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Phys Educ Vol 14 1979 Prlnted In Great Br#ialn

regardedasacting between chargesrather than between bodies. Further doubt was thrown on Maxwell’s statement The discovery of by Erik Edlund, Professor of Physics at the Swedish Royal Academy of Sciences, in an article, which Hall the Ha//effect read, on ‘Unipolarinduction’ (Edlund 1878). This term was used to denotea category of induction phenomena defined by Edlund as ‘Induction due tothe circumstance that the conductor moves in regard to the magnet without the distance from the poles of the latter to the different points of the conductor necessarily varying, and withoutaugmentation or G S LEADSTONE diminution of the ’. Several experi- Physics Department, Atlantic College, mental arrangements illustrating phenomena of this South Wales type were discussed in Edlund’s paper and it was clear to Hall that the assumption made was that, in a fixed conductor, amagnet acts upon the current. Finding that Edlund manifestly disagreed with Maxwell, Hall On 28 October 1879, just one week before the death naturally enough turned to Rowland. of , Edwin Herbert Hall obtained He found that not only did Rowland disagree with the first positive indications of the effect which now Maxwell, but he had already attempted to detect some bears his name. Havinggraduated from Bowdoin action of a magnet on the current flowing in a fixed College, Hall entered the graduate school of the Johns conductor. He had not been successful$, but his mind Hopkins University in Baltimore in 1877 tostudy was far from closed on the subject, and he gave his physics under Henry Rowland, newly appointed to the approvalto Hall’s plan to investigate the matter chair of physics. Reading Maxwell’s and further. Thus began the series of investigations which (Maxwell 1873) in connection with finally led to Hall’s discovery and became the subject Professor Rowland’s lectures,Hall cameacross the of his PhD dissertation, which was entitled ‘On the statement: new action of magnetism on apermanent electric ‘It must be carefully remembered thatthe current’. mechanical force which urges a conductor carrying a current across the lines of magnetic force acts, not on New action the , but on the conductor which The ‘new action’ referred to (Hall 1879, 1880) was the carries it. If the conductor be a rotating disc or a fluid, appearance of atransverse potential difference in a it will move in obedience to this force; and this motion conductor, fixed in position with respect to a steady may or may not be accompanied with a change of applied at right angles to the current position of the electric current which it carries. But if flowing in the conductor. This ‘Hall ’, as it is the current itself be free to choose any path througha now called, is perpendicular to both the current and fured conductor or a network of wires then, when the applied field. As ithappened Rowland, in his a constant magnetic force is madeto act on the unsuccessful experiment, had used anarrangement system, the path of the current through the conductors almost identical to thatultimately used successfully by is not permanently altered, but after certain transient Hall. Furthermore, Wiedemann, in a standard work phenomena, called induction currents, have subsided, (Wiedemann 1872), had described an experiment the distribution of the current will be found to be the using a similar arrangement, specifically conceived as same asif no magnetic force were in action’. a demonstration that the effect did not exist! It is not Hall regarded this claim as ‘contrary to the most surprisingtherefore that, afterdiscussion with natural supposition’ (Hall 1879) and his reasons may Rowland,a different line of attack was initially be summarised as follows: adopted by Hall.This was based on the following (1) A force is exerted only by virtue of there being a reflection (Hall 1879): current flowing in the conductor. ‘If the current of electricity in a fixed conductor is (2) The magnitude of the force is directly propor- itself attracted by amagnet, thecurrent should be tional to thestrength of thecurrent, the size? and drawnto one side of the wire, and thereforethe material of the conductor being ‘matters of resistance experienced should be increased’. indifference’. (3) In electrostaticsthe fundamental forces were $ This was specifically stated by Hall in his original paper (Hall 1879). However,in a letter tothe Irish physicist Fitzgerald written 15 years later, Rowland stated ‘. . . I had t By ‘size’ Hall presumably meant dimensions other than alreadyobtained the Hall effect ona small scale before I the length, suchas the diameterof a wire. made Mr Hall try it. . .’. Ed\vin Herbert Hall 1855-1938. This photograph was Henry Ausustus Rowland 1848-1901. Elected to the taken more than 40 years after Hall, as a young chair of physics at the Johns Hopkins University just graduate of 24, discovered the ‘new action of the two years before Hall’s arrival, Rowland played a magnet on electric currents’. (Courtesy the Ferdinand crucial role in the discovery of the Hall effect. Hamburger JrArchives of the JohnsHopkins (Courtesy the Ferdinand Hamburger JrArchives of University) the Johns Hopkins University)

