# Magnetism Maharashtra Board Textual Questions

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#### 1.1 Expression for Magnetic Dipole of Revolving Electron: • The origin of magnetism in substances can be explained by considering the circular motion of electrons. The negatively charged electrons in atoms move in circular orbits around the positively charged nucleus which are equivalent to a circular coil carrying current.

The period of revolution of the electron The direction of this magnetic moment is into the plane of the paper.

If me is the mass of the electron, multiplying and dividing the numerator and denominator of R.H.S. Lo is the angular momentum of the electron which is coming out of the plane of the paper.

The quantities e, me are constant,

hence the magnetic dipole moment of the electron is directly proportional to its angular momentum.

The angular momentum of electron and magnetic dipole moment are opposite to each other in vector form #### 2.1 To prove Magnetic Moment of electron – evr/2: • The origin of magnetism in substances can be explained by considering the circular motion of electrons. The negatively charged electrons in atoms move in circular orbits around the positively charged nucleus which are equivalent to a circular coil carrying current.

The period of revolution of the electron Proved as required.

#### 3.1 Current Loop as Magnetic Dipole: • The magnetic induction at a point on the axis at a distance of ‘x’ from the centre of a circular coil of radius ‘a’ is given by It is directed along the axis of the coil and away from it and perpendicular to plane of the coil.

For x >>a, we can neglect a² from denominator in the expression. This is an expression for magnetic induction due to current carrying loop

Now, the electric intensity due to an electric dipole on its axis is given by • From the two equations (3) and (4) we can say that the magnetic dipole moment is analogous to electrostatic dipole moment P and the magnetic field is analogous to the electric field. Thus the planar current loop is analogous to a magnetic dipole. i.e. current carrying loop produces a magnetic field and behaves like a magnetic dipole.

#### 4.1 Magnetization:

• The net magnetic dipole moment per unit volume is called as the magnetization of a sample.
• It is denoted by Mz. It is a vector quantity. S.I. unit of magnetization is A/m and its dimensions are [L-1I1].
• By definition, magnetization. #### 4.2  Magnetic Intensity:

• Magnetic intensity is a quantity used in describing the magnetic phenomenon in terms of their magnetic fields. The strength of the magnetic field at a point can be given in terms of vector quantity called magnetic intensity (H).
• S.I. unit of magnetic intensity is A/m and its dimensions are  [L-1I1].
• By definition, magnetic intensity #### 5.1 Explanation of Magnetization of Ferromagnetic Material With Help of Toroid Ring:

• The magnetization of a ferromagnetic material such as iron can be studied with an arrangement called Toroid with an iron core. • Let the toroid have ‘n’ number of turns per unit length and ‘I’ be the current through it. The magnitude of magnetic field inside the coil when iron core is not present is given by

B0 = μn I

When an iron core is present in the toroid, the magnetic field increases, which is given by

B = B0  +  BM    ……… (1)

Where BM is magnetic field contributed by the iron core.

• It is found that BM is directly proportional to magnetization of iron and is given by

BM = μMz        ……. (2)

• The strength of magnetic field at a point can be given in terms of vector quantity called magnetic intensity (H).

Thus  B0 = μH  ……… (3)

Where, H = nI. Unit of magnetic intensity is A/m and its dimensions are [L-1M0T0I1].

Substituting values of equations (2) and (3) in (1)

B = μH + μM

B = μ(H + M)  ………….. (4)

Magnetization can be expressed in terms of magnetic intensity as

Mz   = χ H

Where χ (chi) is called the magnetic susceptibility.

Substituting in equation (4)

B = μ(H + χ H )

∴   B = μ(1 + χ  ) H

The quantity (1 + χ  )  is called relative magnetic permeability and is denoted by μr. It is a dimensionless quantity

