INSTITUTO TECNOLÓGICO DE CIUDAD JUÁREZ
TECNOLOGÍA DE LOS MATERIALES
INVESTIGACIÓN : MATERIALES DIELÉCTRICOS PROFESOR : ING. JESÚS NOÉ BARRAZA ALEGRÍA
ALFREDO PEINADO LAZOS
26 DE OCTUBRE DE 2016
ÍNDICE
INTRODUCCION E HISTORIA..............................................................................2 MATERIALES MA TERIALES MAGNETICOS……...………… MAGNETICOS……...………….…………………………… .…………………………………………….… ……………….… 4
FORMACION DE MA M ATERIALES MAGNETICOS, …………………………………………....9 CURVAS CARACTERISTICAS………………………… CARA CTERISTICAS……………………………………………………… ……………………………………..16 ………..16
MOMENTO MAGNETICO M AGNETICO.. …………………………………………………………………...17 MOMENTO MAGNETICO ATÓMICO.………………..……………………………………1
USOS ! A"LICACIONES DE LOS MA M ATERIALES MAGNETICOS………………………… 2#
$I$LIOGRAF%A………………………………………………………………………………… 22
1
HISTORIA DEL MAGNETISMO
Históricam!t" # !$m%r & magnetta 'i! & #a ci(&a& ma)!sia & Asia m!$r* + ,(r$! #$s )ri)$s #$s -rimr$s .( ti!! tstim$!i$s scrit$s s$%r st mi!ra# m-/a!&$ c$! Ta#s & i#t$ .( &scri%a a #a ma)!tita c$! -r$-i&a&s & atrar a# irr$* Tam%i3! Sócrats a%#a%a & st mi!ra# & c$#$r !)r$ 4-#ica!&$ 5a !t$!cs # ,!óm!$ & i!&(cció! ma)!3tica* A #a ci'i#i/ació! ci!a s #s im-(ta &$s c$s r#'a!ts" # &sc(%rimi!t$ &# cam-$ ma)!3tic$ trrstr 5 #a i!'!ció! & #a %r7(#a* 8$s ,!ici$s (ti#i/ar$! #ar)am!t #a %r7(#a ! s(s 'ia7s c$mrcia#s ! s(s !a's* Cristó%a# C$#ó! (ti#i/ó #a %r7(#a ! s( 'ia7 a# !('$ m(!&$ &scri%i!&$
cóm$
#a
a)(7a
ima!ta&a
!$
marca
4actam!t # !$rt )$)r9,ic$ si!$ .( 4ist (!a :&s'iació! ma)!3tica; Hacia ,i!s &# si)#$
2
Oe%&te' &scri%ió cóm$ # -as$ & #a c$rri!t
#3ctrica a tra'3s & (! ca%# c$!&(ct$r &s'ia%a #a a)(7a ima!ta&a & (!a %r7(#a ! &ircció! -r-!&ic(#ar a# ca%# c$!&(ct$r* $stra!&$ #a 4ist!cia & (!a %e#a()n ent%e e#e(t%('a' * magnet&m!= a -artir & st m$m!t$ a-arcra (!a !('a &isci-#i!a> #
#ctr$ma)!tism$* Am-r 4-#icó .( &$s c$rri!ts #3ctricas c$! #a misma &ircció! 5 ! i#$s -ara##$s s atra!= mi!tras .( si s$! & &ircci$!s $-(stas s r-#!*
Fara&a5 $%sr'ó .( sim-r .( # im9! $ #a %$%i!a st('ira! ! m$'imi!t$> s )!ra c$rri!t #3ctrica= ,!óm!$ .( -$stri$rm!t
##amaram$s
c$rri!t
i!&(ci&a> a #a '/ .( 'is#(m%ró #as #!as & ,(r/a ma)!3tica a# s-arcir #ima&(ra & irr$ ! (! -a-# c$#$ca&$ s$%r (! im9!* a4?## &m$stró #a r#ació! !tr #as ,(r/as #3ctricas 5 ma)!3ticas 5 &sc(%rió .( #a #(/ s -rcisam!t (! ,!óm!$ #ctr$ma)!3tic$* Hrt/ &sc(%rió #as $!&as #ctr$ma)!3ticas 5 arc$!i 7(!t$ a Ts#a s(-ir$! (ti#i/ar#as -ara # (s$ & #a :ra&i$;*
MAGNETISMO
S &,i! !t$!cs magnet&m! c$m$ #a -r$-i&a& s-c,ica .( -rs!ta! a#)(!as s(sta!cias ##ama&as ma)!3ticas & atrars $ rca/ars !tr s= s &cir .( s ma!i,ista c$m$ (!a ,$rma & !r)a m&ia!t ,(r/as .( acta! a &ista!cia* Tam%i3! c$!si&ram$s ma)!tism$ a# c$!7(!t$ & ,!óm!$s .( -r$&(c! stas ,(r/as* 8#amam$s a)!tism$ tam%i3!= a #a rama & #a Fsica .( st(&ia stas ,(r/as= s(s ca(sas 5 #$s ,!óm!$s r#aci$!a&$s* @
8as
,(r/as
ma)!3ticas
s$!
-r$&(ci&as -$r # m$'imi!t$ & -artc(#as
car)a&as=
c$m$
-$r
7m-#$ #ctr$!s= #$ .( i!&ica #a strca
r#ació!
