Chapter 15: Special Topics - Trinity College Dublin · 15.5 Planetary and Cosmic Magnetism Magnetic...

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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: jcoey@tcd.ie

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Further reading

• R. E. Rosencwaig, Ferrohydrodynamics, Dover, New York 1990Everything 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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CoCl2 liquid tube stabilised in water in a

vertical magnetic field

H

1.5 M CoCl2 red ! = 120 10-6

1.4 M NiSO4 green ! = 70 10-6

1 M ErCl3 pink ! = 490 10-6

Paramagnetic liquid tubesParamagnetic liquid tubes

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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

Silicon

Titanium

Buoyancy condition

B$" = -gµ0("0 - "sol) /(!m - !sol)

-9 10-6Water

1290 10-6DyNO3 (1M)

80 10-6CoCl2 (1M)

!sol

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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.

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

surface

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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

Strain MS-1 (Magnetospirillum magnetotacticum)

Thin section of MS-1. Magnetsomes are approx. 45 nm in diameter.

Magnetotactic bacteriae

Row of biogenic magnetite particles

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Magnetic biochip

Another example of a silicon back-endprocess.

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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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