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he stable levitation of magnets is forbid-den by Earnshaw he stable levitation of magnets is forbid-den by Earnshaw

he stable levitation of magnets is forbid-den by Earnshaw - PDF document

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he stable levitation of magnets is forbid-den by Earnshaw - PPT Presentation

Magnet levitation at your fingertips scientific correspondence zr 0 RBi cylinder 1 ID: 114918

Magnet levitation your fingertips scientific

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he stable levitation of magnets is forbid-den by EarnshawÕs theorem, whichstates that no stationary object made ofmagnets in a fixed configuration can beheld in stable equilibrium by any combina-tion of static magnetic or gravitationalforces. EarnshawÕs theorem can be viewedas a consequence of the Maxwell equations,which do not allow the magnitude of amagnetic field in a free space to possess amaximum, as required for stable equilib-rium. Diamagnets (which respond to mag-netic fields with mild repulsion) are knownto flout the theorem, as their negative sus-ceptibility results in the requirement of aminimum rather than a maximum in thefieldÕs magnitude. Nevertheless, levitationof a magnet without using superconductorsis widely thought to be impossible. We findthat the stable levitation of a magnet can beachieved using the feeble diamagnetism ofmaterials that are normally perceived asbeing non-magnetic, so that even humanfingers can keep a magnet hovering in mid-air without touching it.Stable levitation has been demonstratedfor diamagnetic objects such as supercon-ducting pellets and live creatures. Strongdiamagnetism of superconductors allowsthe situation to be reversed, so that a magnetcan be levitated above a superconductorParamagnetic objects can also be levitated ifplaced in a stronger paramagnetic medium,such as ferrofluid or oxygen, which makesthem effectively diamagneticWe set out to lift a magnet by applying amagnetic field and then stabilizing theintrinsically unstable equilibrium withrepulsive forces from a nearby diamagnetic Magnet levitation at your fingertips scientific correspondence zr 0 RBi cylinder 1Ð1 levitating Fiigguurree 11A NdFeB magnet (an alloy of neodymium,iron and boron; 4 mm high and 4 mm in diameter)levitating at the axis of a vertical solenoid of radius10 cm and lengthin a magnetic field of 100gauss. The levitation is stabilized by a bismuth cylin-1.5The photograph shows the top view of the levitatingmagnet. The right-hand plot shows the stability func-height of twice its radius (solid curves). Diamagneticinteraction to the left (dashed curve) and a small region of posi-tive emerges above the point where Fiigguurree 22Levitation at your fingertips. A strong NdFeBmagnet (1.4 tesla) levitates 2.5 metres below a pow-erful superconducting magnet. The field at the levi- devices accessible to everyone (M. D. S.,unpublished data). These could replace theexisting servo levitation devices for someA. K. Geim*, M. D. Simon , M. I. Boamfa*,L. O. Heflinger High Field Magnet Laboratory, University of Nijmegen, 6525 ED Nijmegen, The Netherlandse-mail: geim@sci.kun.nlDepartment of Physics and Astronomy, University of California at Los Angeles,Los Angeles, California 90095, USA 1.Earnshaw, S. Trans. Camb. Phil. Soc.2.Brandt, E. H. Science 3.Berry, M. V. &. Geim, A. K. Eur. J. Phys. 4.Thomson, W. (Lord Kelvin) Reprints of Papers on Electrostaticsand Magnetism(Macmillan, London, 1872).5.Braunbeck, W. Z. Phys.6.Beaugnon, E. & Tournier, R. Nature7.Geim, A. Phys. Today 36Ð39 (September 1998).8.Arkadiev, A. Nature9.Ikezoe, Y. et alNature10.Simon, M. D. et alAm. J. Phys.11.BoerdijkPhilips Tech. Rev. scientific correspondenceNATUREVOL 40022 JULY 1999www.nature.com due to a direct effect of light on the newtsÕperception of the magnetic field, we trainednewts under long-wavelength light by cov-ering the training tank with a long-wave-length-transmitting gel filter (two layers ofLee #101). Under long-wavelength light,these newts orientated themselves parallelto the shoreward axis, indicating that theyhad learned the direction of the shore withrespect to the rotated magnetic informationunder long-wavelength light (Fig. 1c,f).As well as ocular photoreceptors, newtshave extraocular photoreceptors in thepineal complexand possibly the hypothal-amus. To determine which photoreceptorsare involved in the magnetic compassresponse, we manipulated the wavelength oflight reaching the extraocular photorecep- Extraocular magnetic compass in newtsGeomagnetic orientation is widespreadamong organisms, but the mechanism(s) ofmagnetoreception has not been identifiedconvincingly in any animal. In agreementwith