In his first two published accounts (1879,1880) attracting pole pieces of the electromagnet. Hall describes two experimental variations on this The other variation of this type of experiment was theme. In one the conductor was madefrom German- suggested by Rowland. This was topass acurrent silver wire about 0.5 mm in diameter. The wire was radially from the centre to the periphery of a disc of first drawn through a triangular die in order togive it a gold leaf and onceagain to apply a magnetic field cross section of this shape. Hall’s idea was that the perpendicular to the plane of the disc. It was thought sought for increase in resistance would be enhanced if that this would distort the lines of current flow from the current could be squeezed into one of the vertices. radii into spiral arcs and hence cause an increase in The wire was then wound into aflat spiral, sand- the resistance. The outcome was again negative and it wiched between two discs of hard rubber, and placed was decided to abandon this line of investigation and between the poles of an electromagnet so that thelines revert to theform of apparatus used previously by of would pass through the spiral at right Rowland. Hall (1 879) takes upthe story: angles to its plane and hence to the current. Making ‘But though conclusive, apparently, in respect to the spiral one arm of a Wheatstone bridge and using a any change of resistance, the above experiments are low-resistance Thomson galvanometer, Hall achieved not sufficient to prove that a magnet cannot affect an a sensitivity such that he coulddetect a change of electric current. If electricity is assumed to be an resistance of one part in a million. Using a flux density incompressible fluid, as some suspect it to be, we may -0.3 T, no consistent effect of a significant magnitude conceive that the current of electricity flowing in a was observed during 13 series of observations of 40 wire cannot be forced into one side of the wire or readingseach made between 7-1 1 October 1879. made to flow in any but a symmetrical manner. The Earlier in the year there had been some evidence of an magnet may tend to deflect the current without being increase in resistance but this was of such a nature able to do so. It is evident. however, that in this case that Hall had suspected some kind of thermal effect. there would exist a state of stress in the conductor, the Eventually he traced it to the mechanical stress set up electricity pressing, as it were, toward one side of the in the wire by its being squeezed between the wire. Reasoning thus, I thought it necessary, in order

37s galvanometer needle, or to any similar cause. It was, moreover, a permanent deflexion, and therefore not to be accounted for by induction. The effect was reversed when the magnet was reversed. It was not reversed by transferring the poles of the galvanometer from one end of the strip to the other. In short, the phenomena observed were just such as we should expect to see if the electric current were pressed,but not moved, toward oneside of the conductor'. The suggestion of Rowland regarding gold leaf thus turned out to be crucial and this, not because of any special property of gold, but because of thegreat increase in brought about by using a very thin specimen. Rowland had formerly used plates of copper and brass, necessarilymuch thicker than Figure 1 Specimen mounting used by Hall in his early gold leaf. measurements of the transverse potential difference set up in a fured current carrying conductorsubjected to a transverse magnetic field. gggg represents the plate of Further experiments glass upon which the specimen, in the formof a metal strip mmmm,is mounted. Contact with this strip is A few weeks later, on 12 November 1879, Hall made made at the endsby the twothick blocks of brass bb, a series of measurements onthe gold leaf using which are held firmly in place by the four brass clamps different values of the current through the leaf and of worked by means of the screws SSSS. The main the transverse magnetic field. He found a reasonably current of electricity enters andleaves the metal strip constant value for the ratio by means of the binding screws ee. Running out from Current throughgold leaf X strength of magnetic the middle of the strip are twoprojections which make fieldlcurrent through Thomsongalvanometer contact with the clampsCC, worked by the screws SS. In modern notation this is equivalent to the statement From thescrews ii wires lead to the Thomson galvanometer. (The diagramis about half actual size VH a B1 where V, is the Hall voltage, B is the flux and is based on Hall 1880) density of the applied field and Z is the current through the specimen. Inthe following yearHall (1880) published results of measurementsmade on gold, to make a thorough investigation of the matter, totest silver, iron, platinum, nickel and tin, all made using the for a difference of potential between points on arrangement shown in figure 1. This is the familiar opposite sides of the conductor. version of today, with the exception of the potential 'This could be doneby repeating the experiment divider which is incorporatedto enable two equi- formerly made by Professor Rowland, and which was potential points to be established when the current is the following: a disc or strip of metal, forming part of flowing, but in the