!tr
#a
#ctrici&a& 5 # ma)!tism$*
ATERIA8ES AGNETICOS E! a#)(!$s matria#s s $%sr'a .( s(s 9t$m$s $ i$!s s c$m-$rta! c$m$ si ,(s! -.($s ima!s .( i!tracta! !tr s* Est c$m-$rtami!t$ ti! s( $ri)!= -$r 7m-#$= ! # m$'imi!t$ & #$s #ctr$!s &!tr$ & #$s 9t$m$s= 5a .( t$&a c$rri!t #3ctrica -r$&(c (! cam-$ ma)!3tic$* E! st$s cas$s s &ic .( #$s 9t$m$s ti!! (! m$m!t$ ma)!3tic$ &i,r!t & cr$= # c(a# s caractri/a -$r s( ma)!it(& 5 #a &ircció! ! #a .( st9 $ri!ta&$* E! #$ s(csi'$= a st$s -.($s ima!s #$s &!$mi!arm$s s-i!s ma)!3tic$s $ sim-#m!t s-i!s* Pr$ !$ t$&$s st$s matria#s s c$m-$rta! & #a misma ma!ra= &%i&$ a .( s(s -r$-i&a&s ma)!3ticas &-!&! & &$s ,act$rs* st$s s$!" #a ma)!it(& & s(s s-i!s i!&i'i&(a#s= 5 #a $ri!tació! r#ati'a & 3st$s" Si #$s s-i!s !$ t('is! !i!)(!a i!tracció!= 5a sa !tr ##$s $ c$! s(s a#r&&$rs= !t$!cs ca&a (!$ & ##$s -$&ra a-(!tar ! c(a#.(ir &ircció!= -(st$ .( !$ t!&ra -r,r!cia a#)(!a* Si! m%ar)$= 3st !$ s ! )!ra# # cas$" #a $ri!tació! .( t$mar9 ca&a (!$ & ##$s &-!&r9 &# %a#a!c & 'ari$s ,act$rs .( -(&! rs(mirs ! ,act$rs i!tr!$s 5 4tr!$s* C$m$ s( !$m%r #$ i!&ica= #$s ,act$rs i!tr!$s &-!&! & #as caractrsticas i!tr!scas & ca&a matria#= st$ s= &# ti-$ & i!tracci$!s !tr #$s s-i!s* P$r $tr$ #a&$= #$s ,act$rs 4tr!$s s$! #$s .( st9! r#aci$!a&$s c$! # am%i!t= s &cir= .( &-!&! & #a i!tracció! &# sistma c$! s(s a#r&&$rs* C$m$ 7m-#$
& ,act$rs 4tr!$s t!m$s #a -$si%# 4ist!cia & (! cam-$ ma)!3tic$ -r$&(ci&$ -$r (!a ,(!t a7!a a# matria#= 5 -$r $tr$ #a&$= & ma!ra m(5 im-$rta!t= #a tm-rat(ra am%i!ta#= 5a .( # m&i$ am%i!t ,(!ci$!a c$m$ (!a ,(!t & ca#$r 5 a)itació! -ara # matria#* U!
7m-#$
ma)!3tic$=
t-ic$ s
#
&
(!
&
#$s
matria# ima!s
-rma!!ts* E! st cas$= (!a )ra! -art &
#$s
s-i!s
st9
a#i!a&a
-rma!!tm!t ! #a misma &ircció! r#ati'a* + a(!.( # cam-$ -r$&(ci&$ -$r ca&a (!$ st$s s-i!s s m(5 -.($= a# s(mars s(s c$!tri%(ci$!s i!&i'i&(a#s s -r$&(c (! cam-$ ma)!3tic$ .( -(& $%sr'ars macr$scó-icam!t* E! # $tr$ 4trm$ t!m$s #$s matria#s -arama)!3tic$s* E! st$s matria#s #$s s-i!s a-(!ta! ! &ircci$!s t$ta#m!t a/ar$sas= -$r #$ .( #as c$!tri%(ci$!s & #$s s-i!s i!&i'i&(a#s ti!&! a a!(#ars* C$m$ c$!sc(!cia= a !i'# macr$scó-ic$ !$ s $%sr'a (! cam-$ ma)!3tic$ rs(#ta!t* Si! m%ar)$= 4ist! #$ca#m!t -.($s cam-$s ma)!3tic$s -r$&(ci&$s -$r #$s s-i!s= 5 (! -.($ im9! & -r(%a s!tir9 #as 'ariaci$!s & st cam-$ a #$ #ar)$ &# matria#*
Si t$mam$s &$s ima!s -rma!!ts= $%sr'arm$s .( #$s 4trm$s & (!$ 5 $tr$ s atra! $ s r-#!= &%i&$ a .( ca&a (!$ & ##$s ti! &$s ti-$s & -$#$s ma)!3tic$s* C$m$ c$!sc(!cia= si #$s -$!m$s ! c$!tact$ 'rm$s .( ti!&! a a#i!ars & (!a cirta ma!ra .( rs(#ta !at(ra# -ara ##$s* Dcim$s !t$!cs .( #$s ima!s a! t$ma&$ s( -$sició! & m!ima !r)a= $ & .(i#i%ri$* Si a$ra tratam$s & )irar (!$ & ##$s 10= 'rm$s .( !csitam$s acr (! tra%a7$> st$ s= &a&$ .( sta !('a -$sició! s & !r)a ma5$r .( #a a!tri$r= !csitarm$s s(mi!istrar !r)a -ara #$)rar 5 ma!t!r sta !('a -$sició!= 5a .(