∴   B = μμr H  = μ H

#### 6.1 Distinguishing Between Diamagnetic and Paramagnetic Substances:

 Diamagnetic Substance Paramagnetic Substance The magnetic moment of every atom of diamagnetic substance is zero. Every atom is a magnetic dipole having a resultant magnetic moment. They are weakly repelled by external magnetic field. They are weakly attracted by external magnetic field. When placed in a non-uniform magnetic field, they tend to move from the stronger to the weaker part of the field. When placed in a non-uniform magnetic field, they tend to move from the weaker to the stronger part of the field. In an external magnetic field, they get weakly magnetized in the direction opposite to that of the field In an external magnetic field, they get weakly magnetized in the same direction to that of the field When a rod of diamagnetic substance is suspended in a uniform magnetic field, it comes to rest with its length perpendicular to the directions Of the field. When a rod of a paramagnetic substance is suspended in a uniform magnetic field, it comes to rest with its length parallel to the directions of the field. For diamagnetic substances magnetic susceptibility is negative. For paramagnetic substances, magnetic susceptibility is positive and small. In absence of an external magnetic field, the net magnetic moment of diamagnetic substance is zero. In absence of an external magnetic field, the magnetic moments of atomic magnets are randomly arranged, hence the net magnetic moment of the paramagnetic substance is zero. If a watch glass containing a small quantity of diamagnetic liquid is placed on two dissimilar magnetic poles, the liquid shows a depression in the middle. If a watch glass containing a small quantity of paramagnetic liquid is placed on two dissimilar magnetic poles, the liquid shows an elevation in the middle. If a magnetic field is applied to a diamagnetic liquid in one arm of U-tube, the liquid level in that arm is lowered. If a magnetic field is applied to the paramagnetic liquid in one arm of U-tube, the liquid level in that arm rises. If diamagnetic gas is introduced between pole pieces of magnet, it spreads right angle to the magnetic field. If paramagnetic gas is introduced between pole pieces of magnet, it spreads in the direction of the magnetic field.

#### 7.1 Distinguishing Between Ferromagnetic Substances and Diamagnetic Substances

 Ferromagnetic Substance Diamagnetic Substance The substances are made up of a large number of small domains. The atomic magnets in one domain are aligned in the same direction due to strong interaction is known as exchange coupling. The magnetic moment of every atom of diamagnetic substance is zero. They are strongly magnetized when placed in an external magnetic field. They are weakly repelled by external magnetic field. When placed in a non-uniform magnetic field, they tend to move from the weaker to the stronger part of the field. When placed in a non-uniform magnetic field, they tend to move from the stronger to the weaker part of the field. In an external magnetic field, they get strongly magnetized in the same direction to that of the field In an external magnetic field, they get weakly magnetized in the direction opposite to that of the field On removal of the external magnetic field, ferromagnetic substances do not lose their magnetism. i.e. they are permanent magnets. On removal of the external magnetic field, diamagnetic substances lose their magnetism. When a rod of a ferromagnetic substance is suspended in a uniform magnetic field, it comes to rest with its length parallel to the directions of the field. When a rod of diamagnetic substance is suspended in a uniform magnetic field, it comes to rest with its length perpendicular to the directions Of the field. For ferromagnetic substances, magnetic susceptibility is positive and large. For diamagnetic substances magnetic susceptibility is negative. In absence of an external magnetic field, the magnetic moments of domains are randomly arranged, hence the net magnetic moment of a ferromagnetic substance is zero. In absence of an external magnetic field, the net magnetic moment of diamagnetic substance is zero.

#### 8.1 Explanation of Ferromagnetism on the Basis of Domain Theory:

• Ferromagnetism is a special case of Paramagnetism.  In ferromagnetic substances, to the magnetic dipole moment of atoms, the contribution of the spin magnetic moment is very large.
• According to the domain theory, a ferromagnetic substance consists of a large number of small units (regions) known as Domains.  A domain ‘is an extremely small region containing a large number of atomic magnets having magnetic axes aligned in the same direction due to a strong exchange coupling. When a ferromagnetic substance is kept in the magnetic field, the permanent alignment of the domain due to a strong interaction (force) takes place this force is known as exchange coupling. In one domain the magnetic dipole moments of all the atoms are aligned in the same direction. Hence each domain has a resultant magnetic dipole moment.  This permanent alignment is due to a strong interaction (force) known as exchange coupling. • However, in the absence of an external magnetic field, various domains have random orientations and hence their resultant magnetic moment is zero.
• When a ferromagnetic substance is subjected to an external magnetic field, each domain experience a torque.  As a result of this, some domains rapidly rotates and remains aligned parallel to the direction of the field. This is called as domain rotation or flipping.
• At the same time, those domains whose magnetic axes are nearly in line with the external magnetic field grow in size at the cost of the neighbouring domains.  This is called domain growth.
• As the strength of the external magnetic field is increased, more and more domains flip and align in the direction of the external magnetic field.  Finally, at a certain stage, practically all domains get aligned in the direction of the field.  This is known as magnetic saturation.  At this stage, a ferromagnetic substance behaves as a permanent magnet and retains its magnetic property (residual magnetism) even if the external magnetic field is removed.

