03-03-2025 A | General Studies | ESE

Key Concepts

• Magnetic Field Intensity (H): Number of turns (N) times current (I) divided by length (L) of a solenoid; measured in Ampere per meter (A/m).
• Magnetic Flux Density (B): Magnetic flux per unit area; related to H by B = μH, where μ is permeability.
• Permeability (μ): Measure of a material's ability to support the formation of magnetic fields; μ = μr * μ0.
• Relative Permeability (μr): Ratio of a material's permeability to the permeability of free space (μ0); μr = 1 for vacuum.
• Magnetization (M): Magnetic dipole moment per unit volume; measured in Ampere per meter (A/m).
• Magnetic Susceptibility (χm): Dimensionless quantity indicating the degree to which a material will become magnetized in response to an applied magnetic field; χm = μr - 1.
• Magnetic Dipole Moment (pM): Measure of the strength and orientation of a magnet or other object that produces a magnetic field; pM = Current * Area * n̂ (unit vector).
• Bohr Magneton (μB): Unit of magnetic moment, equal to 9.27 x 10^-24 Ampere meter squared (A m^2).
• Curie Law: Describes the temperature dependence of susceptibility in paramagnetic materials: χm = C/T, where C is the Curie constant and T is temperature.
• Curie-Weiss Law: Modified Curie Law for some paramagnetic materials: χm = C/(T - θ), where θ is the Curie temperature.
• Neel Temperature (TN): Temperature above which an antiferromagnetic material becomes paramagnetic.
• Magnetostriction: Change in the dimensions of a magnetic material when subjected to a magnetic field.
• Hysteresis Loop: Graph showing the relationship between magnetic field (H) and magnetization (M) in a ferromagnetic material.
• Retentivity (Br): The ability of a ferromagnetic material to retain a certain amount of residual magnetism upon removal of the magnetizing force.
• Coercivity (Hc): The intensity of the magnetic field required to reduce the magnetization of a ferromagnetic material to zero after it has been magnetized to saturation.
• Eddy Current Loss: Energy loss in a magnetic core due to circulating currents induced by a changing magnetic field.
• Hysteresis Loss: Energy loss in a magnetic material due to the energy required to reorient magnetic domains during alternating magnetization.

1. Magnetic Field and Material Properties

• Magnetic Field Intensity (H): Defined as H = NI/L, where N is the number of turns, I is the current, and L is the length of a solenoid. Unit: Ampere/meter (A/m).
• Magnetic Flux Density (B): Defined as B = μH, where μ is the permeability of the medium.
• Permeability (μ): Represents the material's ability to support the formation of magnetic fields. μ = μr * μ0, where μr is relative permeability and μ0 is the permeability of free space (4π x 10^-7 Henry/meter).
• Relative Permeability (μr): μr = 1 for vacuum and not equal to 1 for other materials.
• Magnetization (M): When a magnetic material is placed in a magnetic field, it either attracts or repels the field. This phenomenon is called magnetization.
• Magnetic Dipole Moment (pM): Defined as pM = I * A * n̂, where I is the current, A is the area of the loop, and n̂ is the unit vector perpendicular to the plane of the loop. Unit: Ampere meter squared (A m^2) or Bohr Magneton (μB). 1 μB = 9.27 x 10^-24 A m^2.
• Magnetization (M) Quantified: M = n * pM, where n is the number of magnetic dipoles per unit volume (dipoles/m^3). Unit: Ampere/meter (A/m).
• Total Magnetic Flux Density (B): B = μ0(H + M) = μ0H + μ0M. Also, B = μrμ0H.
• Relationship between M, H, and μr: M = (μr - 1)H.
• Magnetic Susceptibility (χm): χm = μr - 1. M = χmH.
• Vacuum: μr = 1, therefore χm = 0. Vacuum is the only true non-magnetic medium.
• χm > 0: Material is attracted towards the magnetic field.
• χm < 0: Material is repelled away from the magnetic field.

2. Origin of Permanent Magnetic Dipole Moment

• Angular Motion of Charge: Results in magnetism.
• Atomic Level Factors:
  • Electron orbital angular momentum.
  • Electron spin angular momentum.
  • Nuclear spin angular momentum.
• Strong Magnetic Materials: Magnetic properties are mainly influenced by electron spin angular momentum.
• Elements with Unpaired Electrons: Possess non-zero electron spin dipole moment.
• Spin Dipole Moment: pM = j * μB, where j is the number of unpaired electrons in the inner d-orbit of the element.
• Example: Iron (Fe): Atomic number 26. Electronic configuration: [Ar] 3d^6 4s^2. Four unpaired electrons in the 3d orbital. pM = 4μB.