! # m$m!t$ ! .( &7m$s & a&mi!istrar sta !r)a 4tra= $ sa= ! c(a!t$ &7m$s & acr ,(r/a -ara &t!r a #$s ima!s 5 #s -rmitam$s )irar #i%rm!t= 3st$s cam%iar9! & &ircció! 5 s a#i!ar9! & !('a c(!ta ! s( a!ti)(a &ircció!= st$ s= r)rsar9! a s( sta&$ & m!ima !r)a* A#)$ simi#ar s(c& a !i'# micr$scó-ic$ c$! #$s matria#s a .( !$s m$s r,ri&$= !icam!t .( ! '/ & t!r (! -ar & ima!s= t!&rm$s (! !mr$ &# $r&! & 10 a #a 2@ -.($s ima!s i!tract(a!&$ !tr s* E!t$!cs= ca&a -ar & s-i!s tratar9 #$ca#m!t & $ri!tars & #a ,$rma m9s !at(ra# -$si%#= s &cir= & ma!ra .( #a !r)a & s -ar sa m!ima* C$m$ rs(#ta&$ & st -r$cs$ t!m$s (!a )ra! &i'rsi&a& & c$m-$rtami!t$s ! #$s &i,r!ts matria#s ma)!3tic$s*
S ##ama +e%mea$#'a' ma)!3tica a #a -r$-i&a& .( ti!! #as s(sta!cias & &7ars atra'sar -$r #as #!as & ,(r/a & (! cam-$ ma)!3tic$* D ac(r&$ c$! sta -r$-i&a& #$s matria#s -(&! sr"
Fe%%!magn,t(!& = Est$s matria#s= c(a!&$ s$! 4-(st$s a (! cam-$
ma)!3tic$= &ist$rsi$!a! ! &masa #as #!as & ,#(7$* Est$ s &% a .( s -r$&(c (! $r&!ami!t$ & #$s m$m!t$s ma)!3tic$s &# matria# ! #a misma &ircció! 5 s!ti&$ .( # cam-$ 4tri$r* Si rtiram$s # matria# & #a acció! &# cam-$= c$!sr'ara &(ra!t (! tim-$ #as -r$-i&a&s ma)!3ticas a&.(iri&as* A.( #a -rma%i#i&a& ma)!3tica s c#aram!t s(-ri$r a #a &# 'ac$= -$r ##$ st$s matria#s s caractri/a! -$r -)ars a #$s ima!s* 8$s trs matria#s ,rr$ma)!3tic$s -$r 4c#!cia s$! irr$= c$%a#t$ 5 !.(#*
6
Damagn,t(!&= st ti-$ & matria#s ,( &sc(%irt$ 5 !$m%ra&$ -$r
ica# Fara&a5* C(a!&$ (! matria# &iama)!3tic$ s s$mti&$ a #a acció! & (! cam-$ ma)!3tic$= #as #!as & ,(r/a & st s$! r-#i&as acia # 4tri$r= $ &ic$ & $tr$ m$&$= (! matria# &iama)!3tic$ sra r-#i&$ -rma!!tm!t -$r c(a#.(ir -$#$ & (! im9! -$r.( # ,#(7$ ma)!3tic$= a &i,r!cia & #$s -arama)!3tic$s= &ismi!(5 !$ta%#m!t* S ma)!ti/a! &3%i#m!t ! s!ti&$ $-(st$ a# cam-$ ma)!3tic$ a-#ica&$ 5 s$! r-#i&$s #'m!t -$r #$s ima!s* S( ma)!tism$ !$ s ma!ti! si # cam-$ ma)!3tic$ s rtira&$= 5 s( -rma%i#i&a& ma)!3tica s i!,ri$r .( #a &# 'ac$= -(s $,rc! ma5$r rsist!cia .( st a #a -r$-a)ació! &# cam-$ ma)!3tic$* S$! &iama)!3tic$s # %ism(t$= # i&ró)!$= #$s )ass !$%#s= c#$r(r$ & s$&i$= )rma!i$= )ra,it$= tc3tra*
Pa%amagn,t(!&= st$s matria#s s$! #$s .( c$m!m!t (ti#i/am$s c$! m9s
,aci#i&a& ! !(stra 'i&a c$ti&ia!a a#)$&ó!= -#9stic$= !tr $tr$sJ* S caractri/a! -$r sr #'m!t atra&$s -$r #$s cam-$s ma)!3tic$s= s &cir= si c$#$cam$s (! matria# -arama)!3tic$ crca & (! cam-$ ma)!3tic$= atrar9 acia si #as #!as & ,(r/a &# cam-$* Si rtiram$s # c(r-$ & #a acció!
&#
cam-$=
,rr$ma)!3tic$s= -r$-i&a&s
a
st$s
ma)!3ticas*
&i,r!cia !$ 8a
&
rt!&r9!
