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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 [°]