Magnetism and matter chapter 5 12th physics

 Ferromagnetism

• Ferromagnetic substances get strongly magnetised when placed in external magnetic field.
• They have strong tendency to move from a region of weak magnetic field to strong magnetic field, i.e., they get strongly attracted to a magnet.
• The individual atoms (or ions or molecules) in a ferromagnetic material possess a dipole moment as in a paramagnetic material. They align themselves in a common direction over a macroscopic volume called domain. Each domain has a net magnetisation.
  
• When we apply an external magnetic field B0, the domains orient themselves in the direction of B0 and grow in size and form a single ‘giant’ domain.
  
• In a ferromagnetic material the field lines are highly concentrated.
• In non-uniform magnetic field, the sample tends to move towards the region of high field.
• When the external field is removed, in some ferromagnetic materials the magnetisation persists. Such materials are called hard magnetic materials or hard ferromagnets. Alnico, an alloy of iron, aluminium, nickel, cobalt and copper, is one such material. The naturally occurring lodestone is another example. Such materials are used to make permanent magnets.
• ferromagnetic materials, in which the magnetisation disappears on removal of the external field are called soft ferromagnetic materials. Examples are Soft iron, iron, cobalt, nickel, gadolinium, etc. They are used to make electromagnets.
• The relative magnetic permeability is >1000!
  The ferromagnetic property depends on temperature.
• At high enough temperature, a ferromagnet becomes a paramagnet. The domain structure disintegrates with temperature. The temperature of transition from ferromagnetic to paramagnetism is called the Curie temperature Tc.
  The susceptibility above the Curie temperature, i.e., in the paramagnetic phase is described by,
  χ = Cµo /(T-Tc)

Qn. What is meant by Curie temperature of a material?

Paramagnetism:

• Paramagnetic substances are those which get weakly magnetised in the direction of external magnetic field.
• They have tendency to move from a region of weak magnetic field to strong magnetic field, i.e., they get weakly attracted to a magnet.
• Its individual atoms (or ions or molecules) possess a permanent magnetic dipole moment of their own. On account of the ceaseless random thermal motion of the atoms, no net magnetisation is seen.
• In the presence of an external field, the individual atomic dipole moment can be made to align and point in the direction of external field.
• Figure shows a bar of paramagnetic material placed in an external field.

• The field lines get concentrated inside the material, and the field inside is enhanced.
• When placed in a non-uniform magnetic field, the paramagnets tend to move from weak field to strong.
• The magnetisation of a paramagnetic material is inversely proportional to the absolute temperature M = CBo/T or equivalently, χ = Cµo /T ,This is known as Curie’s law. The constant C is called Curie’s constant.
• As the field is increased or the temperature is lowered, the magnetisation increases until it reaches the saturation value Ms, then all the dipoles are perfectly aligned with the field. Beyond this, Curie’s law is no longer valid.
  Examples of paramagnetic substances: aluminium, sodium, calcium, oxygen (at STP) and copper chloride.

Qn. State Curie's Law?

Diamagnetism

• Diamagnetic substances are those which have tendency to move from stronger to the weaker part of the external magnetic field.
• A magnet would repel a diamagnetic substance.

Figure shows a bar of diamagnetic material placed in an external magnetic field.

• The field lines are repelled or expelled and the field inside the material is reduced.
• When placed in a non-uniform magnetic field, a diamagnet will tend to move from high to low field.

Examples of diamagnetic materials: bismuth, copper, lead, silicon, nitrogen (at STP), water and sodium chloride.

Explanation for diamagnetism:

Electrons in an atom orbiting around nucleus possess orbital angular momentum. These orbiting electrons are equivalent to current-carrying loop and thus possess orbital magnetic moment. Diamagnetic substances are the ones in which resultant magnetic moment in an atom is zero. When magnetic field is applied, those electrons having orbital magnetic moment in the same direction slow down. Thus, the substance develops a net magnetic moment in direction opposite to that of the applied field and hence repulsion.

Meissner effect:

Superconductors are metals, cooled to very low temperatures which exhibits both perfect conductivity and perfect diamagnetism. Here the field lines are completely expelled! χ = –1 and µr = 0. A superconductor repels a magnet and is repelled by the magnet. The phenomenon of perfect diamagnetism in superconductors is called the Meissner effect.