#$s s(s
-rma%i#i&a&
ma)!3tica ! st$s matria#s s s(-ri$r a #a &# 'ac$ 5 a #a &# air= rs-cti'am!t* P$r $tra -art= #$s matria#s -arama)!3tic$s ti!! (!a c(a#i&a& &staca%#m!t -artic(#ar &# rst$ & #$s matria#s 4-(st$s a cam-$s ma)!3tic$s= .( s #a & ma!i,star # mism$ ti-$ & atracció! 5 r-(#sió! .( #$s ima!s !$rma#s c(a!&$ s$! im-(#sa&$s -$r (! cam-$ ma)!3tic$* Si! m%ar)$= a# rtirar # cam-$ ma)!3tic$ sta c$!&ició! &sa-arc -$r.( # a#i!ami!t$ ma)!3tic$ !$ st9 m9s ,a'$rci&$ !r)3ticam!t* E7m-#$s & st$s matria#s s$!" a#(mi!i$= ma)!si$= tita!i$= ?$#,rami$= tc3tra* K
8a -rma%i#i&a& ma)!3tica & #$s matria#s &iama)!3tic$s 5 -arama)!3tic$s s -r9cticam!t i)(a# a #a &# 'ac$ -$r #$ .( carc! & i!tr3s i!&(stria#* 8$s matria#s ,rr$ma)!3tic$s= si! m%ar)$= s caractri/a! -$r -rs!tar s(sc-ti%i#i&a&s m(5 a#tas 5= -$r #$ ta!t$= s$! ca-acs & a&.(irir (!a ,(rt ma)!ti/ació!= #$ .( s a-r$'ca i!&(stria#m!t -ara )!rar cam-$s ma)!3tic$s & a#ta i!t!si&a&* Es 'i&!t .( #$s matria#s ma)!3tic$s s$! im-$rta!ts -ara # 9m%it$ c$mrcia#= -(s (!a c$rri!t #3ctrica .( 'ia7a a #$ #ar)$ & (! a#am%r c$!&(ct$r -r$&(c (! cam-$ ma)!3tic$ c$!c3!tric$* P$r $tra -art= as c$m$ (!a c$rri!t #3ctrica )!ra (! cam-$ ma)!3tic$= (! cam-$ ma)!3tic$ -(& )!rar (!a c$rri!t #3ctrica* P$&m$s &isti!)(ir st$s matria#s= &s& # -(!t$ & 'ista c$mrcia#= & #a si)(i!t ,$rma" Mate%a#e& magn,t(!& met-#(!&" s$! #$s ,rr$ma)!3tic$s 5a m!ci$!a&$s .( s -(&! c#asi,icar ! $#an'!& * '"%!&* 8$s matria#s ma)!3tic$s %#a!&$s s$! a.(##$s .( ti!! (!a %a7a rma!!cia ma)!3tica= s &cir= s -(&! &sma)!ti/ar c$! m9s ,aci#i&a& 5 s s(#! m-#ar ! #ctr$ima!s= -ara -$&r 'ariar ! ##$s # ,#(7$ ma)!3tic$ 5 c$!tr$#ar as #a c$rri!t i!&(ci&a ! %$%i!as= !c#$s & tra!s,$rma&$rs= )!ra&$rs= tc3tra* 8$s m9s c$m(!s s$! #as a#aci$!s & irr$* 8$s matria#s ma)!3tic$s &(r$s s$! a.(##$s .( -rs!ta! (! cam-$ ma)!3tic$ rma!!t )ra!&= s &cir= s$! #$s .( c$!sr'a! i!icia#m!t (! )ra! cam-$ ma)!3tic$ 5 -$r #$ ta!t$ s$! a-t$s -ara ima!s -rma!!ts* P$r 7m-#$= a#aci$!s & F= A#= Ni= C$* Mate%a#e& magn,t(!& (e%-m(!& " s$! #$s &!$mi!a&$s matria#s ,rr$ma)!3tic$s* A(!.( s( $ri)! s cr9mic$= -rs!ta! a#)(!as -artic(#ari&a&s ! s( str(ct(ra atómica= & ta# ,$rma .( ti!! (! m-ar7ami!t$ -artic(#ar & #$s s-i!s & #$s #ctr$!s -r$-i&a& ,sica & #as -artc(#as= r#aci$!a&a c$! s( m$m!t$ a!)(#arJ= -$r #$ .( s -(&! ma)!ti/ar* A#)(!$s & st$s matria#s s$! #as &!$mi!a&as s-i!#as= .( s$! a#aci$!s & != Ni= L!= ) 5 C$> s s(#! (ti#i/ar c$m$ #m!t$s -asi'$s -ara s(-rimir i!tr,r!cias ! circ(it$s #ctró!ic$s= c$m$