biophysical models proposing that thegeomagnetic field interacts with photo-receptors, changes in the wavelength oflight have been shown to influence magneticcompass orientation in an amphibian, aninsect and several species of birds (reviewedin ref. 5). We find that light-dependent mag-netic orientation in the eastern red-spottednewt, Notophthalmus viridescens, is mediatedby extraocular photoreceptors, probablylocated in the pineal complex or deeper inthe brain (perhaps the hypothalamus).Experiments investigating shorewardmagnetic compass orientation have demon-strated that the newtÕs perception of thedirection of the magnetic field is rotated 90under long-wavelength (greater than 500nm) light. We recently trained newtsunder natural skylight to aim for the shoreby placing them for 12Ð16 hours in water-filled tanks with an artificial shore at one. The magnetic orientation of individ-ual newts was then tested in a circular, visu-ally symmetrical indoor arena underdepolarized light. Under full-spectrum light(from a xenon arc source), they exhibitedbimodal magnetic orientation parallel tothe shoreward axis in the training tank (Fig.1a,d). In contrast, under long-wavelengthlight, they orientated themselves perpendic-ular to the shoreward direction (Fig. 1b,e).To demonstrate that the 90shift in ori-entation under long-wavelength light wastors. Small round ÔcapsÕ (5 mm in diameter)were attached to the dorsal surface of thehead of each newt using cyanoacrylate glue,and remained in place during both trainingand testing. Equal numbers of newts werecapped with either a clear filter (Lee #130)or a filter that transmitted only long-wave-length light (equivalent to two layers of Lee#101). The caps were positioned to alter thespectral properties of light reaching thepineal and surrounding structures, whereaslight reaching the eyes was unaffected.Clear-capped newts were tested to controlfor any nonspecific effects of the caps on thenewtsÕ orientation behaviour.All newts were trained outdoors undernatural skylight and tested for magnetic ori-entation in the testing arena under long- " mShore mShore 1 mShore mShore mShore 1 1 agfedcbh Fiigguurree 11Effects of long-wavelength light and head caps on bimodal magnetic orientation in newts. Pre-dicted orientation of newts (double-headed arrow) and their perception of the direction of the magnetic field(single-headed arrow). Training tanks have the shore towards magnetic north (mN); circular test arenasshow the predicted response of the newts under either full-spectrum (beige) or long-wavelength light (yel-Full-spectrum training and testing: newts should perceive the shore to be towards magnetic northand exhibit bimodal magnetic orientation along the shoreward axis. Full-spectrum training, long-wavelengthtesting: newtsÕ perception of magnetic north in testing, and their orientation in the test arena, should be rotated) from magnetic north during training. Long-wavelength training and testing: newtsÕ perception ofthe magnetic field should be rotated 90¼ relative to the actual field during training and testing. Their percep-tion of the magnetic field in the arena would be the same as in the outdoor tank. Results. Data pointsshow the magnetic bearing of a newt tested in one of four symmetrical alignments of an Earth-strength mag-netic field (magnetic north is geographic north (gN), east (gE), west (gW) or south (gS)). The magnetic fieldwas altered by two orthogonally orientated, double-wrapped, RubenÕs coils around the test arena. Data areplotted with respect to the magnetic direction of shore (mShore) in the training tank (shore direction, 360¼).Double-headed arrows indicate mean axis of orientation with the mean axis length, , proportional to thestrength of orientation (diameter of the circle corresponding to intervals for the mean axis. Distributions are significant at 0.05 or less by the Rayleigh test and -valuesbetween circle plots indicate significant differences between distributions (Watson Newts trainedunder natural light and tested under full-spectrum light orientated along the shoreward axisNewts trainedunder natural light and tested under long-wavelength light orientated 90¼ from the shoreward direction (filledcircles; tested under broadband long-wavelength (500 nm) light; filled squares, tested under a 550-nm light,40 nm bandwidth, 12.50.1 log Quanta cm; ref. 5). Newts trained and tested under long-wavelight orientated along the shoreward axisAfter training under natural light, clear-capped newts testedunderlong-wavelength light orientated ~90¼ from the shoreward direction. After training under natural light, newtswith long-wavelength-transmitting caps orientated along the shoreward axis under long-wavelength light.