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Magnetic fields. Magnetic field of a planet (Earth) Dipole Higher orders Short period variations Secular variations Polar drift Paleomagnetism Magnetic fields of other planets Remnant fields Reference: Physics of the Earth, F. D. Stacey & P. M. Davis, Cambridge University Press, 2008.

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magnetic fields
Magnetic fields
  • Magnetic field of a planet (Earth)
  • Dipole
  • Higher orders
  • Short period variations
  • Secular variations
  • Polar drift
  • Paleomagnetism
  • Magnetic fields of other planets
  • Remnant fields


Physics of the Earth, F. D. Stacey & P. M. Davis, Cambridge University Press, 2008

magnetic fields of a planet
Magnetic fields of a planet
  • Many planets/moons have a magnetic field
  • In first order it is a dipolar field, higher orders exist
  • The source is inside the planet
  • The magnetic field axes do not necessarily coincide with the rotation axis of the planet
  • The dipole centre can be offset from the planetary centre
  • The magnetic field is variable on any timescale [ms – Myears]
  • The pole direction can reverse
  • A planetary magnetic field can vanish if the driving mechanism is diminished (Mars)
Magnetic properties of lodestones were recognised already by ~600BC

It was attributed to a effluvium in Greece or qi in China which was essentially a life energy

Initially only the horizontal orientation (declination) was used for navigation

The magnetic declination i.e. the deviation of the magnetic poles from the geographic poles was recognised and applied in navigation maps in the 16th century

The inclination of the magnetic field was confirmed in the 16th century but still was disputed later on

At 1600 the magnetic field of spherical lodestones was described as a quadrupole field (W. Gilbert, De Magnete, 1600, ISBN-10: 048626761X )

Secular variations were reported from the 15-16th century on

The magnetic field as an internal field was confirmed not before the early 20th century and was contested by e.g. Einstein until 1940

field creation mechanism
Field creation mechanism
  • A planetary magnetic field is assumed to be created by electric currents in a liquid electrical conducting part of the outer core.
  • The magnetic induction equation describes the field creation by a moving fluid
  • ηm is the magnetic diffusivity,
  • δelectricalconductivity,
  • μ magneticpermeabiltiy,
  • v fluid velocity which is sustained by convection
  • When v → 0 the dipole would vanish within some tens of thousands years

Image: USGS

field propagation attenuation
Field propagation & attenuation
  • Field generated in core < Re/2
  • Small scale features are hidden because of distance to surface and magnetisation in crust
  • Electrical conductivity in mantle is contributing to field attenuation
    • (Gaillard et al. Carbonatite Melts and Electrical Conductivity in the Asthenosphere. Science, 2008; 322 (5906): 1363 DOI: 10.1126/science.1164446)
  • Unmaintained electric currents in the core would decay due to ohmic dissipation within 104 years

Electrical conductivity map of earth mantle. Image:  Anna Kelbert, Oregon State University 2009

best fitting dipole
Best fitting dipole
  • A planetary magnetic field can (mostly) be represented in first order by a dipole field with the magnetic moment m
  • The magnetic potential Vm of the best fitting dipole is
non dipole elements
Non dipole elements
  • About 20% of earths magnetic field are contributions from higher pole orders.
  • Spherical harmonic coefficients for a internal field can be found using:
  • The coefficients g and h are given in nanoTesla (nT) and can be derived from satellite measurements
  • The angle ηbetween the magnetic and geographic axes is 10.26°
short period variations
Short period variations
  • Short period variations are mostly induced by external events
    • Solar Flares
    • Magnetic storms in the solar wind
  • -> See next unit on magnetospheres and solar planetary interactions
secular variations
Secular variations
  • Changing patterns in the core motion drive slow variations in the magnetic field (> 1 year)
  • Most extra-terrestrial effects are shot periodic
  • Changes are not uniform on a global scale
  • Currently we observe a field drift of about 0.2°/year for the higher harmonics
  • The total field strength over the last centuries has decreased by ~6.3%/century
  • Over geological timescales pole reversals have been found
  • Iron rich lava can trap the current local magnetic field direction while cooling
  • The paleomagnetic field can be reconstructed from bore stems
polar drift
Polar drift
  • Over geologic timescales the position of the magnetic poles can change
  • Thus far about 170 polar reversals have been found
  • Today the north pole is moving towards Siberia with an average speed of 10 km/year
  • Recently the speed has increased to ~40 km/year
remnant magnetic field of mars
Remnant Magnetic Field of Mars
  • Due to the lack of plate tectonics i.e. large internal convection the dynamo process on Mars has stopped
  • The remnant magnetic field is very weak and consists mostly of multi-pole contributions
  • The paleomagnetic field was observed from orbit by the MGS orbiter in 1999


induced magnetic field
Induced magnetic field
  • The solar wind can produce an induced magnetic field around planets/moons with an atmosphere or rather an ionosphere
  • E.g. Venus and Titan when outside the Saturn magnetosphere

Image: MPS, M. Fränz