3. Classification of Magnetic Materials

• Diamagnetic Materials:
  • Do not contain permanent electron spin dipole moments.
  • Have completely paired electrons.
  • Magnetism is a very weak form and non-permanent.
  • Induced by a change in the orbital motion of electrons due to an applied magnetic field.
  • The induced magnetic moment is small and in a direction opposite to that of the applied magnetic field.
  • χm is small and negative.
  • Perfect diamagnetic materials repel all magnetic flux (B = 0, μr = 0, χm = -1).
  • Examples: Bismuth, copper, diamond, gold, lead, mercury, hydrogen, water.
• Paramagnetic Materials:
  • Contain permanent electron spin dipole moments.
  • Dipoles are randomly oriented.
  • Net magnetization is zero in the absence of a magnetic field.
  • Each dipole experiences a torque due to the applied magnetic field, which tries to orient them towards the applied field.
  • Small and positive value of magnetic susceptibility.
  • Examples: Aluminum, calcium, lithium, oxygen, platinum, chromium.
  • Curie Law: χm = C/T (Susceptibility is inversely proportional to temperature).
  • Curie-Weiss Law: χm = C/(T - θ) (Modified Curie Law for some paramagnetic materials).
  • Neel Temperature (θ): Below this temperature, the material is ferromagnetic; above it, paramagnetic.
• Ferromagnetic Materials:
  • Characterized by the presence of parallel alignment of permanent magnetic dipoles.
  • Strongly magnetized on the application of a magnetic field along the direction of the field.
  • Remain magnetized even after the removal of the field (spontaneous magnetization).
  • Exhibit hysteresis.
  • Remain ferromagnetic up to the Curie temperature.
  • Examples: Iron (Curie temperature: 1043 K), Nickel (631 K), Cobalt (1404 K), Gadolinium.
  • Retentivity: Maximum value of spontaneous magnetization (maximum value of flux stored at zero applied magnetic field).
  • Coercivity: Field required to be applied to make spontaneous magnetization zero.
• Antiferromagnetic Materials:
  • Contain permanent magnetic dipoles that are equal in magnitude but aligned in an antiparallel manner.
  • Spontaneous magnetization is zero.
  • Small and positive value of magnetic susceptibility.
  • Remain antiferromagnetic up to the Neel temperature.
  • Examples: Manganese oxide (MnO), Cobalt oxide (CoO), FeO.
  • Neel's Law: χm = C/(T + θN), where θN is the Neel temperature.
• Ferrimagnetic Materials:
  • Characterized by the presence of antiparallel arrangement of magnetic dipoles, which are not equal in magnitude.
  • General formula for ferrites: MFe2O4, where M is any divalent metal.
  • Remain ferrimagnetic up to the Curie temperature.
  • Ferrites are used in designing the core of high-frequency transformers and inductors.
  • Examples: Nickel and zinc ferrite (used in TV transformers), Yttrium iron garnet (YIG) (used at microwave frequencies).
  • Ferrites change the direction of polarization vector of electromagnetic waves (Faraday rotation).

4. Core Losses in Magnetic Materials

• Magnetic materials are used in the design of cores of transformers and inductors.
• Two types of losses are generally observed in core materials:
  • Eddy Current Loss:
    • Due to alternating magnetic field, an EMF is induced across the core material, which results in the flow of circulating currents at the surface of the core material (eddy currents).
    • Eddy current loss is given as: Pe = (π^2 * f^2 * B^2 * t^2) / (ρ * β), where f is frequency, B is magnetic flux density, t is thickness of the core, ρ is resistivity of the core, and β is a material constant.
    • To reduce eddy current loss:
      • Laminated cores are used.
      • Silicon steel (up to 5% silicon) is used because it has higher resistivity than pure iron.
  • Hysteresis Loss:
    • Hysteresis loss is directly proportional to the area (width) of the hysteresis loop.
    • Hysteresis loss is given as: Ph = η * B^n * f, where η is a constant, B is magnetic flux density, n is an exponent, and f is frequency.
    • To reduce hysteresis loss, magnetic materials with narrow hysteresis loops are preferred.

5. Magnetostriction

• When magnetic materials are magnetized, changes in dimensions are generally observed.
• This property of magnetic materials is known as magnetostriction.
• Magnetostriction is responsible for humming noise in transformers.

6. Classification Based on Hysteresis Loop Width

• Hard Magnetic Materials:
  • Wide hysteresis loop.
  • Difficult to demagnetize.
  • Permanent magnetic materials.
  • High retentivity, high coercivity, high hysteresis loss, low susceptibility.
  • Examples: Carbon steel, tungsten steel, Alnico, Cunife.
• Soft Magnetic Materials:
  • Narrow hysteresis loop.
  • Can be easily magnetized and demagnetized.
  • Used in high-frequency applications.
  • Low retentivity, low coercivity, low hysteresis loss, high susceptibility.
  • Examples: Ferrites, silicon steel, Permalloy, Supermalloy, Mumetal, metallic glasses.

7. Synthesis/Conclusion

The video provides a detailed overview of magnetic properties of materials, starting from basic definitions like magnetic field intensity and flux density, and progressing to the classification of materials based on their magnetic behavior. It covers the origin of magnetic dipole moments, the different types of magnetic materials (diamagnetic, paramagnetic, ferromagnetic, antiferromagnetic, and ferrimagnetic), and their characteristic properties. The discussion includes the temperature dependence of magnetic properties, core losses in magnetic materials, magnetostriction, and classification based on hysteresis loop width. The content is technically precise and provides actionable insights for understanding and applying magnetic materials in various engineering applications.