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<in ~t.p.e·. sumor writing about nanocrystalline î .A related source of CO~OI\'san.pc magnell prefen tesla (P40). g . ttaoed back !Xl the differef!~-.essions The Système International d'Unités "propose<! by Arthur'. Klonne,!1y' fl936) (SI) was ==ende<! as the modem and Arnold So=erfel\l,(lH(l)4'or,the 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.