tra!s-$!&$r ! circ(it$s & ra&i$,rc(!cia= .( -(&! (sars -ara i&!ti,icar a!ima#s $ ##a's & a(t$mó'i#s*
FORMACION
DE
MATERIALES
MAGNÉTICOS
IMN
S ##ama im9! a c(a#.(ir s(sta!cia $ c(r-$ .( t!)a #a -r$-i&a& ma)!3tica* E4ist! ima!s !at(ra#s c$m$ #a ma)!tita .( s (! ó4i&$ & irr$ F@OJ 5 $tr$s arti,icia#s $%t!i&$s c$! &i,r!ts matria#s 5 -$r &i,r!ts m,t!'!& 'e manta()n = c$m$ #a n'"(()n magn,t(a = # /%!tament! (!n "n m-n $ -$r #a acció! & #a (!%%ente e#,(t%(a* A
#$s ima!s c$mrcia#s s #s &a #a ,$rma m9s a&c(a&a a s( (s$ c$m$ ci#i!&r$s= %arras= %$t$!s= ci!tas= ar$s= &isc$s 5 #a c#9sica rra&(ra* Seg0n &" !%gen:
IANES NATURA8ES" s r,ir a mi!ra#s !at(ra#s= #$s c(a#s ti!! #a -r$-i&a& & atrar #m!t$s c$m$ # irr$= # !.(#= tc* 8a ma)!tita s (! im9! & st ti-$= c$m-(st$ -$r ó4i&$ ,rr$s$ ,3rric$= c(5a -artic(#ari&a& -ri!ci-a# c$!sist ! atrar ,ra)m!t$s & irr$ !at(ra#* IANES ARTIFICIA8ES" sta &!$mi!ació! rca s$%r a.(##$s c(r-$s ma)!3tic$s .(= tras ,ricci$!ar#$s c$! ma)!tita s tra!s,$rma! & ma!ra arti,icia# ! ima!s* Seg0n #a +e%'"%a()n 'e &"& +%!+e'a'e& magn,t(a&:
IANES TEPORA8ES" #$s ima!s tm-$ra#s st9! c$!,$rma&$s -$r irr$ &(#c 5 s caractri/a! -$r -$sr (!a atracció! ma)!3tica & c$rta &(ració!* M
IANES PERANENTES" c$! st t3rmi!$ s a#(& a a.(##$s ima!s c$!stit(i&$s -$r acr$= #$s c(a#s c$!sr'a! #a -r$-i&a& ma)!3tica -$r (! tim-$ -r&(ra%#* IANES CERICOS O FERRITAS* Esta c#as & ima!s ti! (! as-ct$ #is$ 5 c$#$r )ris9c$* S(#! sr & #$s m9s (ti#i/a&$s &%i&$ a s( ma#a%i#i&a&* A(!.(= -$r $tr$ #a&$= a# sr ,r9)i#s= c$rr! # ris)$ & r$m-rs c$! ,aci#i&a&* IANES DE A8NICO" # !$m%r &ri'a & (!a c$!tracció! & #as -a#a%ras" a#(mi!i$= !.(# 5 c$%a#t$= #m!t$s & #$s .( s c$m-$!* Esta c#as & ima!s -rs!ta! (! %(! c$m-$rtami!t$ ,r!t a #a -rs!cia & a#tas tm-rat(ras= si! m%ar)$= !$ c(!ta! c$! c$!si&ra%# ,(r/a* IANES DE TIERRAS RARAS" sta c#as & ima!s s s(%&i'i&! ! &$s cat)$ras & ac(r&$ a# matria# .(mic$ &# .( s c$m-$!" •
N$&imi$" st9! ,$rma&$s -$r irr$= !$&imi$ 5 %$r$* Prs!ta! (!a $4i&ació! ,9ci#= 5 s (ti#i/a! ! a.(##$s cas$s &$!& #as tm-rat(ras !$
•
a#ca!/a! #$s 0 C* Samari$ c$%a#t$" !$ s(#! $4i&ars & ma!ra ,9ci#= a(!.( # -rci$ a# .( c$ti/a! s m(5 #'a&$*
IANES F8E
P$r ta# m$ti'$= # -$#$ & #a %r7(#a .( s $ri!ta a-r$4ima&am!t acia # N$rt trrstr s &!$mi!a -$#$ N$rt 5 # $-(st$ c$!stit(5 # -$#$ S(r* Ta# &isti!ció! !tr -$#$s ma)!3tic$s s -(& 4t!&r a c(a#.(ir ti-$ & ima!s* 8as 4-ri!cias c$! ima!s -$!! & ma!i,ist$ .( +!#!& 'e# m&m! t+! &e %e+e#en * +!#!& 'e '&tnt! t+! &e at%aen.
