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10 MAONITIC SYSUMS
.
1.1\
1.6.-
1.4
1.2' ...
1.0.-
O.fi
0.6
0.4 -.- -".. __o
~~. -.., "",. .~'"''
l'lg. 1.7. Magnetization.
,curves.
2500 3000
.'
500 1000 I~' 2000'.. ".~",'..',.,<.;",'MP'/. '. ",'-.," ..,-\~." ~
wound011'a lorus of cast steelof the sort u.sedin electricmachinery.thenthe
n~d~tredmagnetíz~tioncurveis typicallyIhatof themiddlecurveof Fig. 1.7.
::~t;ris convenientto corisíderthatthetluxdensityproducedin theferromagnetic
'oru~,is madeupof twocomp()nents:
:; B =Bo+B.,,'T (1.22)
whe;\:'80is thefluxdensitywhichwouldoccu'rin a coil containingavacuum,and
8" s'.he additionalfluxdensity,dueto thepresenceof theferromagnetic.torus.At
'I '. 1000amperes per.meter. the value of Bo would be 41Tx IO-~=O.0012~T.
. ;'roin Fig. 1.7,theyalueof B for a cast-iron.torus.atthisvalue.ofH is seento be
1'.513T: thus.fromEq. (1.22),8.6=-0.512T. The prcsenceofthe castironresults
ir.a Ikx densityabóut500times'asgreataswouldbeproducedin air.
"~"~:OuxdensityB." is a resultof lhe partialalignmenl'óftheatomicmagnetic
md',~,tsoftheireinwilh thedireclionoftheappliedmagneticfie!d'H.Ifthe atomic
IVI:-mf,illsarevisualize'dasdueJO minule'currenlloopsarisingfromelectronspin,
ar" ..,ssectionaf IlJe ironlorusmayberepresenledby thediagramo':Fig. l.8(a)"
i!W)ugh in fact manymillionspf currentloops shouldbe shown,in anypraclical
cn:s:'.'~:etionarea.Insidelhe iroo,eachminuteloopcurrentis adjaceriftoa similar
IqG" \;Jrrentflowingin theopposiledirection.The'effectsof lheadjacentcurrenls
I
:"'.
(a)
Flg. 1:8 Magncli7a1ionof a ferTOmagnelic,lorus..
(b)
.may,thereforebe consideredto'caneel.()ril~ontheoulersurfaceis therenocan-,
.celh,Ition,amlthcrctheeffeet.is identicalwíththatof a liçtitiuussur1'acecurrcnt. .
, ':lI is 'kílOwnth,JIeachatomotíron hasa magnclicmornent~.~limesthebasic
quaritumof magnel.icmoment(9~~7x 10'~4\ ' 012).The ~pacingbctweenatomsof
..me.talliciron is <I.'.-~2.27,X 10-'"meter.The areaoccupiedby a si~gleatomin á
'c'rosssectionof an imospeei~n.will thusbe <l2.-andtheatornicnlagneticmomen!
iriaybevísualízedasdueto a curre'nti 11 f10wingina loop01'arcaif2.Thus.for une
atom,
and
'P.. = i~.J~.=2.2x'.9.~7x IO-~4A rÍi2 ( I. ~3)
( 1.~4)
The effuctof thetotal/yalígnedmagneticmomentsof a singlelayerof atomsin
thecrosssection01'the.torussho'wnin Fig. 1.8(a)is nowseento beequivalenl!~a
currentf" completel'yencirclingthecross sectionof the torus.Othe.flayersôf-
aloms,spaceddistanced fromoneanother.will hcequivalentto furtherencirding
'current,s,ill1dtheeffeetuf ali theatomsin thct.'TUSwill bethatpf a turoidalcoil
. carryingcurrent'i",andhavingtumsspacedcI=2.27X 10''''meterfromone'
.another.The equivalentmagneticfieldintensitydlieto'thisIktitiollscoil willbe
. ,
H ' =;11 =i.~d:, '" P '" Aí ( I 25)
""UII' d fJJ {f'1-' m .
. ~inC
:J
J is thevolume'ofa
,
n at~. H<quh'e'xl'resseslhema~imumpossiblemagnctic
momenpertmitvolumeof theiran.' .:'.. .. I