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Magnetic Materials

The introduction of material media into the study of magnetism has very different consequences as compared to the introduction of material media into the study of electrostatics. When we dealt with dielectric materials in electrostatics, their effect was always to reduce Description: 74101.png below what it would otherwise be, for a given amount of free electric charge. In contrast, when we deal with magnetic materials, their effect can be one of the following:
  1. To reduce Description: 74093.png below what it would otherwise be, for the same amount of free electric current (diamagnetic materials)
  2. To increase Description: 74086.png a little above what it would otherwise be (paramagnetic materials)
  3. To increase Description: 74078.png a lot above what it would otherwise be (ferromagnetic materials) 

Magnetisation, or Magnetic Polarisation

Magnetisation is the property of some magnetic materials which describes a magnetic field created by those materials themselves and the effects of some external magnetic field on those materials.
Magnetisation Description: 76459.png is defined as the amount of magnetic moment per unit volume. It is expressed in amperes per metre (A/m).
The origin of the magnetic moments that create the magnetisation can be microscopic electric currents (bound current, Ib) due to
  • either the rotation of electrons around the positive nucleus, or
  • the spin of the electrons
Both of these electronic motions produce internal magnetic fields Description: 74046.png that are similar to the magnetic field produced by a current loop. The equivalent current loop has the magnetic moment,
Description: 74038.png
where S is the area of the loop and Ib is the bound current.

Magnetisation in Maxwell’s Equations

Magnetic Susceptibility (χm)
The magnetic susceptibility χm of a magnetic material is a measure of the degree of magnetisation of a material in response to an applied magnetic field.
Permeability (μ) is the degree of magnetisation of a material that responds linearly to an applied magnetic field.

Classification of Magnetic Materials

Depending upon the values of the magnetic susceptibility (χm) or the relative permeability (μr), magnetic materials are broadly classified into three groups as
1. Paramagnetism
2. Diamagnetism
3. Ferromagnetism
  1. Paramagnetism
The atoms or molecules comprising paramagnetic materials have a permanent magnetic dipole moment. In the absence of any applied external magnetic field, the permanent magnetic dipoles in a paramagnetic material are randomly aligned and thus do not have any magnetisation Description: 73597.png and thus, the average magnetic field Description: 73587.png is also zero.
However, when we place a paramagnetic material in an external field Description: 73580.png, the dipoles experience a torque that tends to align Description: 73573.png with Description: 73564.png, thereby producing a net magnetisation Description: 73555.png parallel to Description: 73542.png. Since Description: 73535.png is parallel to Description: 73528.png, it will tend to enhance the field. Hence, for paramagnetic materials, magnetic permeability, μ > μ0.
In most paramagnetic substances, the magnetisation Description: 73521.png is not only in the same direction as Description: 73511.png, but also linearly proportional to it. This is possible because without the external field there would be no alignment of dipoles and hence no magnetisation.
The linear relation between Description: 73502.png and Description: 73494.png is expressed as,
Description: 73487.png
where χm is a dimensionless quantity called the magnetic susceptibility.
Thus, the net magnetic field can be written as,
Description: 73480.png
where μr = (1 + χm) is called the relative permeability of the material.
For paramagnetic materials, μr > 1 or magnetic susceptibility, χm > 0 (positive), although χm is usually of the order of 10-6 to 10-3. Paramagnetism is temperature dependent.
Examples of Paramagnetic Materials are air, platinum, tungsten, potassium, aluminium, chromium, palladium, copper sulphate, manganese, etc.
  1. Diamagnetism
In the case of diamagnetic materials, the magnetic fields due to electronic motions completely cancel each other and thus, the magnetic material does not have permanent magnetic dipoles. The presence of an external field Description: 73471.png will induce magnetic dipole moments in the atoms or molecules. However, these induced magnetic dipoles are antiparallel to Description: 73462.png, leading to a magnetisation Description: 73451.png and average field antiparallel to Description: 73444.pngand therefore a reduction in the total magnetic field strength. Hence, for diamagnetic materials, magnetic permeability, μ < μ0.
For diamagnetic materials, relative permeability, μr<1, or magnetic susceptibility, χm < 0 (negative), although χm is usually of the order of -10-5 to -10-9.
Examples of Diamagnetic Materials are copper (χm = -0.95 × 10-5), gold (χm = -3.2 × 10-5), silver (χm = -2.6 × 10-5), lead, silicon, diamond, bismuth (χm = -16.6 × 10-5), antimony, mercury, tin, zinc, alcohol, hydrogen, nitrogen, water, etc.
  1. Ferromagnetism
In ferromagnetic materials, there is a strong interaction between neighbouring atomic dipole moments. Ferromagnetic materials are made up of small patches called magnetic domains, as illustrated in Fig. An externally applied field Description: 73437.png will tend to line up those magnetic dipoles parallel to the external field, as shown in Fig. The strong interaction between neighbouring atomic dipole moments causes a much stronger alignment of the magnetic dipoles than in paramagnetic materials.
Examples of Ferromagnetic Materials are iron, steel, nickel, cobalt.