Esta
caractrstica
&#
ma)!tism$ & #$s ima!s ,( 4-#ica&a -$r #$s a!ti)($s c$m$ #a c$!sc(!cia & (!a -r$-i&a& m9s )!ra# & #a !at(ra#/a c$!sist!t ! #$ .( ##$s ##amar$! #a atracció! & #$s $-(st$s Q*
Otra -r$-i&a& caractrstica &# c$m-$rtami!t$ & #$s ima!s c$!sist ! #a im-$si%i#i&a& & ais#ar s(s -$#$s ma)!3tic$s* As= si s c$rta (! im9! rct$ ! &$s mita&s s r-r$&(c! $tr$s &$s ima!s c$! s(s rs-cti'$s -$#$s !$rt 5 s(r* + #$ mism$ s(c&r9 si s r-it # -r$c&imi!t$ !('am!t c$! ca&a (!$ & ##$s* N$ s -$si%#= !t$!cs= $%t!r (! im9! c$! (! s$#$ -$#$ ma)!3tic$ sm7a!t a (! c(r-$ car)a&$ c$! #ctrici&a& & (! s$#$ si)!$*
ELECTROIMN
U! #ctr$im9! s (! ti-$ & im9! ! # .( # cam-$ ma)!3tic$ s -r$&(c m&ia!t # ,#(7$ & (!a c$rri!t #3ctrica= &sa-arci!&$ ! c(a!t$ csa &ica c$rri!t* 8$s #ctr$ima!s )!ra#m!t c$!sist! ! (! )ra! !mr$ & s-iras 11
m(5 -ró4imas !tr s & a#am%r .( cra! # cam-$ ma)!3tic$* 8as s-iras & a#am%r a m!(&$ s !r$##a! a#r&&$r & (! !c#$ ma)!3tic$ c$ & (! matria# ,rr$ma)!3tic$= c$m$ # irr$> # !c#$ ma)!3tic$ c$!c!tra # ,#(7$ ma)!3tic$ 5 ac (! im9! m9s -$t!t* 8a -ri!ci-a# '!ta7a & (! #ctr$im9! s$%r (! im9! -rma!!t s .( # cam-$ ma)!3tic$ s -(& cam%iar & ,$rma r9-i&a m&ia!t # c$!tr$# & #a ca!ti&a& & c$rri!t #3ctrica ! # &'a!a&$* Si! m%ar)$= a &i,r!cia & (! im9! -rma!!t .( !$ !csita & a#im!tació!= (! #ctr$im9! r.(ir (! s(mi!istr$ c$!ti!($ & c$rri!t -ara ma!t!r #$s cam-$s* A!ts & .( #a c$rri!t ! # #ctr$im9! s acti'a= #$s &$mi!i$s ! # !c#$ & irr$ st9! ! &ircci$!s a# a/ar= -$r #$ .( s(s cam-$s ma)!3tic$s -.($s s a!(#a! !tr s= 5 # irr$ a! !$ ti! (! cam-$ ma)!3tic$ & )ra! sca#a* C(a!&$ (!a c$rri!t -asa a tra'3s &# a#am%r !'(#t$ a#r&&$r & #a -#a!ca= s( cam-$ ma)!3tic$ -!tra ! # irr$= 5 ac .( #$s &$mi!i$s )ir!= a#i!9!&$s ! -ara##$ a# cam-$ ma)!3tic$= -$r #$ .( s(s cam-$s ma)!3tic$s &imi!(t$s s aa&! a# cam-$ &# a#am%r= cra!&$ (! cam-$ ma)!3tic$ .( s 4ti!& ! # s-aci$ a#r&&$r &# im9!* C(a!t$ ma5$r s #a c$rri!t .( -asa a tra'3s & #a %$%i!a & a#am%r= m9s &$mi!i$s s$! a#i!a&$s= a(m!ta!&$ #a i!t!si&a& &# cam-$ ma)!3tic$* Fi!a#m!t= t$&$s #$s &$mi!i$s star9! a#i!a&$s= !('$s a(m!t$s ! #a c$rri!t só#$ ca(sa! #i)r$s a(m!t$s ! # cam-$ ma)!3tic$" st ,!óm!$ s &!$mi!a sat(ració!* C(a!&$ #a c$rri!t ! #a %$%i!a st9 &sacti'a&a= #a ma5$ra & #$s &$mi!i$s -ir&! #a a#i!ació! 5 '(#'! a (! sta&$ a#at$ri$ 5 as &sa-arc # cam-$* E# ti-$ m9s sim-# & #ctr$im9! s (! tr$/$ & a#am%r !r$##a&$* U!a %$%i!a c$! ,$rma & t(%$ rct$ -arci&$ a (! t$r!i##$J s ##ama s$#!$i&= 5 c(a!&$ a&m9s s c(r'a & ,$rma .( #$s 4trm$s c$i!ci&a! s &!$mi!a t$r$i&* P(&! -r$&(cirs 12
