MHT-CET : Physics Entrance Exam

### MHT - CET : Physics - Magnetism Page 2

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3.

Magnetic Potential at Any Point Due to a Short Magnetic Dipole:

Consider a magnetic dipole of dipole moment . Let P be any point at a distance 'r'
from the centre 'O' of a dipole. Magnetic length of the dipole be 2
l. Line OP makes an angle q with dipole moment .

1.

Potential at P due to north pole is

V1 =

 m0 4p

 m r1

2.

Potential at P due to south pole is

V2 =

 m0 4p

 (-m) r2

3.

Total potential V = V1 + V2 =

 m0 4p

[

 r2 - r1 r1r2

]

4.

For a short dipole, substitute r2 - r1 = 2l cos q and r1r2 = r2 in equation (1)

\ V =

 m0 4p

 M cos q r2

… for a short dipole.

5.

Special Cases:

(i)

Point on axis:

Vaxis = ±

 m0 4p

 M r2

(q = 0° or 180°)

(ii)

Point on equator: Vequator = 0

(q = 90°)

Remember: Magnetic potential is a scalar quantity.

SI unit of magnetic potential: J/A-m or Wb/m.

4.

Diamagnetism, Paramagnetism and Ferromagnetism

Introduction:
According to modern Physics, electric charges produce magnetic effects. The magnetic properties of solids, liquids and gases arise due to orbital motion and spinning of electrons in their atoms. Electrons revolve in circular orbits around the nucleus which is at the centre. Each electron orbit can be imagined as a circular loop of wire and revolving electron in loop produces current. The current carrying loop has a magnetic moment. Therefore, due to the orbital motion of an electron, it has an orbital magnetic moment 0. In addition, an electron also spins about its own axis. This spinning of an electron, gives rise to a spin magnetic moment s.
\ The net magnetic moment of electron due to orbital motion and spinning motion is then given by a vector sum
e = 0 + s
Thus, each electron in an atom has a magnetic moment and hence an atom of an element may have magnetic moment. The overall magnetic moment of atom is known as the atomic (magnetic) dipole moment and is given by the vector sum of magnetic moments of all electrons in an atom.
i.e., atom =
Se

If vector sum S e vanishes, then the atom has no magnetisation.
If vector sum
S e is finite then atom has resultant moment and magnetisation. Thus, cause of magnetisation of matter lies with motion of an electron in atom.

According to the behaviour of the substances in an external magnetic field, they are divided into three categories:
1) Diamagnetic substances
2) Paramagnetic substances
3) Ferromagnetic substances

 Property Diamagnetic substance Paramagnetic substance Ferromagnetic substance Behaviour in non-uniform magnetic field Moderate tendency to move from stronger to weaker parts of the field Moderate tendency to move from weaker to stronger part of the field Strong tendency to move from weaker to stronger part of the field Magnetic dipole moment of atom Zero Non-zero Non-zero Directions of magnetic moment and external field Opposite Same Same Position of a rod suspended in uniform field Perpendicular to the field Parallel to the field Parallel to the field If external field is removed Substance loses magnetism Substance loses magnetism Substance retains some magnetism Examples Bismuth, antimony, copper, water, alcohol, hydrogen Manganese, aluminium, platinum, titanium, crown glass, oxygen Iron, cobalt, nickel, gadolinium, dysprosium. Magnetic permeability m < m0 m > m0 m >> m0 Attraction / Repulsion by a magnet Weakly repelled by a magnet. Weakly attracted by a magnet Strongly attracted by a magnet.

5.

Ferromagnetism on the Basis of Domain Theory and Curie Temperature

In a ferromagnetic material, each atom has a resultant magnetic moment and strong interactions are present between the moments. Due to these interactions, the magnetic moments of neighbouring atoms are aligned parallel when there is no external magnetic field. As a result of this, tiny regions of a very strong magnetism is formed in ferromagnetic material. These regions are called domains.

Ordinarily, the magnetic moments of different domains are oriented at random, so that the resultant magnetic moment of a substance is zero.

When an unmagnetised specimen of a ferromagnetic substance is placed in a WEAK external magnetic field, the domains whose magnetic moments are in the direction of the external field grow in size at the expense of the neighbouring non-aligned domains i.e., the domain boundaries are shifted in such a way that the number of atoms lined up in the direction of the applied field increases. When external applied field is removed, the domain boundaries return to their original positions leaving the substances in an unmagnetised state. (Fig. ii)
When the specimen is placed in a STRONG external magnetic field, the axes of all domains rotate abruptly. All atomic magnets orient themselves in the direction of external magnetic field and magnetisation increases. When this happens, the domains do not come back to their original positions after the removal of external field and hence material is permanently magnetised. (Fig. iii)

Curie Temperature: As the temperature of the ferromagnetic substance is increased, the increased thermal motion of atoms tends to break up the coupling between various atomic magnets in a particular domain. Therefore, the magnetic moments of the atoms in a domain get oriented in different directions and hence domain structure collapses.

The temperature at which the domain structure collapses is called the curie temperature.

At curie temperature, a ferromagnetic substance loses its magnetic properties. If the temperature of the substance is above curie temperature, the substance becomes paramagnetic.

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