Hysteresis in Ferromagnetic Materials

The permeability μ of a ferromagnetic material is not a constant, since neither the total field nor the magnetisation Description: 73387.png increases linearly with Description: 73379.png. Although the relation Description: 73372.png is applicable for all types of magnetic materials, the relation between Description: 73365.png and Description: 73356.png for ferromagnetic materials is not unique, but is dependent on the previous magnetic history of the material. The phenomenon is known as hysteresis. The variation of Description: 73347.png as a function of the externally applied field Description: 73336.png is shown in Fig. The curve is known as a hysteresis curve or magnetisation curve or B–H curve.

Hysteresis curve or magnetisation (B-H) curve
From the hysteresis loop, a number of primary magnetic properties of a material can be determined.
  1. Retentivity
    (The value of Description: 73273.png at the point b on the hysteresis curve) It is a measure of the residual magnetic flux density corresponding to the saturation induction of a magnetic material. In other words, it is the ability of a material to retain a certain amount of residual magnetic field when the magnetising force is removed after achieving saturation.
  2. Residual Magnetism or Residual Flux
    It is the magnetic flux density that remains in a material when the magnetising force is zero. The residual magnetism and retentivity are the same when the material has been magnetised to the saturation point. However, the level of residual magnetism may be lower than the retentivity value when the magnetising force did not reach the saturation level.
  3. Coercive Force
    (The value of Description: 73264.png at point c on the hysteresis curve.) This is the amount of reverse magnetic field which must be applied to a magnetic material to make the magnetic flux return to zero.
  4. Hysteresis Loss
    The area of a hysteresis loop gives the energy loss per unit volume during one complete cycle of periodic magnetisation of a ferromagnetic material. This is called hysteresis loss. This loss is in the form of heat.
  5. Permeability
    As has been previously mentioned, permeability is a material property that describes the ease with which a magnetic flux is established in a material. It is the ratio of the flux density to the magnetising force and is represented by the equation Description: 73255.png.
This equation describes the slope of the curve at any point on the hysteresis loop. The permeability value given in papers and reference materials is usually the maximum permeability or the maximum relative permeability. The maximum permeability is the point where the slope of the B–H curve for the unmagnetised material is the greatest. This point is often taken as the point where a straight line from the origin is tangent to the B–H curve as shown in Fig.
Description: 148942.png
 Determination of permeability from hysteresis curve

The relative permeability is arrived at by taking the ratio of the material’s permeability to the permeability in free space (air).
Description: 73244.png
  1. Reluctance
    It is the opposition that a ferromagnetic material shows to the establishment of a magnetic field. Reluctance is analogous to the resistance in an electrical circuit.
    The shape of the hysteresis loop tells a great deal about the material being magnetised. The hysteresis curves of two different materials are shown in the graph.
Relative to other materials, a material with a wider hysteresis loop has
  • Lower permeability
  • Higher retentivity
  • Higher coercivity
  • Higher reluctance
  • Higher residual magnetism
  • Higher loss
Relative to other materials, a material with a narrower hysteresis loop has
  • Higher permeability
  • Lower retentivity
  • Lower coercivity
  • Lower reluctance
  • Lower residual magnetism
  • Lower loss
Description: 148962.png
Different shapes of hysteresis curves

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