absence of the magnetic field. Hall's an electric circuit, was placed between the poles of an own method of solving this problem was original and electromagnet, the disccutting acrossthe lines of basic. With reference to figure 1 he wrote (Hall 1880) force. The two poles of a sensitive galvanometer were 'The projections from the metal strip . . . make the then placed in connexion with different parts of the apparatus very easy to adjust,for by scraping off little disc, through which an electric current was passing, particles from the prbper part of the projections, while until two nearly equipotential points were found. The the current is allowed to run through the metal strip, magnet current was then turned on and the galvano- the current through the Thomson galvanometer may meter was observed, in order to detect any indication be reduced to the extent desired'. of a change in the relative potential of the twopoles. In relating measurements made on different speci- 'Owing tothe fact that the metaldisc used had mens Hall's greatestproblem, interestingly enough, considerablethickness, the experiment atthat time was not associated with the sensitive electrical failed to give any positive result. Professor Rowland measurements, but with the determination of a reliable now advised me, in repeating this experiment, to use value for the effective thickness of the specimen in gold leaf mounted on a plate of glass as my metal each case. He had hoped to find a universal constant strip. I did so, and, experimenting as indicated above, expressing the magnitude of his new effect for all succeeded on 28 Octoberin obtaining, as the effect of specimens, irrespective of dimensions and material. the magnet's action, a decided deflexion of the The nearest he came to this was to show that, for a galvanometer needle. given metal (using modem notation), 'This deflexion was much too large to be attributed BJbI V, constant to thedirect action of the magnetic field onthe

376 where J is the current density in the specimen, b is its breadthand B and V, areas before. On the elementaryclassical theory of theHall effect for a single carriersystem the significance of Hall’s constant is easily shownt to be ne, where n isthe numberdensity of chargecarriers and e is the electroniccharge. Hall used the reciprocal of this quantity, now termed the Hall coefficient R,, as repre- sentative of themagnitude of the effect in different metals. He subsequently realised that it could not be expected to havethe same value for all metals, because of the nature of the quantity J, the current density. As he put it (Hall 1889) ‘We must, however, think of a metal as not strictly continuous, but consisting of metallic particles more or less compactly aggregated in the space occupied by Figure 2 Modified form of apparatus used by Hall to thebody as a whole. Evidently,therefore, the cross allow rotation of the specimen about its long axis. This section effective in conduction would vary in different enabled him to test for a potentialdifference in a conductors of the same nominal cross section’. direction parallel to theapplied magnetic field. (After And with prophetic insight he continued Hall 1880) ‘It can hardly be doubted that the action we have been considering, placing at our command, as it does, a new point of view from which to study the interior workings of the substance examined, is destined to teach us agood deal in regard tothe molecular structure of bodies, while helping us toward an under- standing of thephysical nature of electricity and magnetism’. In the same paper (Hall 1880) in which he placed his new effect on a firm quantitative basis, Hall also describes several associatedexperiments, mostly prompted by Rowland as resulta of theoretical l/D speculations of various kinds. The first of these is J illustrated in figure 2. The specimen is made narrower Figure 3 Hall’s search for his effect in dielectrics. A than in figure 1 and the side projections (not shown) glass plate was drilled and fitted with brass plugs to are much shorter. With the specimen in the position allow connections to be made toa source of high indicated by the full lines, Hall obtained the expected voltage (wires A and B) and a charge detector (wires transverse voltage. When rotatedinto the position C and D). The magnetic field was directed shown by the dotted lines, however, the effect disap- perpendicular to thelarge faces of the plate peared. Hehad thus established that no potential difference is set up in a direction parallel to the applied Faraday effect (the rotation of the plane of polar- magnetic field. isation of light by a magnetic field applied parallel to the direction of propagation), thus providing a most Early responses important link between and light, as Hall’s announcement of his discoverywas quickly required by Maxwell’s theory.It onlyremained to followed by a paper from Rowland (1879) in which he show that the Hall effect existed in dielectric as well as suggested a rotational interpretation of the Hall effect. metallic substances. In response to this, Hall investi- Hall’s transverse e.m.f., when compounded with the gated a piece of plate glass, drilled with four holes, as primarylongitudinal e.m.f., could be regardedas shown in figure 3. Brass plugs were cemented into