Units and unity in magnetism: a call for consistency
What's the difference between a tesla and a gauss, the B-field and the H-field, or one joule per tesla squared per metre cubed and 10-7 emu per cubic centimetre? .John Crangle and Mike Gibbs report on a magnetic Tower of Babel . (.. . WHEN wc measure any quantity it is discussions and makes recommendations important ta define the units that wc use. for usage in the simplest possjhle'I.~.uÇ
If other worken are ta use the resuIts of rigorousJ temlS. ..~i::·;:~> our measurements it is essential rhat they SI unill have been adopted .complet;iy know how ta convert. our units inta their and are used unambiguou:sIYLin,ja1pl~st preferred unia. Ir is conve.nient ifthey use evay ares of science and ~~,;m co~~ ~ the lame unita, especia11y if everyone uses magnetismJ howeverJ a the same set 'of uniOi, universal1y defined of SI (in various versions) a.tt~,~~q11s and agreed. This· is not the case in still used. To illustrate· wa\.çonfuJÎ01;1,. magnetism as, for example, the two Hmagnetic field" can meaI}-:t'B-ti~d:·.>or feature articles in this issue of Physics "H-field". The SI unill for.th..e.are teila World illustrate. The article on giant .cT) or amperes pa m~tt:e:{4.lIl.-~);:in magne!Xlresisœnce (P34) Us.. oenreds 1 cgs they are gauss (G) and oena!â for the ma.gnetic field, whilst the i - (Oe). Al! four,unill are version of the metrie sysœm by the magnetic induction, B J iD. a.p'olarizalile Ilth Conférence Génénle d.. Poids et medium. There is no fundamèntal MesUtts in 1960. It replaoed the old ment in cither - bath 'are eqUiVaIent cgs - ceDrimetI'e, gram and second in SI - and there is no reason why bath system with seven fundamental, or should not be used in parallel. . 1 ;, 1 "base"J unit!: me mette, kilograrn, In the Sommerfeld conve.nponj second, ampere, kelvin, mole and . which was adopted by ..the Intel' candela, an definêd in an agreëd way. national Union of Pure and Applied ~uderived" unit! can he con Physics (IUPAPl. strueted from the base units. Sorne B = Jlo(H + M) = Bo+ l'oM have special names - the joule for where Jlo is the permeability of free energyJ the ohm for resistance etc space, H is the H-fieldJ M is the whilst othersJ such as those for velocity magnetization per unit volumeJ and and momentum, do not. Ba is the free-space induction that In magnetism three derived units would remain if the !Jled!u.m. were have special names: the henry for taken away (the B-fie1d). inductance, the weber for magnetic 10 the Kennelly sY'tqn,. which la flux and the tesla for magnetic induc traditionaUy favoured ..by .electrical tion (also known as the magnetic flux engineersJ B is given by density). HowCV'er, the derived units B=JloH+J=Bo+J . for other magnetic quanrities, such as where J is the magnetic polarization. permeability and magnetization, do These [wo equations'dci~not confliet not have special names. SI does it - the Teslatron supercônd4cüng magnet from if we accept that magnetization and In sr there are also two "supple Oxford Instruments pro.duces a field pf'2Q T at 2.2 K. The polarizarion are indeed diffc:reI;l.t quan mentaryJJ units - for plane angle and tesla is the SI unit for magnl}!ic J.,~~ction {B-fJeld} tities and use different' symbols for for solid angle - that are dimensionless ·.;ii:... ~l • them as shawn here. The SI units for ~s (i.e. have no units). FinaUy, decimal tute of Ph)".iics Magnetism Group ttied B J M and J are given in the œblej Jlo 1 multiples of sr units can be constructed again and set up a unies 'oforking party. units of henrys per mette CH m- ) and H 1 by using one of the 20 SI prefixesJ which As a resuIt, and be.cause of worldwide has units of amperes per mette CA m- ). tang<: trom yocro- (10-"') te yottll- (10"). interestJ a discussion on magnetic unies But it is important ta note that there is was held at the joint Magnetism and Which rnagnetic field? only one SI unit for each physical quantity. Magnetic Materials-Intermag Conference in Albuquerque, New Mexico J in June. When dcaling with the magnetic field we The trouble with rnagnetisrn One of the authon (MG) was a member of can use either the B-field or the H-field. the international panel of magnetism These are distinguished by their behaviour sr unit! are almost universally accepted specialists that presided over the evening at a boundary between media having and l!l"C always used in schools and to train discussionJ which was attended by sorne different relative permeabilities (J.1). The young scientists. In the early days of 150 participants. The rest of this article nonnal camponent of the B-field and the magnerismJ howeverJ there was room for has been distilled from these various rangential componem of the H-field are !4JjI~!lIIJ!R!!!!!