# Magnetism Maharashtra Board Additional Questions

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### Short Notes and Definitions

#### Magnetic Permeability:

• The ratio of the magnitude of the total field inside the material to that of the magnetic intensity of the magnetising field is called magnetic permeability.
• S.I. unit of magnetic permeability is H/m. Its dimensions are[L1M1T-2I-2].
• By definition  μ = B / H.

#### Relative Permeability:

• The ratio of the magnitude of the total field inside the material to that of magnetising field is called relative permeability.
• Relative permeability is dimensionless and unitless quantity.
• By definition,  μr  = B / B0

### Concepts and Explanations

#### Origin of Magnetism on the Basis of Circulating Charges:

• The origin of magnetism in substances can be explained by considering the circular motion of electrons. The electrons in atoms move in circular orbits around the nucleus which are equivalent to a circular coil carrying current.
• 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.
• These small magnets are called elementary or atomic magnets. When the material is not magnetised, these elementary magnets form closed chains thereby annualising each other’s effect. When the material is magnetised, these elementary magnets are aligned in the same direction. • On the basis of magnetic properties, substances are classified into three groups namely diamagnetic, paramagnetic and ferromagnetic.
• The Atomic theory of magnetism explains the following facts.
•  Single poles cannot exist. Poles always exist in a pair.
• The magnetic poles of a magnet are of equal strength.
• When a magnet is heated, the thermal energy of atomic magnet increases. Due to which they again form closed chain and
magnetism is lost.

#### Curie’s Law of Magnetization:

• The magnetization of a paramagnetic sample is directly proportional to the external magnetic field and inversely proportional to the absolute temperature. #### Relation Between Permeability and Susceptibility of a Substance:

• The magnitude of the magnetic field inside the coil when the 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 the magnetization of iron and is given by

BM = μMz        ……. (2)

• The strength of the 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

This is the relationship between permeability and susceptibility of a substance

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

∴   B = μμr H  = μ H

#### Effect of Heat on Ferromagnetic Substance:

• Curie temperature 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.

#### Characteristics of Diamagnetic Substances:

• The magnetic moment of every atom is zero.
• They are weakly repelled 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.
• In an external magnetic field, they get weakly magnetized in the direction opposite 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. • For diamagnetic substances magnetic susceptibility is negative.
• In absence of an external magnetic field, the net magnetic moment of diamagnetic substance is zero.
• On removal of the external magnetic field, diamagnetic substances lose their magnetism.
• 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 magnetic field is applied to a diamagnetic liquid in one arm of U-tube, the liquid level in that arm is lowered. • If diamagnetic gas is introduced between pole pieces of magnet, it spreads right angle to the magnetic field.

### Characteristics:

#### Characteristics of Paramagnetic Substances:

• Every atom is a magnetic dipole having a resultant magnetic moment.
• They are weakly attracted 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.
• In an external magnetic field, they get weakly magnetized in the same direction to that 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.
• 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.
• On removal of the external magnetic field, paramagnetic substances lose their magnetism.
• 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 the paramagnetic liquid in one arm of U-tube, the liquid level in that arm rises. • If paramagnetic gas is introduced between pole pieces of magnet, it spreads in the direction of the magnetic field.
• For paramagnetic substances, magnetic susceptibility is positive and small.
• The susceptibility decreases with increase in the temperature.

#### Characteristics of Ferromagnetic Substances:

• They are strongly magnetised when placed in an external magnetic field.
• 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.
• They do not lose magnetism when the external magnetic field is removed.
• When heated above Curie temperature they become paramagnetic.
• They are strongly attracted by an 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.
• In an external magnetic field, they get strongly magnetized in the same direction as that of the field
• 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.
• 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.
• On removal of the external magnetic field, ferromagnetic substances do not lose their magnetism. i.e. they are permanent magnets.
• For ferromagnetic substances, magnetic susceptibility is positive and large.

#### Distinguishing Between Ferromagnetic Substances and Paramagnetic Substances

 Ferromagnetic Substance Paramagnetic 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. Every atom is a magnetic dipole having a resultant magnetic moment. They are strongly magnetized when placed in an 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 weaker to the stronger 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 strongly magnetized in the same direction to that of the field In an external magnetic field, they get weakly magnetized in the same direction to that of the field For ferromagnetic substances, magnetic susceptibility is positive and large. For paramagnetic substances, magnetic susceptibility is positive and small. 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 magnetic moments of atomic magnets are randomly arranged, hence the net magnetic moment of the paramagnetic substance is zero.

### Scientific Reasons

#### Diamagnetic Substances are weakly repelled by a magnet

• The magnetic moment of every atom of diamagnetic substance is zero. In an external magnetic field, they get weakly magnetized in the direction opposite to that of the field.
• Hence when placed in a non-uniform magnetic field, they tend to move from the stronger to the weaker part of the field. Hence diamagnetic substances are weakly repelled by external magnetic field.

#### 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.

• When the dissimilar poles are separated by small distance then the magnetic field is stronger at midway than at the poles. In an external magnetic field, diamagnetic substances get weakly magnetized in the direction opposite to that of the field. Hence when placed in a non-uniform magnetic field, they tend to move from the stronger to the weaker part of the field.
• Thus the liquid at the centre moves from stronger to weaker section of the field creating a depression at the centre. #### 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.

• When the dissimilar poles are separated by small distance then the magnetic field is stronger at midway than at the poles. In an external magnetic field, paramagnetic substances get weakly magnetized in the same direction to that of the field. Hence when placed in a non-uniform magnetic field, they tend to move from the weaker to the stronger part of the field.
• Thus the liquid at the edge moves from weaker to a stronger section of the field creating an elevation at the centre. #### Paramagnetic substances cannot be used for making permanent magnets.

• 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. In an external magnetic field, they get weakly magnetized in the same direction to that of the field.
• On removal of the external magnetic field, the magnetic moments of atomic magnets again become randomly arranged.  Hence the paramagnetic substances lose their magnetism. Thus paramagnetic substances are temporary magnets. Hence Paramagnetic substances cannot be used for making permanent magnets.

#### Ferromagnetic substances are used for making permanent magnets.

• In absence of an external magnetic field, the magnetic moments of domains of ferromagnetic substance are randomly arranged, hence the net magnetic moment of a ferromagnetic substance is zero.  In an external magnetic field, they get strongly magnetized in the same direction as that of the field. The domain size increases.
• On removal of the external magnetic field, ferromagnetic substances the increased domain structure is maintained and thus ferromagnetic substance do not lose their magnetism. Hence they are used in making permanent magnets.
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