Chapter 15: Special Topics
1.
Magnetic Liquids
2.
Magnetoelectrochemistry
3.
Magnetic Levitation
4.
Magnetism in Biology and Medecine
5.
Planetary and Cosmic Magnetism
Comments and corrections please: [email protected]
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Further reading
• R. E. Rosencwaig, Ferrohydrodynamics, Dover, New York 1990
Everything you need to understand ferrofluids
• P. A. Davidson An introduction to Magnetohydrodynamics, CUP, 2001.
A lucid and readable introduction to MHD.
• M Yamaguchi and Y Tanamori (editor), Magneto-science, Kodansha, Tokyo 2006,
A compendium of unusual applications of magnetism.
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Myths and Dreams - Perpetual Motion
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Myths and Dreams - Levitation
Gulliver waving at
Laputa, the flying
magnetic island
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15.1 Magnetic Liquids
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15.1.1 Ferrofluids.
Ferrofluids are colloidal suspensions of ferromagnetic nanoparticles, 10 - 15 nm in size.
They are coated with surfactant or embedded in a polymer bead (dynabead).
Thermal energy kBT 4 10-21 must prevent sedimentation. Particles must not agglomerate due to
dipole-dipole forces, nor move appreciably in a field gradient.
Typical ferrofluid has 10 % by volume magnetite. M ! 50 kA m-1. (J ! 0.05 T).
m = 103 - 105 Bohr magnetons
M = M0 (coth x - 1/x) where x = mB/kT
Can approach saturation in sub-tesla fields.
!= 0.005 - 0.5
Note that magnetic self-energy -(1/2)µ0MHd = -(1/2) µ0 NM2 ! 1000 J/m3 NB "g ! 50,000 J/m3
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Peaked instability in a vertical field
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• Ferrofluid Applications
Seals. Rotary seals for high vacuum
Magnetic separation
Magnetorheological fluids.
Magnetic Bernoulli equation:
"(#v/#t) + "v.$v = -$P* + µ0M$H + "g
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Magnetic confinement
1 mm iron track in perspex disc
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Paramagnetic liquid tubes
H
CoCl2 liquid tube stabilised in water in a
vertical magnetic field
1.5 M CoCl2 red ! = 120 10-6
1.4 M NiSO4 green ! = 70 10-6
1 M ErCl3 pink ! = 490 10-6
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Horizontal field, antitube
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Iron track immersed in water
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15.2 Magnetoelectrochemistry
There are two magnetic body forces which an produce measurable effects in electrochemical cells:
Lorentz force Fl = j x B
Field gradient force F = c!mol B$B/µ0
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14.3 Magnetic Levitation
A sumo wrestler standing on a
magnetic plate levitated above
a large disc of cuprate
superconductor
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Levitation of diamagnetic ‘holes’
Graphite
Buoyancy condition
B$" = -gµ0("0 - "sol) /(!m - !sol)
!sol
Silicon
Titanium
Water
-9 10-6
CoCl2 (1M)
80 10-6
DyNO3 (1M)
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Earnshaw’s theorem (1842)
It is impossible to levitate a fixed magnetic dipole with any configuration of static magnetic field.
This is true for any object whose energy satisfies Laplace’s Equation $2U = 0 (charges, masses)
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Magnetic bearings
%V$.Fd3r = %SF.dS = 0.
surface
The potential has a saddle point.
Bearing stiffness K is defined as a vector with components -
#Fx/#x, -#Fy/#y, -#Fz/#z.
Kx + Ky + Kz = 0
Axial bearing
Radial bearing
Linear bearing
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Maglev
Pudong airport (Shanghai)
Transrapid Maglev train
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Any diamagnet can be levitated by an appropriate combination of magnetic field and magnetic field
gradient.
U = -µ0V!H2/2 The force -$U must balance the weight -"gV
B $B = -gµ0/!m
Levitation condition for graphite B $B = 250 T2 m-1
Levitation condition for water B $B = 1400 T2 m-1 (!m = -9 10-9 m3 kg-1)
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15.4 Magnetism in Biology and Medecine
Magnetotactic bacteriae
Row of biogenic magnetite particles
Strain MS-1 (Magnetospirillum magnetotacticum)
Thin section of MS-1. Magnetsomes are approx. 45 nm in diameter.
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Magnetic biochip
Another example of a silicon back-end
process.
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15.5 Planetary and Cosmic Magnetism
Magnetic fields spanning 21 orders of magnitude are found in the cosmos. The ambient field in
interstellar space is 0.1 nT. Interplanetary fields are 1 - 10 nT. Field at the surface of earth or sun is
0.1 mT. Fields of 108 - 1011 T exist in neutron stars and magnetars.
The Earth s magnetic Field
Self-sustaining dynamo
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Magnetic moment of planets and moons
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• The Sun
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From Japan’s Hinode Solar Optical Telescope
A magnetic map of the flare zone on the southern flanks of sunspot 930
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