The physics of (geo)magnetism

Enough magnetism to be dangerous… The basics: Magnetism Electromagnetism Dipoles Geomagnetism

Magnetism Our recorders (mostly) qualitative analyses …a few ‘easy’ calculations It’s all about UNITS Electromagnetism Our ‘equipment’

Electricity…

What are potential (V) and current (i) ?

Units: Potential (V): Volts [V] Current (i): Ampère [A] Power (P): Volt-Ampère or Watt [W] (equals Joule/second) What are potential (V) and current (i) ?

Volta, Ampère, and Watt… Alessandro Volta Andre-Marie Ampère James Watt

Magnetic field H Ampère’s law

Magnetic field H Ampère’s law simplified Maxwell’s equation James Clerk Maxwell

Magnetic field H Units: Current (i): Ampere [A] Radius (r): meter [m] Magnetic field (H): Ampere per meter [A/m] or [Am -1 ]

Magnetic moment m (dipole)

coil: n = number of windings

Magnetic moment m (dipole) Units: Number of windings (n): - Current (i): Ampère [A] Radius (r): meter [m] Magnetic moment (m): Ampère-meter-squared [Am 2 ]

Magnetic induction B B Earth = μ T B magnet = ~ 1 T Refrigerator magnet = 5 mT MRI scan = 1.5 – 7.0 T

Magnetic induction B Units: Potential (V): V Velocity (v): m/s Length (l): meter [m] Magnetic induction (B): Vs/m 2 or Tesla [T] or N/(Am)…

Nikola Tesla

Nikola Tesla

Magnetic induction B Some sense of scale: Strongest fields ever reached: 100 T MRI scans = 1.5 – 12.0 T Refrigerator magnet: 5 mT Earth’s magnetic field: μ T

μ = permeability [Hm -1 ] Difference between H and B In pmag/geomag: Outside magnetic body: M = 0 Free space: μ = μ 0 = 4π × Hm -1

Magnetostatic energy (E m ) Chinese compass, Han Dynasty

Remanent magnetization (M r ) ‘Normalized magnetic moment’: Unit of magnetic moment: Am 2

Magnetization Normalization of a magnetic moment: Per volume: M Per mass: Ω Units: Magnetic moment (m): Am 2 Volume: m 3 Mass: kg Magnetization per volume: A/m or Am -1 Magnetization per mass: Am 2 /kg or Am 2 kg -1

Induced magnetization (M I ) Magnetization in the presence of a magnetic field H:

Magnetic susceptibility ( χ ) Units: Magnetization (M): A/m Magnetic field (H): A/m Magnetic susceptibility ( χ b ): Dimensionless [-]

Total magnetization In pmag/geomag: All about remanent magnetization Induced magnetization is a (lab-)tool!

It’s all about units… SI cgs: ‘meter-kilogram-second’centimeter-gram-second ParameterSIcgsconversion Moment (m)Am 2 emu1 Am 2 = 10 3 emu Magnetization/volume (M)Am -1 emu cm -3 1 Am -1 = emu cm -3 Magnetization/mass (Ω)Am 2 kg -1 emu gm -1 1 Am 2 kg -1 = 1 emu gm -1 Magnetic field (H)Am -1 Oersted (Oe)1 Am -1 = 4π ×10 -3 Oe Magnetic induction (B)Tesla (T)Gauss (G)1 T = 10 4 G

A nice application of obscure units… Magnetic field (H): 1 Am -1 = 4π × Oe μ 0 : 4π × Assuming ‘free space’:

- Magnetic field H[A/m] - Magnetic moment m[Am 2 ] - Magnetic induction B[T] - Magnetic susceptibility  [-] - Magnetisation M[A/m] - Magnetic permeability μ[Hm -1 ] (Electro-)magnetism: a wrap-up

Simple: bar magnet (dipole)Not so simple: dynamo process in fluid outer core (Glatzmaier & Roberts, Nature, 1995) The Earth’s magnetic field

Where does the field originate? `Geodynamo’

Just yesterday…

The concept of a geodynamo ‘Self-exciting disk dynamo’

The concept of a geodynamo conditions to be met: moving electrical conductor initial magnetic field interaction between magnetic field and the conductor supply of energy

The dipole assumption

Tauxe, 2005 eclination nclination Spherical coordinates q ~(co)lat f ~ long Main elements of the dipole field

Geomagnetic pole = (90%) best fitting dipole di- quadru- octu- Dipole… and non-dipole fields

IGRF: International Geomagnetic Reference Field Intensity [μT]Inclination [°] Declination [°]