Magnetism and Matter

• Introduction & Basic Concepts

  • Bar Magnet
    • Magnetic poles (North and South)
    • Magnetic Dipole Moment ($\vec{M}$): Direction from South to North
    • Uniform magnetic field torque ($\vec{\tau} = \vec{M} \times \vec{B}$) and potential energy ($U = -\vec{M} \cdot \vec{B}$)
  • Magnetic Field Lines
    • Continuous closed loops
    • Tangent gives field direction
    • Never intersect

• Earth’s Magnetism (Geomagnetism)

  • Geographic vs. Magnetic Poles
  • Elements of Earth's Magnetic Field
    • Magnetic Declination ($\theta$): Angle between geographic and magnetic meridian
    • Magnetic Inclination or Dip ($\delta$): Angle made by total field with horizontal
    • Horizontal Component ($B_h$): $B_h = B \cos\delta$

• Magnetization and Magnetic Intensity

  • Magnetic Intensity ($H$): Magnetizing force ($H = \frac{B_0}{\mu_0}$)
  • Intensity of Magnetization ($I$ or $M$): Magnetic moment per unit volume ($I = \frac{M}{V}$)
  • Magnetic Induction ($B$): Total field inside material ($B = \mu_0(H + I)$)
  • Magnetic Susceptibility ($\chi_m$): Ratio of $I$ to $H$ ($\chi_m = \frac{I}{H}$)
  • Magnetic Permeability ($\mu$): Ratio of $B$ to $H$ ($\mu = \frac{B}{H} = \mu_0(1 + \chi_m)$)

• Magnetic Materials

  • Diamagnetic Materials
    • Repelled by magnets
    • Negative susceptibility ($\chi_m$)
    • E.g., Bismuth, Copper, Water
  • Paramagnetic Materials
    • Weakly attracted by magnets
    • Small positive susceptibility ($\chi_m$)
    • Temperature dependent (Curie's Law: $\chi \propto \frac{1}{T}$)
    • E.g., Aluminum, Oxygen, Sodium
  • Ferromagnetic Materials
    • Strongly attracted by magnets
    • Large positive susceptibility
    • Contains Domains
    • E.g., Iron, Cobalt, Nickel
  • Curie Temperature ($T_c$): Temp above which ferromagnetism becomes paramagnetism

• Hysteresis

  • Hysteresis Loop ($B-H$ curve): Lag of $B$ behind $H$
  • Retentivity: Residual magnetism when $H = 0$
  • Coercivity: Reverse field needed to reduce $B$ to zero
  • Applications: Selection of core materials for electromagnets, transformers, and permanent magnets