- :as::ae;:.'''..,~. '.UE a;::wt2a ••b !Il!.§1I33l12I!!11iJJl!!I3&l!!IYJI!!l.!.._t_5_lIlblllt3l1l;l!I!!.. !l!I.5l1l.Jl!I!!.ll.!!l!.1II331!lX;,;!-AAIll'•.'''''''''''''''''...... ;.".__:o------..... 32 Physlc, World Novcmber 1~ continuous across thc bound SI units for important magnetic quantities and their equivalent in cgs quamity which is not defined ary. In &ce space B = J.loH in in the SI system. both the Sommerfeld and Quantity being Symbol SI unit cgs unit Kcnnelly s1'stcms. In SI measured I-Iystcrcsis loops J.lo =4r. x 10 1-1 m l, so thc Magnetic field D, T 10· Oe ll- and J·/-ficlds have diffcr- Magnetic induction D T 10· Oe 1[ysleresis loops 2:oe an im 1 1 1 em numerical values. In cgsJ Magnetization per CT JT- kg- 1 erg Oe- g' portant characteristic of ferro howeverJ J.lo = Il so thc B- and unit mass 1 emu g-' magnelie malerials. The H-ficlds have the same num magnerizarion, and hence the Magnetization per M JT-'m-3 lr erg Oe-1 cm-3 erical valuej this has always unit volume lr emucm-1 induction and polarization, in caused gauss (for the B-field) relatively weak applied fields J~-.2kg-1 and oerned (for the H-field) Z depend on the recent history ta become confused. (Note of the specimen with respect that the relative penneabilityJ ta the field. flit \>roperties Ji = B/BoJ is dimensionless displayed by t:h"t loops are and has the same value in often very important in tech both the sr and the cgs nical and applied tna.gnetism. systems.) It is possible to draw hysœr• So how do the B-field and esis loops in several, equally the H-field differ? Fonnulae validJ ways. dealing -,with forceJ energyJ magnetic the magnetic moment ofone eleetron spin: (i) The induction B (in tesla) is plotted on 24 1 moment and so on always use the B-field ~B = 9.2732 X 10- JT- • Ali other mag the ~s against the field B o (in tesla) on (for exampleJ the Lorentz force on a netic moments are derived from thîs. The the »-axis. particle with charge e moving with vela energy (in joules) ofone Bohr magneton in (ü) The mass magnetization a (measured l city v in a magneric field B is ev x B). The a magnetic field of Bo is J.ln.Bo. In cgs in JT- kg-I) or the volume magnetization 21 l l 3 H-field is rarely used alone. It oruy arises JJ.B =9.2732 X 10- ergOe- (the erg is the M (in JT- m- ) is plotted on the y-axis when calculating the magnetic effect of an cgs unit for energy: 1 J is equivalent ta against the field B o (in tesla) on the x-axis. electric currcnt or in similar cases. 107 erg). Altematively) M can he plotted against l The main attraction of quoring fields as When the temperature (and hence the BoIJ.lo with both axes given in A m- . B-fields is that the comparison ofnew data densiry) of a sampIe varies, its mass is (iii) The polarization J (in tesla) is plotted (in SI) and old data (in cgs) is precise and almost always better known than ilS on the y-axis agamst the field B o (in tesla) simple. Thus solid-state physicists working volume. 1berefore the magnetization per on the X'-axis. in fundamental magnetism tend to use unit massJ a, is frequently usedj thîs has The magnetic remanence and coercivity B-fields. For instance, a 10 T supercon units of J T 1kg-l. The cgs unit for a are often derived from hysteresis loops. ducting magner (100 kOe or 100 kG in erg Oe-l g-I (often loosely and ambigu The remanence is the quantity remaining cgs) would never be described as being a ously referred to as emu g-J) - is numeri on they-axis when the field (i.e. the x-axis) 1 7.958 MAm- Magnet. caUy equal tO the SI unit. is reduced te zeroJ frequently from satura HoweverJ electrical engineers often use In SI the unit for mapetization per unit tion. The coercive field is the reverse field 1 H-ficlds in kAm- and physicists working volume, M, is JT 1 m- . HoweverJ the cgs rhat has ta be applied ta reduce the in applied magnetism have foUowed. But unit for M- ergOe-J cm-3 Ooosely called quantity being plotted on the y-axis (i.e. the advantages of using H-fields are not emu cm-') - is equal to 10-4 of the SI unit induction, magnetization or polarization) obvious. IndeedJ there appear to be (see table). to zero. Therefore the value of the disadvantages, one of which is the present remanence