cam-$s ma)!3tic$s m(c$ m9s ,(rts si s sita (! !c#$Q & matria# -arama)!3tic$ $ ,rr$ma)!3tic$ !$rma#m!t irr$ &(#c $ ,rrita= a(!.( tam%i3! s (ti#i/a # ##ama&$ acr$ #3ctric$J &!tr$ & #a %$%i!a* E# !c#$ c$!c!tra # cam-$ ma)!3tic$= .( -(& !t$!cs sr m(c$ m9s ,(rt .( # & #a -r$-ia %$%i!a* 8$s #ctr$ima!s s$! #$s c$m-$!!ts s!cia#s & m(c$s i!trr(-t$rs= si!&$ (sa&$s ! #$s ,r!$s 5 m%ra)(s #ctr$ma)!3tic$s & #$s a(t$mó'i#s* E! a#)(!$s tra!'as= #$s ,r!$s #ctr$ma)!3tic$s s a&ir! &irctam!t a #$s ri#s* S (sa! #ctr$ima!s m(5 -$t!ts ! )ras -ara #'a!tar -sa&$s %#$.(s & irr$ 5 acr$= 5 -ara s-arar ma)!3ticam!t mta#s ! catarrras 5 c!tr$s & rcic#a7* 8$s tr!s & #'itació! ma)!3tica (sa! -$&r$s$s #ctr$ima!s -ara ,#$tar si! t$car #a -ista* A#)(!$s tr!s (sa! ,(r/as atracti'as= mi!tras $tr$s m-#a! ,(r/as r-(#si'as* 8$s #ctr$ima!s s (sa! ! #$s m$t$rs #3ctric$s r$tat$ri$s -ara -r$&(cir (! cam-$ ma)!3tic$ r$tat$ri$ 5 ! #$s m$t$rs #i!a#s -ara -r$&(cir (! cam-$ ma)!3tic$ iti!ra!t .( im-(#s #a arma&(ra* A(!.( #a -#ata s # m7$r c$!&(ct$r & #a #ctrici&a&= # c$%r s (sa&$ m9s a m!(&$ &%i&$ a s( r#ati'$ %a7$ c$st$= 5 a 'cs s m-#a a#(mi!i$ -ara r&(cir # -s$*
CAMPO MAGNÉTICO
S ##ama cam-$ ma)!3tic$ a #a /$!a &# s-aci$ .( r$&a a# im9! &$!& st ma!i,ista s( acció! ma)!3tica* Es (! cam-$ & ,(r/as a &ista!cia .( s ac 'isi%# m&ia!t (! s-ctr$ ma)!3tic$ 5 ! # c(a# -(&! a-rciars !t$!cs #as #!as & ,(r/as*
1@
S ##ama e&+e(t%! magn,t(! a #a r-rs!tació! &# cam-$ & (! im9! .( s #$)ra )!ra#m!t s-arci!&$ irr$
s$%r
#ima&(ras (!a
,i!as
&
#9mi!a
!$
ma)!3tica c$#$ca&a s$%r # im9!*
S ##ama! #1nea& 'e /"e%2a &# cam-$ ma)!3tic$ a #a tra5ct$ria ima)i!aria .( s)(ira (! -$#$ !$rt ais#a&$ si s #$ #i%ra &!tr$ &# cam-$ ma)!3tic$* Estas #!as & ,(r/a s$! a-rcia%#s ! # s-ctr$ ma)!3tic$* U!a a)(7a ima!ta&a c$#$ca&a ! # cam-$ s $ri!tar9 ta!)!t a #a #!a & ,(r/a .( -asa -$r s #()ar* P$r c$!'!i$ s c$!si&ra !t$!cs .( (!a #!a & ,(r/a sa# &# -$#$ !$rt 5 s &iri) a# -$#$ s(r* S ##ama #!a $ /$!a !(tra# a #a #!a c!tra#= .(i&ista!t & am%$s -$#$s &$!& #a acció! ma)!3tica s m!ima* S ##ama manta()n $ ma)!ti/ació!= a# ,!óm!$ ! # .( (! c(r-$ s tra!s,$rma arti,icia#m!t ! (! im9!* Est -r$cs$ -(& -r$&(cirs -$r i!&(cció!= ,r$tami!t$ $ #ctr$ma)!tism$* S ##ama n'"(()n magn,t(a a# ,!óm!$ -$r # .( (! matria#= -$r # só#$ c$ & star i!mrs$ ! (! cam-$ ma)!3tic$= $ ! #as crca!as & (! im9!= s ma)!ti/a* S ##ama! /"e%2a& magn,t(a& a #as ,(r/as & atracció! $ & r-(#sió! !tr &$s ima!s* S ##ama ene%g1a magn,t(a a #a !r)a -$t!cia# $ ci!3tica .( ti! (! c(r-$ a# sr atra&$ $ m$'i&$ -$r #as ,(r/as ma)!3ticas* 1
H$5 s sa% .( #$s #ctr$!s -ri,3ric$s & #$s 9t$m$s r$ta! 5 )!ra! (! cam-$ ma)!3tic$ -r$-i$* Est cam-$ -(& star c$m-!sa&$ $ !$ -$r # & $tr$s #ctr$!s crca!$s= c(a!&$ !$ #$ st9= # 9t$m$ sr9 ma)!3tic$* Est$s 9t$m$s ti!&! a (!irs c$! $tr$s crca!$s ! #a misma $ri!tació! ma)!3tica* S ##ama '!mn! magn,t(! a st c$!7(!t$ & &i-$#$s atómic$s -rma!!ts $ri!ta&$s !
