1. The physics of (geo)magnetism

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

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

4. Electricity…

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

6. 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) ?

7. Volta, Ampère, and Watt… Alessandro Volta 1745 - 1827 Andre-Marie Ampère 1775 - 1836 James Watt 1736 - 1819

8. Magnetic field H Ampère’s law

9. Magnetic field H Ampère’s law simplified Maxwell’s equation James Clerk Maxwell 1831 - 1879

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

11. Magnetic moment m (dipole)

12. coil: n = number of windings

13. 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 ]

14. Magnetic induction B B Earth = 30-60 μ T B magnet = ~ 1 T Refrigerator magnet = 5 mT MRI scan = 1.5 – 7.0 T

15. 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)…

16. Nikola Tesla 1856 - 1943

17. Nikola Tesla

19. 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: 30-60 μ T

20. μ = permeability [Hm -1 ] Difference between H and B In pmag/geomag: Outside magnetic body: M = 0 Free space: μ = μ 0 = 4π × 10 -7 Hm -1

21. Magnetostatic energy (E m ) Chinese compass, Han Dynasty

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

23. 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

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

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

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

27. 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 = 10 -3 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

28. A nice application of obscure units… Magnetic field (H): 1 Am -1 = 4π × 10 -3 Oe μ 0 : 4π × 10 -7 Assuming ‘free space’:

29. - 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

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

31. Where does the field originate? `Geodynamo’

32. Just yesterday…

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

34. 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

35. The dipole assumption

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

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

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