Chapter 5: Magnetism and Matter

Properties of Magnets

• Poles: Every magnet has two poles - North and South
• Magnetic Dipole: A bar magnet is a magnetic dipole
• Magnetic Field Lines:
  • Emerge from North pole, enter at South pole
  • Form closed loops
  • Never intersect
  • Closer lines indicate stronger field

Magnetic Field of a Bar Magnet

Axial Field:

Equatorial Field:

• M = magnetic dipole moment
• Field decreases as 1/r³ at large distances (dipole field)

Magnetic Dipole Moment

• Definition: Product of pole strength and magnetic length
• Vector: Points from South to North pole
• Unit: A·m² (ampere-meter squared)

Torque on a Bar Magnet in Uniform Field

• Tends to align magnet with field
• Potential energy: U = -M·B

Earth as a Magnet

• Earth behaves like a bar magnet with magnetic axis tilted from geographic axis
• Geographic North is near magnetic South pole (magnetic poles are named by where compass needle points)

Elements of Earth's Magnetic Field

• Declination (θ): Angle between magnetic meridian and geographic meridian
• Inclination or Dip (δ): Angle between magnetic field and horizontal
• Horizontal Component (BH): BH = B cos δ
• Vertical Component (BV): BV = B sin δ
• Total Field (B): B² = BH² + BV²

Variations in Earth's Magnetic Field

• Secular Variations: Slow changes over years
• Daily Variations: Small changes during day
• Magnetic Storms: Sudden, irregular disturbances

Gauss's Law in Magnetism

• Net magnetic flux through any closed surface is zero
• ∮B·dA = 0
• No magnetic monopoles exist (unlike electric charges)

Magnetisation (M)

• Definition: Magnetic moment per unit volume
• Unit: A/m (ampere per meter)

Magnetic Intensity (H)

• Definition: B/μ₀ - M
• Unit: A/m (ampere per meter)
• Relation to B: B = μ₀(H + M)

Magnetic Susceptibility (χm)

• Definition: Ratio of magnetisation to magnetic intensity
• M = χm H
• Dimensionless quantity

Magnetic Permeability (μ)

• Definition: Ratio of magnetic induction to magnetic intensity
• B = μH
• μ = μ₀(1 + χm)
• μr = μ/μ₀ = 1 + χm (relative permeability)

Diamagnetism

• Characteristics:
  • Weakly repelled by magnets
  • χm is small and negative (≈ -10⁻⁵)
  • μr slightly less than 1
• Examples: Bismuth, Copper, Gold, Silver, Water
• Cause: Induced magnetic moment opposes external field
• Temperature Independence: Not affected by temperature

Paramagnetism

• Characteristics:
  • Weakly attracted by magnets
  • χm is small and positive (≈ 10⁻⁵ to 10⁻³)
  • μr slightly greater than 1
• Examples: Aluminum, Platinum, Oxygen, Rare earth salts
• Cause: Alignment of atomic magnetic moments with field
• Temperature Dependence: χm ∝ 1/T (Curie's Law)

Ferromagnetism

• Characteristics:
  • Strongly attracted by magnets
  • χm is large and positive (≈ 10³ to 10⁵)
  • μr much greater than 1
• Examples: Iron, Cobalt, Nickel, Gadolinium
• Cause: Spontaneous alignment of magnetic moments (domains)
• Temperature Dependence: Loses ferromagnetism above Curie temperature
• Hysteresis: Magnetisation depends on history of applied field

Domain Theory

• Definition: Regions of aligned magnetic moments
• Domain Wall: Boundary between domains with different orientations
• Domain Alignment: External field causes favorable domains to grow

Hysteresis

• Hysteresis Loop: B-H curve showing magnetisation history
• Remanence (Br): Residual magnetisation when H = 0
• Coercivity (Hc): Field required to demagnetise material
• Energy Loss: Proportional to area of hysteresis loop

Permanent Magnets

• Desirable Properties: High remanence, high coercivity
• Materials: Alnico, Ferrites, Rare-earth magnets (Neodymium, Samarium-Cobalt)

Electromagnets

• Construction: Current-carrying solenoid with soft iron core
• Desirable Properties: High permeability, low coercivity, low hysteresis loss
• Materials: Soft iron, Silicon steel
• Applications: Motors, generators, transformers