03-03-2025 A | General Studies | ESE

Key Concepts

• Magnetic properties of materials
• Magnetic field intensity (H)
• Magnetic flux density (B)
• Permeability (μ), relative permeability (μr)
• Magnetization (M)
• Magnetic dipole moment (p_m)
• Magnetic susceptibility (χ_m)
• Diamagnetism, Paramagnetism, Ferromagnetism, Antiferromagnetism, Ferrimagnetism
• Curie's Law
• Bohr Magneton (μ_B)
• Electron spin, orbital angular momentum, nuclear spin

Magnetic Properties of Materials

Magnetic Field and Solenoids

• A solenoid with length L and N turns carrying current I generates a magnetic field.
• Magnetic Field Intensity (H): Defined as H = NI/L. Unit: Ampere/meter (A/m).
• Magnetic Flux Density (B): Related to H by B = μH, where μ is the permeability of the material.
• Permeability (μ): A measure of how easily a material allows magnetic lines of force to pass through it.
  • μ = μrμ₀, where μ₀ is the permeability of free space (4π × 10⁻⁷ Henry/meter) and μr is the relative permeability.
• Relative Permeability (μr): Dimensionless quantity indicating how much more permeable a material is compared to free space. μr = 1 for vacuum.

Magnetization

• Magnetic Material: A material that gets magnetized when placed in a magnetic field, either attracted or repelled.
• Non-Magnetic Material: A material that does not interact with a magnetic field.
• Magnetization (M): Defined as the magnetic dipole moment per unit volume.
  • If n is the number of magnetic dipoles per cubic meter and p_m is the magnetic dipole moment of each dipole, then M = n p_m.
  • Unit: Ampere/meter (A/m), same as magnetic field intensity.
• Total Magnetic Flux Density (B) in a Material: B = μ₀(H + M). This represents the sum of the applied field and the field induced by the material's magnetization.
• Relationship between B, H, and M: B = μ₀(H + M) = μrμ₀H.
• Magnetic Susceptibility (χ_m): Defined as χ_m = M/H = μr - 1. It indicates how easily a material can be magnetized in response to an applied field.
  • A positive χ_m indicates attraction to the field, while a negative χ_m indicates repulsion.
  • For vacuum, χ_m = 0.

Magnetic Dipole Moment

• A small circular current-carrying loop acts as a magnetic dipole.
• Magnetic Dipole Moment (p_m): Defined as p_m = IA n̂, where I is the current, A is the area of the loop, and n̂ is a unit vector perpendicular to the plane of the loop.
• Unit: Ampere-meter² (A·m²).
• Bohr Magneton (μ_B): A unit for measuring magnetic dipole moment at the atomic level. 1 μ_B = 9.27 × 10⁻²⁴ A·m².

Origin of Permanent Magnetic Dipole Moment

• Arises from the angular motion of charged particles, primarily electrons.
• Three main contributions at the atomic level:
  1. Electron Orbital Angular Momentum: Electrons orbiting the nucleus create a magnetic dipole.
  2. Electron Spin Angular Momentum: Electrons spinning on their axis create a magnetic dipole. This is the dominant factor in strong magnetic materials.
  3. Nuclear Spin Angular Momentum: The nucleus spinning on its axis creates a magnetic dipole.
• Electron Spin Magnetic Dipole Moment:
  • Elements with completely paired electrons have a net zero electron spin dipole moment.
  • Elements with unpaired electrons (e.g., transition elements) possess a non-zero electron spin dipole moment.
  • If z is the number of unpaired electrons in the inner d-orbitals of an element, then the electron spin dipole moment is given by p_m = zμ_B.

Example: Iron (Fe)

• Atomic number: 26
• Electronic configuration: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶
• Number of unpaired electrons in 3d orbitals: 4
• Spin dipole moment: p_m = 4μ_B

Classification of Magnetic Materials

Diamagnetic Materials

• Do not contain permanent electron spin dipole moments.
• Have completely paired electrons in their electronic structure.
• Exhibit a very weak form of magnetism that is non-permanent and persists only while an external field is applied.
• Magnetization is induced by a change in the orbital motion of electrons due to the applied magnetic field.
• The induced magnetic moment is in a direction opposite to that of the applied field.
• Have a small and negative magnetic susceptibility (χ_m < 0).
• A perfect diamagnetic material will repel all magnetic flux (B = 0 inside the material).
  • For perfect diamagnetism: χ_m = -1 and μr = 0.
• Examples: Bismuth, copper, diamond, gold, lead, mercury, hydrogen, water.

Paramagnetic Materials

• Contain permanent electron spin dipole moments.
• Dipoles are randomly oriented in the absence of a magnetic field, resulting in zero net magnetization.
• When a magnetic field is applied, each dipole experiences a torque and tries to align itself with the field.
• Exhibit a small and positive magnetic susceptibility (χ_m > 0).
• Curie's Law: Describes the relationship between magnetic susceptibility (χ_m) and temperature (T): χ_m = C/T, where C is the Curie constant.
  • Susceptibility decreases with increasing temperature.
• Examples: Aluminum, calcium, lithium, oxygen, platinum.

Conclusion

The magnetic properties of materials are determined by their electronic structure and how they interact with external magnetic fields. Diamagnetic materials are repelled by magnetic fields due to induced orbital motion, while paramagnetic materials are weakly attracted due to the alignment of existing dipoles. The strength and behavior of these materials are quantified by parameters like permeability and susceptibility, and their temperature dependence is described by Curie's Law.