rotating thecurrent vector slightly. This seemed to each hole and leading outfrom each plug was an Rowland to pave the way for an explanation of the insulated wire. One pair of opposite wires, A and B, was connected to the inner and outer coatings of a battery of Leyden jars, and the other pair, C and D, t Accordingto this theory the transverse voltage is wasconnected to a quadrant electrometer. On developed until the transverse associated with applyinga magnetic field perpendicular to thelarge this exerts a force on each which is equal and opposite to that exerted on it by the applied magnetic field. faces of the glass plate, no significant deflection of the Thus Bel7 = eV,/b where iiis the mean , given electrometer was obtained. Hall cautiously concluded byT= Jlne.HenceBJIn = eVH/borBJb/VH =ne. (Hall 1880)

377 ‘. . . theequipotential lines in thecase ofstatic Table 1 Measurements of the Hall coeflcient RHfor induction in glass, if affected at all by the magnet, are various metals, presented to the British Association affected much less than the equipotential lines in the for the Advancement of Science at the York meeting case of a current in iron; but we cannot say that any of 1881 (Hall l88lb).For comparison modern values such possible actionin glass has been shown to be are given for the nonferromagnetic metals (Condon smaller thanthe analogousaction in the case of a and Odishaw 1958) current in tin’. At all eventsRowland developed his rotational Metal Hall’svaluesModern values of theory(Rowland 1881)and in duecourse Hall ofRH/lO-” Rn m’ C-’ adoptedthe term ‘rotational coefficient’ for the (units not stated) quantity EH/J where EH is the transverse electric field Iron + 78 Cobalt + 25 (Hopkinson 1880, Hall 188 la). Zinc + 15? +3.3 Rowland’s theoreticalspeculations also placed Lead No value listed +0.9 great emphasis on the direction of the Hall effect. Both Tin-0.4 -0.2? men had expected the direction of the transverse e.m.f. Brass - 1.3? Platinum-2.4 -2.4 to be the same as thatof the ordinary force exerted on Gold -6.8 - 1.2 a current carrying conductor in a magnetic field. It Silver-8.4 -8.6 was, however, found to be in the reverse direction for Copper -IO? -5.5 the first two metals examined, gold and silver. Aluminium - 50? - 3.0 Drawing further analogies with the Faradayeffect, for Magnesium - 50? -9.4 Nickel - 120 which there was evidence of opposite signs in diamagnetic and ferromagnetic media (Rowland Note: Values denoted by (?)were regarded by Hall as 1879), Rowland urged Hall to investigateiron. As uncertain by anything up to 100%. predicted, this showed a Hall effect of opposite sign to that observed in gold and silver. This turned out to be attract eachother. a false clue, however,for when nickel was investi- ‘It is, of course, perfectly well known thattwo gated its sign was the same as gold and silver. Thus conductors, bearing currents parallel and in the same theearly promise of a dramatic confirmation of direction, are drawn toward each other. Whether this Maxwell’s electromagnetic theory of light was not fact,taken in connection with whathas been said realised. above, hasany bearingupon the question of the On theother hand, Hall fully realised that the absolute direction of the electric current, it is perhaps constancy of the direction of his effect in most of the too early to decide’. metals tested (five out of the first six) did have funda- Variousobjections were raised when Hallfirst mental significance. Atthe time of his experiments announced his effect. In particular it was suggested fluid theories of electricity were common, though it that a conducting strip, necessarily fured as in Hall‘s wasnot known whether one or two fluids were apparatus, would be undermechanical strain as a involved, and if the former which was the ‘absolute result of the force exerted on it by virtue of its being a direction’. Once again his conclusions were tempered current carrying conductor. Heat would be generated with caution. In the following passage (Hall 1879) the at the stress boundaries within the specimen and this italics are Hall’s own would give rise to thermoelectric e.m.f.s of which ‘In regard tothe directionof this pressure or Hall’s transverse e.m.f. could be one manifestation. tendency, as dependent on the direction of the current This cause was shown by Hall to be insignificant, by in the gold leaf andthe direction of the lines of the simple expedient of using two similar strips of soft magnetic force, the following statement may be made: steel (in which the magnitude of the effect was large), if we regard an electric currentas a single stream each fixed to a plate of glassbut using different flowing from the positive to the negative pole, i.e. from methods of attachment so that the strain patterns set the carbon pole of the battery7 through the circuit to up would be different. thezinc pole, in this case the phenomena observed indicate that two currents, parallel and inthe same direction,tend to repel each other. If, on theother British Association paper hand, we regard the electric currentas a stream In the summer of 1881 Hall travelled in Europe and flowing from the negative to the positive pole, in this made a number of furthermeasurements in casethe phenomenaobserved indicate thattwo Helmholtz’s laboratory in Berlin. He summarised all currents, parallel and in the same direction, tend to his results in a paper read to the British Association at its York meeting in the same year (Hall 1881b). These t Hall is referring here to the Bunsen cell, using zinc and are presented in table 1 together with more recent carbon electrodes. He used a battery of such cells to power his electromagnet. Each cell had an emf. of approximately values of the Hall coefficient. Hall placed the metals in 1.9 V. order of decreasing coefficient, with due regard to

