Chapter 3. Maxwell’s Second Law
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2. Magnetic Materials and Magnetization
1. Magnetic Field
⑴ Definition : A vector quantity that represents the magnetic flux density per unit area, denoted as B, with magnitude and direction.
⑵ Generation : Generated through the motion of charged particles or currents.
⑶ Direction : Illustrated by the right-hand rule, where the direction is determined by the motion of charged particles or current.
⑷ Magnetic Force : Also known as Lorentz force.
⑸ Generation of Electromagnetic Waves : Occurs when electric and magnetic fields vary with time.
① Energy calculations involve the concept of Poynting vector.
② The existence of electromagnetic waves in a vacuum is due to the mutual induction of electric and magnetic fields.
③ Radio frequency (RF) is used in MRI.
2. Magnetic Materials and Magnetization
⑴ Intrinsic Magnetization
① Magnetic susceptibility or magnetization : The degree to which a substance becomes magnetized when subjected to an external magnetic field.
② In most materials, internal polarization M 0 is proportional to the magnetic field B 0: the proportionality constant is magnetic susceptibility.
② Protons with spin-up have the lowest energy level.
③ Even if energy is temporarily absorbed, the MR signal is generated as the substance returns to its original state.
④ Increasing the magnetic field strength → increasing intrinsic magnetization M 0 → increasing MR signal.
⑵ Magnetic Materials and Magnetization
Figure 1. Classification of Magnetic Materials
Figure 2. Magnetic Hysteresis Curve and Magnetic Materials
① Diamagnetic : Except for superconductors, χ value is very small and negative.
○ Macroscopic cause : The entire material is weakly magnetized in the opposite direction of the external magnetic field.
○ Microscopic cause : All materials exhibit weak diamagnetism due to the motion of electrons around nuclei (Lenz’s law).
○ Weak repulsion under a magnetic field.
○ Superconductors are also diamagnetic (Meissner effect).
② Paramagnetic : χ is small and positive.
○ Macroscopic cause
○ No external magnetic field : Magnetic moments become disorderly.
○ External magnetic field present : Aligns magnetically moments in a parallel direction, creating weak attraction (due to rotation caused by torque).
○ Reason for weak attraction : Thermal motion of atoms disrupts the alignment of magnetic moments.
○ Lowering temperature in paramagnetic materials enhances magnetization.
○ Microscopic cause
○ Present in molecules with unpaired electrons in MO theory.
○ Specifically in molecules with unoccupied electron shells.
○ Examples: Transition elements, rare earth elements, actinides.
③ Ferromagnetic : χ is very large and positive.
○ Macroscopic cause
○ Ferromagnetic materials have internal regions called magnetic domains.
○ Exchange coupling : Interaction between the spin of one atom and the spin of adjacent atoms.
○ Despite atomic thermal motion, magnetic moments within specific domains remain aligned in the same direction due to exchange coupling.
○ No external magnetic field : Magnetic moments of each domain are disorderly, so no overall magnetic field is observed.
○ External magnetic field present : Magnetic moments within each domain align in the direction of the external magnetic field (due to rotation caused by torque).
○ After the removal of an external magnetic field : Magnetic moments within each domain remain orderly, and magnetization persists for a long time.
○ Mainly found in metallic materials: iron, cobalt, nickel, gadolinium, ferric oxide, etc.
○ Ferromagnetic materials can also be further classified as ferro-magnetic, ferri-magnetic, antiferro-magnetic, etc.
○ Curie temperature
○ When the temperature of a ferromagnetic material exceeds a critical temperature, exchange coupling is disrupted, and the alignment of magnetic domains can no longer be maintained.
○ Above this temperature, atomic thermal motion becomes significant, causing ferromagnetic materials to lose ferromagnetism and become paramagnetic.
○ This temperature is called the Curie temperature.
Table 1. Curie Temperatures of Various Substances
○ Lightning-Induced Remanent Magnetism
○ Phenomenon where the surrounding magnetite becomes magnetized and turns into a magnet when struck by lightning.
○ Mechanism for the formation of natural magnets.
○ Magnetic Hysteresis Phenomenon
○ Hysteresis phenomenon : Physical quantities of a material are determined not only by its current state but also by the process of change in its state.
○ Hysteresis is not unique to magnetic hysteresis.
○ Examples: Hysteresis in stress-strain curves, rate functions.
○ Represented as μH is magnetic flux density.
○ Magnetic flux density : Describes the strength of a magnetic field.
○ Hysteresis Loop : Curve depicting the process of change in the magnetic field of ferromagnetic or ferrimagnetic materials in response to varying external magnetic fields.
Figure 3. Hysteresis Loop or Hysteresis Curve
○ 1st Initial Magnetization Curve (O → D)
○ Initially, the magnetic field of the material increases rapidly when an external magnetic field is applied to a demagnetized ferromagnetic substance.
