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 Volta1745 - 1827

Andre-Marie Ampère1775 - 1836

James Watt1736 - 1819

Magnetic field H

Ampère’s law

Magnetic field H

Ampère’s law

simplifiedMaxwell’s equation

James Clerk Maxwell1831 - 1879

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)

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 [Am2]

Magnetic induction B

Magnetic induction B

Units:Potential (V): V Velocity (v): m/sLength (l): meter [m]

Magnetic induction (B):Vs/m2 or Tesla [T]or N/(Am)…

Nikola Tesla

Nikola Tesla1856 - 1943

Nikola Tesla

Nikola Tesla

Magnetic induction BSome sense of scale:Strongest fields ever reached: 100 TMRI scans = 1.5 – 12.0 TRefrigerator magnet: 5 mTEarth’s magnetic field: 30-60 μT

μ = permeability [Hm-

1]

Difference between H and B

In pmag/geomag:Outside magnetic body: M = 0

Free space: μ = μ0 = 4π × 10-7 Hm-1

Magnetostatic energy (Em)

Chinese compass, Han Dynasty

Remanent magnetization (Mr)

‘Normalized magnetic moment’:Unit of magnetic moment: Am2

Magnetization

Normalization of a magnetic moment:• Per volume: M• Per mass: Ω

Units:Magnetic moment (m): Am2

Volume: m3

Mass: kg

Magnetization per volume: A/m or Am-1

Magnetization per mass: Am2/kg or Am2kg-1

Induced magnetization (MI)

Magnetization in the presence of a magnetic field H:

Magnetic susceptibility (χ)

Units:Magnetization (M): A/m Magnetic field (H): A/m

Magnetic susceptibility (χb):Dimensionless [-]

Total magnetization

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

It’s all about units…

SI cgs:‘meter-kilogram-second’ centimeter-gram-second

Parameter SI cgs conversion

Moment (m) Am2 emu 1 Am2 = 103 emu

Magnetization/volume (M)

Am-1 emu cm-3 1 Am-1 = 10-3 emu cm-3

Magnetization/mass (Ω) Am2kg-1 emu gm-1 1 Am2kg-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 = 104 G

A nice application of obscure units…

Magnetic field (H): 1 Am-1 = 4π × 10-3 Oe μ0: 4π × 10-7

Assuming ‘free space’:

- Magnetic field H [A/m]

- Magnetic moment m [Am2]

- 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

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 [°]