Magnetisation:

Intensity of magnetization M of the sample is equal to its net magnetic dipole moment per  unit volume: 

M = m/V

M is a vector. It's SI unit is A/m

Magnetic field in a solenoid

B0 = µ0 ni = µ0H

Magnetizing field intensity, H =ni = Bo / µo

It is a vector quantity. It's SI unit is also A/m.

Net magnetic field inside the solenoid, when iron is inserted

B = µoni + µoM

B = µo(H + M)

Magnetization is proportional to applied magnetic field intensity

M = xH

x is called magnetic susceptibility

B = µo(H + xH) = µoH(1 + x) 

B = µo(1 + x)H

(1 + x) = µr (relative permittivity)

B = µoµrH = µH

µ= µoµr is called the magnetic permeability of the material

Magnetic meridian: magnetic meridian at a place is a vertical plane containing Earth's magnetic axis.

Geographic meridian: the geographic meridian at a place is a vertical plane containing Earth's geographic axis of rotation.

Elements of earth’s magnetic field:

Magnetic declination (θ)= It is the angle between magnetic meridian and geographic meridian.

Angle of Dip (δ) or inclination= It is the angle between Earth's magnetic and the horizontal at the place.

Horizontal component of earth’s magnetic field (BH): 

BH = B cos δ

BV = B sin δ

tan δ = Bv/BH

Example 5.9 In the magnetic meridian of a certain place, the

horizontal component of the earth’s magnetic field is 0.26G and the dip angle is 60º. What is the magnetic field of the earth at thas location?

5.11 At a certain location in Africa, a compass points 12º west of the
geographic north. The north tip of the magnetic needle of a dip circle placed in the plane of magnetic meridian points 60º above the horizontal. The horizontal component of the earth’s field is measured to be 0.16 G. Specify the direction and magnitude of the earth’s field at the location.

Define Magnetic flux and write its SI unit.

The number of magnetic field lines passing through a surface held normal to the lines, is called magnetic flux.

Magnetic Flux = B.A = BAcosθ

It is a scalar quantity. It's SI unit is T.m2 or Webber(Wb)

Magnetic potential energy of magnetic dipole kept in uniform magnetic field:

The work done to rotate the dipole in magnetic field is stored as potential energy in it.

The magnetic potential energy Um is given by

W= ∆Um

= ∫τdθ = mB∫ sinθ.dθ

= -mB(cosθ2-cosθ1)

If we select zero of potential energy when dipole axis (m) is perpendicular to B, then

θ1 = 900 and θ2 = θ, U1= 0

U2-0 =Um= -mBcosθ

Torque on a bar magnet placed in uniform external magnetic field B:

Using the similarity with the electric dipole we can write the expression just by replacing p = m and E = B

τ = mxB vector quantity

τ = mBsinθ

m is magnetic dipole moment

5.3 A short bar magnet placed with its axis at 30º with a uniform external magnetic field of 0.25 T experiences a torque of magnitude equal to
4.5 × 10-2 J. What is the magnitude of magnetic moment of the magnet?

Properties of bar magnet: 

• Magnetic poles exist in pairs. 
• Like poles repel while unlike poles attract. 
• It aligns in the direction of geographic north and south when suspended freely. 
• It attracts other magnets and magnet like materials.

Properties of magnetic lines of force: 

b magnetic field lines

c electric field lines

• They emerge out of North Pole and directed towards South Pole. 
• They never cross each other. 
• They form closed loops. 
• They pass through conductors. 
• The relative density of lines gives the intensity of the magnetic field in that region. 
• They emerge out normal to the surface.

Magnetic dipole: a bar magnet, a compass needle, solenoid and a circular current loop are examples of magnetic dipole having North and South poles.

Dipole axis is a line, South to North pole outward.

Magnetic dipole moment of a circular loop

m = iNA

We can create magnetic field equal to that of a bar magnet by passing a suitable current through a coil(solenoid).

Remember the magnetic field on the axis of circular current loop

B=µ0.2m/4πx3

Magnetic field due to a short bar magnet: 

At any point on its axial line:

Bax = µo.2m/4πr3  

along the axis, r= distance of the point from the centre of the bar magnet.

Example 5.8 The earth’s magnetic field at the equator is approximately 0.4 G. Estimate the earth’s dipole moment.

At any point on its equatorial line: 

Beq = µo.m/4πr3  

(anti parallel to the axis.)