#### 9.1 Curie Temperature and its Significance:

• It is the temperature required to destroy the alignment of domains and to make a ferromagnetic substance demagnetised.
• Above Curie temperature. a ferromagnetic substance behaves as paramagnetic.  When a ferromagnetic substance is heated, the exchange coupling between neighbouring atoms becomes loose and ultimately the domain structure gets vanished.
• If the heating is continued then at the Curie temperature, the exchange coupling disappears and the domain structure is destroyed and hence the substance becomes paramagnetic.
• Curie temperature is the characteristic property of the substance.
• It is different for different materials. e.g.  Fe (1043 K), Ni (631 K), Co (1394 K), Gadolinium (317 K), Fe2O3 (893 K).

#### 10.1 Classification of Material on the Basis of Behaviour in Magnetic Field:

• On the basis of magnetic properties, substances are classified into three groups namely diamagnetic, paramagnetic and ferromagnetic.
• #### Diamagnetic substances:

• Those substances which are weekly magnetised when placed in an external magnetic field, in a direction opposite to the applied field are called diamagnetic substances. The magnetism exhibited by these substances is called diamagnetism.
• Examples: Copper, gold, antimony, bismuth, silver, lead, silicon, mercury, water, air, hydrogen, nitrogen etc.
• #### Paramagnetic Substances:

• Those substances which are weekly magnetised when placed in an external magnetic field in the same direction as the applied field are called Paramagnetic substances.  They tend to move from weaker to the stronger part of the field. The magnetism exhibited by these substances is called paramagnetism.
• Examples: Aluminium, platinum, manganese, chromium, sodium, calcium, lithium, tungsten, niobium, copper chloride, crown glass, oxygen etc.
• #### Ferromagnetic substances:

• Those substances which are strongly magnetised in an external magnetic field in the same direction as the external applied field and retain its magnetic moment even after the removal of external field are Called Ferromagnetic substances.  They have very strong tendency to move from weaker to the stronger parts of the external field. The magnetism exhibited by these substances is called ferromagnetism.
• Examples: Iron, cobalt, nickel.

#### 11.1 Origin of Diamagnetism on The Basis of Atomic Structure:

• The orbital motion of electrons gives rise to an orbital magnetic moment. In addition, the electrons spin about its own axis constituting a spin magnetic moment.  The resultant magnetic moment of an atom is the vector sum of orbital and spin magnetic moment. In an atom, electrons can have clockwise or anticlockwise spin. Similarly, the electrons can revolve around the nucleus in clockwise or anticlockwise direction.
• In diamagnetic substances, the orbital magnetic moments and magnetic moments of atoms are oriented in such a way that the vector sum of the magnetic moment of an atom is zero.
• When a diamagnetic substance is placed in an external magnetic field, the induced e.m.f. in each atom increases.  As a result, the speed of electrons revolving in one direction increases and those revolving in opposite direction decreases.  Thus the substance as a whole acquires a net magnetic moment in a direction opposite to the applied field.

#### 12.1 Origin of Paramagnetism on The Basis of Atomic Structure:

• In paramagnetic substances, the orbital and spin magnetic moments of atoms are oriented in such a way that, each atom has a permanent magnetic dipole moment. However, due to thermal motion (vibration), the direction of the magnetic moments of the atoms have random orientations.  As a result of this, the net magnetic moment of a paramagnetic substance is zero. • When a paramagnetic substance is placed in an external magnetic field, each atomic magnets tend to align in the direction of the field.  Thus a paramagnetic substance acquires a net magnetic moment (magnetisation).
• However, the degree of alignment depends directly on the strength of the external field and inversely on the temperature of the specimen.
• When the paramagnetic’ substance is removed from the magnetic field, the alignment is once again disturbed by thermal vibrations and it gets demagnetised.  For this, reason, paramagnetic substances cannot be used as permanent magnets.
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