378 sign. Although he claimed no absolute significance for relating to and for access to the doctoral his numerical values it appears from his 1880 paper dissertation of John David Miller. To this latter work that the conversion factor to modem unitsshould the author is greatly indebted. He also wishes to involve a simple power of 10, though one cannot be acknowledge the assistance givenby the Natural certain about this. Suffice it to say that the correlation Philosophy Department in the University of Aberdeen is convincing for those metals whichhe claimed to in obtaining many of the references. have measured with reasonable accuracy. The ferro- magnetic metals are a special case inview of their more complicated behaviour in magnetic fields, and References values quoted by different observers vary widely. Bridgman P W 1939 Biog. Mem. Nat. Acad. Sci.21 73-94 Modem values for these metals have therefore been Condon E U and Odishaw H (eds) 1958 Handbook of omitted; Hall’s values are retainedfor historical Physics 4-74 (New York: McGraw-Hill) completeness. Edlund E 1878 Phil. Mag.(5) 6 289-306 TheBritish Association paper was wellreceived, Hall E H 1879 Am. J. Math. 2 287-92 (republished in Phil. and Kelvin said (Bridgman 1939) ‘The subject of the Mag. (5) 9 225-30) communication is by far the greatest discovery that Hall E H 1880 Am. J. Sci. (3) 20 161-86 (republished in has been made in respect to the electrical properties of Phil. Mag.(5) 10 301-28) metalssince the times of Faraday-a discovery Hall E H 1881a Phil. Mag.(5) 12 157-72 comparable with the greatest made by Faraday’. The Hall E H 1881b Brit. Assoc. Adv. Sci. Reports552-3 seal of authenticity thus beiig placedon the Hall Hopkinson J 1880 Phil. Mag.(5) 10 430-1 Maxwell J C 1873 A Tkeatise on Electricity and Magnetism effect, many investigators moved into the field. It was Vol. 2 (Oxford: Clarendon) soon found that it is one of four transverse effects, the Miller J D 1970 ‘Rowland and his electromagnetic others nowbeing known by the names of Ettings- researches’ ch. IX Doctoraldissertation Oregon State hausen, Nernst and Righi-Leduc. Hall himselfdevoted University a great deal of effort to the accurate determination of Rowland H A 1879 Am. J. Math. 2 354-6 the coefficients associated withall foureffects. The Rowland H A 1881 Phil. Mag.(5) 11 254-61 delicacy of the measurements involved is indicated by Wiedemann G H 1872 Die Lehre vom Galvanismus und the fact that one of the sources of error which Hall Elektromagnetismus nebst technischen Anwendungen had to consider and eliminate in hislast apparatus was (Brunswick 2nd edn) due to convection currents in the air created by the magnetic field as a result of the slight of oxygen. As Bridgman (1939) records ‘The daunt- lessness ofhis experimental attack on this problem was characteristic of the man’. Ofhimself Hall wrote‘I am insome respects distinctly handicapped in all my scientific endeavours, being unskilful of hand and slow of apprehension. On the other hand, I amvery persistent, and fond of wrestling with a difficultproblem in my own slow Kent lectures way; any success I mayhave attained is to be The Institute of Physics (Kent area) and the Kent attributed to these two qualities’. Physics Centre are organising a number ofevening The other factors involved in the discovery of the lectures in thecoming months. Amongthese are Hall effect are succinctly identified by Miller (1970). ‘Physics,thedisintegrated science’ (9 October, ‘By going to Johns Hopkins University in 1877 Edwin speaker Dr J M Warren, Brunel University), ‘Nearly Herbert Hall found two expedients for carrying out 50 years in the cold’(25 October, reviewof low physical research which were uncommon in American physics by Professor D Schoenberg, universities: he gained access to instruments of Cavendish Laboratory), ‘TheVoyager mission’ (13 precision and to the counsel of Henry Rowland‘. November, Dr G F .Hunt, UniversityCollege It isnot altogether frivolous to point out the London),‘Colour isfun’ (4 December, Dr A W S appropriateness of denoting the Hall coefficient by the Tarrant, University of Surrey) and ‘Somehistorical symbol R,. aspects of photobiology’ (6 December, Professor I A Magnus, Institute of Dermatology). All lectures will be held at the Physics Laboratory, University of Kent at Acknowledgments Canterbury, at 19.30. The author wishes to acknowledge the very ready Further detailsmay be obtained from Dr C I assistance given by the Johns Hopkins University, in Isenberg, Physics Laboratory, University of Kent at particular the Special Collections Department of the Canterbury, Canterbury CT2 7NR (tel. 0227 66822 Milton S Eisenhower Library for general information ext. 293).

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