnetic field, it moves
from weaker part of the field to the stronger part
of the field.
2. If a rod made-up of a paramagnetic substance is
placed in a uniform magnetic field, it comes to
rest with its length parallel to the direction of the
magnetic field.
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3. When a solution of a paramagnetic substance is
taken in a watch glass and is kept between two
dissimilar poles of the magnets, there is a small
elevation at the middle.
4. When a paramagnetic liquid is taken in a U
shaped glass tube and one of its arms is held in
between two dissimilar poles of the magnets,
liquid level in that arm is raised.
5. When a paramagnetic gas is passed through two
poles of the magnets, it spreads in the direction
of the magnetic field.
Examples : Aluminium, manganese, platinum, chromium,
oxygen are paramagnetic in nature.
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Ferromagnetic Substances The substances which are strongly attracted by a
magnet are called ferromagnetic substances.
The properties of ferromagnetic substances are
similar to that of the paramagnetic substances, but
they are large in extent. When the external field is
removed these substances do not loose their
magnetism completely.
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Origin The origin of ferromagnetism can be explained on the
basis of domain theory.
Magnetic DomainsA small region in which the magnetic moments of all
the atomic magnets are lined in the same direction is
called a domain. Each domain has a certain magnetic
moment.
1. According to the domain theory,
a. a ferromagnetic substance
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is made-up of number of small regions called
domain.
b. all the atomic magnets have the same
direction of dipole moment, so that the domain
has some resultant magnetic moment.
2. In the absence of external magnetic field, the
domains are randomly oriented. Therefore, the
substance has zero resultant magnetic moment
( fig 1 )
3. In a weak external magnetic field, the
domains having magnetic moment in
the direction of the external magnetic
field begin to grow in size.
There is a shift of the boundaries between the
domains and the substance gets magnetized.
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When the external field is removed, the
boundaries return to their original positions and
the material looses its magnetism. (Fig. 2)
4. In a strong magnetic field, the
domains rotate in the direction of the
external magnetic field and the
substance gets strongly magnetized. The
boundaries vanish forever. When the external
field is removed, the domains and their magnetic
moments do not return to their original position.
( fig 3 ) This is how the ferromagnetic substances
retain their magnetism.
Examples :- Iron, nickel, cobalt, steel and their
alloys are ferromagnetic in nature.
Curie Temperature
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When a ferromagnetic substance is heated, thermal
random motion of the atoms in the domain is
enhanced. So, the coupling between the atomic
dipoles becomes weak. When the temperature is
increased further, at a certain temperature, all these
couplings are broken and the domain structure
collapses completely and each domain looses its
large magnetic moment completely.
This temperature at which the domain structure is
destroyed completely is called Curie temperature.
If the substance is held above the curie temperature,
the ferromagnetic substance is converted in to
paramagnetic substance, since the force of
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interaction between the atomic magnets responsible
for the ferromagnetism vanishes.
Curie temperatures for nickel, iron and cobalt are
360 oC , 770 oC, and 1150 oC respectively.
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