○ The increase in the magnetic field’s strength slows down, and the magnetic field stops increasing.
○ Each magnetic domain within the ferromagnetic substance aligns completely with the external magnetic field.
○ Magnetic Saturation : The phenomenon where further increases in the external magnetic field do not lead to an increase in the ferromagnetic substance’s magnetic field.
○ 2nd Decreasing External Magnetic Field (D → E)
○ The magnetic domains of the ferromagnetic substance maintain a certain level of alignment rather than returning to their initial state.
○ Consequently, the hysteresis loop does not return to point O.
○ Residual Magnetic Field : The magnetic field at point E.
○ 3rd Applying an Opposite External Magnetic Field (E → F → G)
○ At point F, the magnetic field of the ferromagnetic substance decreases further until it reaches zero.
○ The external magnetic field at point F is called coercive force or coercivity.
○ Increasing the strength of the opposite external magnetic field realigns the magnetic domains in the opposite direction, leading to saturation.
○ 4th Decreasing the Opposite External Magnetic Field and Reapplying the Initial Magnetic Field
○ The material returns to state D after passing point J.
○ Measured using a Vibrating Sample Magnetometer (VSM).
○ Application 1: Permanent Magnets : Maintain a magnetic field without an external magnetic field → Hysteresis loop is rectangular, and coercivity should be high.
○ Application 2: Used in electromagnets or transformer iron cores : Sensitive to external magnetic fields → Residual magnetic field is large, and coercivity is small.
○ Ferromagnetic materials cause significant artifacts in MRI compared to diamagnetic and paramagnetic materials.
④ Summary of Magnetic Material Characteristics
Table 2. Summary of Magnetic Material Characteristics
⑶ Superconductors
① Overview
○ Definition : Materials with zero electrical resistance at or below a certain temperature.
○ Example : Hydrogen gas can be compressed into a solid, becoming a superconductor.
② Cooper Pairs
○ Proposed by Leon Cooper in 1956.
○ 1st Generally, electron-electron interactions result in repulsion.
○ 2nd As electrons move, they interact with lattice, causing electron-phonon interactions.
○ 3rd At lower temperatures, the influence of electron-phonon interactions becomes apparent.
○ 4th Pairs of electrons (spin: ±1/2) form Cooper pairs and behave like integer-spin bosons.
○ 5th While electrons cannot have the same quantum state (Pauli exclusion principle), boson-like behavior is possible.
○ 6th Bose-Einstein condensate : Cooper pairs all have the same quantum state, behaving as a single entity.
○ 7th Cooper pairs move without scattering.
○ 8th Electrical resistance becomes zero.
○ The concept of Cooper pairs applies not only to superconductors but also to helium’s superfluidity (fluid with zero resistance).
③ Meissner Effect
○ Definition : Phenomenon in which a superconductor expels an external magnetic field, making it also a diamagnetic material.
Figure 4. Meissner Effect
○ Example : Levitation of a magnet over a superconductor, maglev trains.
④ High-Temperature Superconductors
○ Discovered superconductors with a critical temperature of 28 K in 1986.
○ Currently, superconductors with critical temperatures of 150 K have been discovered.
○ High-temperature superconductors play a crucial role in practical applications of superconductivity.
⑤ Example 1: Yttrium-Barium-Copper-Oxide [YBCO] Superconductor
○ Has a critical temperature around 92 K (-181 ℃).
○ When cooled using liquid nitrogen, the temperature can be lowered to 77 K (-196 ℃), leading to the Meissner effect.
⑥ Example 2: Bismuth-Strontium-Calcium-Copper-Oxide [BSCCO] Superconductor
○ Has a critical temperature around 110 K (-163 ℃).
○ When cooled using liquid nitrogen, the temperature can be lowered to 77 K (-196 ℃), leading to the Meissner effect.
⑷ Applications of Magnetic Materials
① Iron cores in electromagnets.
② Hard disk drives.
③ Rubber magnets.
④ Coin sorters in vending machines.
⑤ Capsule endoscopy.
⑥ Liquid magnets.
⑦ MRI : Utilizing superconductors.
⑧ Maglev trains : Utilizing superconductors.
⑨ Quantum computers : Utilizing superconductors.
⑩ Lossless power transmission : Utilizing superconductors.
3. Maxwell’s Second Law (Gauss’s Law for Magnetism)
⑴ Definition : There are no magnetic monopoles.
⑵ Mathematical Expression
⑶ μH is referred to as magnetic flux density.
⑷ Quantum mechanically, magnetic monopoles might exist : The hypothesis that magnetic monopoles existed in the early universe during the Big Bang also exists.
Input: 2022.04.23 19:45