and cocrcive field will depend confusion over units. When working with Suseeptibility The susceptibility of a on how the y-axis is defined. the B-fieldJ howeverl we must take care ta ferromagnerie material is the ratio of the A vital figure-of-merit for pennanent distinguish between the field (free-space magnetization to the field which induces it. magnets is the maximum energy product induction) and the inductionJ BI within a Therefore the mass susceptibilityJ XJ is (or srorage density). This is defined from polarized medium. defined as 1=amo and is measured in the induction hysteresis loop (i.e. B vs B o) IT 2kg 1; the volume susceptibility, Je, is - it is the maximum value of the product J RecoIIUIlendations: defined as Je = MlBo and has SI units of (I/J1o)BoB and has SI units k)m- . 2 • In SI we should only use one fieldJ the JT- m ' . B-field. The fre....pace field should be The corrcsponding units in the cgs 2 Looking forward given a special symbol, such as Bo• ta system for susceptibility are erg Oe- g-I distinguish it from the induction, B. Both and ergOe 2cm-', for which emug-l and If these conventions (summarized in the Ba and B should be measured in tesla. emu cm ' are frcquently and ambiguously table), and others which derive from them• • The H-field should not be used. Where uscd. ln Cg5J the emu that is used for could be applied rigorously to the results H was used in cgsJ it should he replaced by magnetization is not the same as the emu of magnetic measurements, a pattern that Bo/J.lo in SI (in units ofAm-1 ifnecessary). used for susceptibility. is self-eonsistent would result. It would Note that the SI unit for Je, the volume also be casier ta relate magnetic measure susceptibility, is the inverse of that for J.loJ ments with data from other areas of Keeping it consistent l that is metres per henry (m H- ), since science. Moreover, scientists involved in Once it has been decided ta usc the B-field ~ =BIBo=l + J.loMlBo =1 + ~oJe, and Il is magnetic measurements for the first rime, and teslaJ the dcfinitians for other mag dimensionless. having worked in areas where SI is used nctie properties of intcrcst - magnetiza exclusively, would be less confused. The tionJ suseeptibililY. hystcrcsis loops and so Polarization This is the part of the various working parties hope thatl if these on - follow naturally. The main magnerie magnctic induction within a magnetized suggestions are followcd, uniry in the quantities are summarized in the table body which is not the applied field - that is literature of magnctism will follow ta the (which also relates SI and egs units) and 1 in the Kcnnelly equation (D = Ba +J). 1 benefit of the whole communiry. are explained briefly bclow. has the same units as n and B o in the SI syst.em (tesla). In cgs the Kennelly equa ..John Crangle and Mike Gibbs are in the Magnctizatian 'lbe fundamemal unit of tion was wrilten as B =H + 4r.:I l where l Department of Physics, University of magnetization is the Bohr magneton, ~1l1 was the intensity of magnetization, a Sheffield, Sheffield S3 7RH, UK ._-----~------_. ~ ...,;;;;..",..-....,.....----_._---- .- --_ .._.. --_. - ...-.....-...- S '1 S ~ÈIM.Q. le.. K:OSSFL: :r..:, 6 ~ ~.H t-j)( (" ke.;."t.\I" 5'jsiel;..") J 178 TAULES Table d'unités mécaniques et éleclriques (L'errr el correspondance entre système ."1 K SA cl système CGS de Gauss Vitesse Unité CGS Constan Gnilé MKSA ~ombre Grandeur 1Symbole c)le Gauss k IH- E Voll'm-1 slalvolt'cm-1 ! '10-' Champ électrique 3 Constar Coulomb. rn-li staLvoll'cm-1 4",3,10' Déplacement électrique D PremieJ Polarisation électrique p Coulomb' m-' slatvolt·cm-1 3·10' u Dipôle électrique p Coulomb·m slatcoulomb· cm 3·10 Capacité C Farad cm 9 ·10' Rayon Inductance L Henry cm -1. S2 ID' 1 Constal Résistance H Ohm --u ~'tJ,. 9·10 Longur z Induction magnétique B \Vebcr·m- Gauss ID' de l'. l 4n: .10-1 Champ magnétique H Ampère' fi Œrsted Weber = V's (Maxwell) 10' Flux d'induction :vIagné! Magnétisation p~ \\"cbcr' ID-1 101/4" l IS'PI ln Moment magnétique !J. Weher·m erg Gauss Momen (Energie = p.. H) :vIagnél Moment électromagnétique m=J. Ampère'm! (Energie = m'B) p, :\-lomer Consta Les facteurs 3 ou 9 intervenant dans la table correspondent à l'approxi Consta 1 l matioo c = 2,9979 ... X 10' ms- '" :l· 10' ms- Consta Les caractéristiques électromagnétiques du vide sont données par de \ \'-A-' _1 flo= 4n'IO 7 henry'm-1 ':;' ~ Vv'\ Corres rt 1 l E =- farad'm- o <'Po Carres êneI , " _v- l' ~T - :-,.)'" , 1 •• ;-