#a misma &ircció!* Est$s &$mi!i$s st9! )!ra#m!t &is-(st$s & ,$rma a#at$ria 5 -$r #$ ta!t$ # c(r-$ rs(#ta!t !$ s (! im9!= -r$ si s $r&!a! t$&$s c$! s(s -$#$s i)(a#s acia # mism$ #a&$= # c$!7(!t$ t!&r9 (!a -$#ari&a& marca&a 5 sr9 (! im9!* E! # cas$ & #$s ima!s !at(ra#s c$m$ #a ma)!tita= s !ti!& .( st$s &$mi!i$s s ,(r$! $ri!ta!&$ s)! # cam-$ ma)!3tic$ trrstr mi!tras #a #a'a '$#c9!ica $ri)i!aria s i%a s$#i&i,ica!&$* 8$s matria#s ,rr$ma)!3tic$s s$! #$s .( -rs!ta! &$mi!i$s ma)!3tic$s ,9ci#s & $r&!ar -$r acció! & (! cam-$ 4tr!$ 5 ! st$ c$!sist #a ima!tació! -$r i!&(cció!* E# ma)!tism$ i!&(ci&$= a(!.( &3%i#= s s(,ici!t i!t!s$ c$m$ -ara im-$!r a# ,ct$ ma)!3tic$* Para c$m-arar #$s trs ti-$s & ma)!tism$ s m-#a #a ra/ó! !tr # cam-$ ma)!3tic$ i!&(ci&$ 5 # i!&(ct$r* 8as c$rri!ts #3ctricas cra! cam-$ ma)!3tic$* A&m9s= 4ist! matria#s !at(ra#s $ si!t3tic$s .( cra! cam-$ ma)!3tic$* 8$s cam-$s cra&$s -$r #$s matria#s ma)!3tic$s s(r)! & &$s ,(!ts atómicas" #$s m$m!t$s a!)(#ars $r%ita#s 5 & s-! & #$s #ctr$!s= .( a# star ! m$'imi!t$ c$!ti!($ ! # matria# 4-rim!tas ,(r/as a!t (! cam-$ ma)!3tic$ a-#ica&$* P$r #$ ta!t$= #as caractrsticas ma)!3ticas & (! matria# -(&! cam%iar -$r a#ació! c$! $tr$s #m!t$s= &$!& s m$&i,ica! -$r #as i!tracci$!s atómicas* P$r 7m-#$= (! matria# !$ ma)!3tic$ c$m$ # a#(mi!i$ -(& c$m-$rtars c$m$ (! matria# ma)!3tic$ ! matria#s c$m$ a#!ic$ a#(mi!i$!.(#c$%a#t$J $ ma!)a!s$a#(mi!i$car%$!$* Tam%i3! -(& a&.(irir stas -r$-i&a&s m&ia!t tra%a7$ mc9!ic$ ( $tra ,(!t & t!si$!s .( m$&i,i.( #a )$mtra & #a r& crista#i!a*
1
8a 3&t,%e&& magn,t(a s #a t!&!cia & (! matria# a c$!sr'ar s(s -r$-i&a&s= -$r 7m-#$= si a# ma)!ti/ar (! ,rr$ma)!t$ 3st ma!ti! #a sa# ma)!3tica tras rtirar # cam-$ ma)!3tic$ .( #a a i!&(ci&$*
CURVAS DE MAGNETIZACION Para -$&r a-#icar #$s matria#s ,rr$ma)!3tic$s ! i!)!ira= s im-rsci!&i%# -$&r c(a!ti,icar s(s -r$-i&a&s ma)!3ticas* P$r a!a#$)a c$! #as -r$-i&a&s mc9!icas & #$s matria#s* N$s i!trsa ! cam%i$ c$!$cr #a rs-(sta ima!tació! 4citació! BH= & #a .( $%t!&rm$s #$s 'a#$rs & -rma%i#i&a& ma)!3tica &# matria# 5 $tr$s -ar9mtr$s & i!tr3s as$cia&$s
c$!
#a
c(r'a
&
3&t,%e&&
ma)!3tica* Para # tra/a&$ & #a c(r'a BH & ima!tació! s
-art
i!icia#m!t
&
(!a
-r$%ta
&sma)!ti/a&a &# matria# a !sa5ar= .( s c$#$ca ! # ma)!tómtr$* U!a '/ m$!ta&a s a-#ica! 4citaci$!s H crci!ts m&ia!t # i!crm!t$ & #a i!t!si&a& I .( circ(#a -$r (!a %$%i!a 4cita&$ra* E# i!crm!t$ $%sr'a&$ ! B s &% a .(= c$!,$rm H a(m!ta= #$s &$mi!i$s ma)!3tic$s= c(5$s m$m!t$s s !c(!tra! i!icia#m!t $ri!ta&$s ! &ircci$!s simi#ars 5 &# mism$ s!ti&$ .( H= crc! a 4-!sas & #$s m!$s ,a'$ra%#m!t $ri!ta&$s* Est crcimi!t$ ti! #()ar i!icia#m!t -$r # m$'imi!t$ & #as -ar&s &# &$mi!i$* Si H si)( a(m!ta&$ ti! #()ar ,i!a#m!t (!a r$tació! & #$s &$mi!i$s !$ $ri!ta&$s ,a'$ra%#m!t= asta .( t$&$s ##$s s c$#$ca! -ara##$s a H 5 c$! #a misma &ircció! & s(s m$m!t$s ma)!3tic$s* C(a!&$ st$ $c(rr= s m94ima" t$&$s #$s &i-$#$s -$si%#s &# matria# st9! c$!tri%(5!&$ a #a ma)!ti/ació!* 16
A(!.( H si)a a(m!ta!&$= B s$#$ crcr9 &%i&$ a #a -rma%i#i&a& &# 'ac$ 0* S &ic .( # matria# st9 sat(ra&$ 5 a# 'a#$r m94im$ & i!&(cció! Bs= caractrstic$ & ca&a matria#= s &!$mi!a i!&(cció! & sat(ració! Bs* Nóts .( ! #$s matria#s ,rr$ma)!3tic$s= #a -rma%i#i&a& !$ -rs!ta (! 'a#$r c$!sta!t= si!$ .( 'ara c$!,$rm a(m!ta #a 4citació! H a-#ica&a=
MOMENTO MAGN&TICO E# m!ment! magn,t(! & (! im9! s (!a ca!ti&a& .( &trmi!a #a ,(r/a .( # im9! -(& 7rcr s$%r #as c$rri!ts #3ctricas 5 # -ar .( (! cam-$ ma)!3tic$ 7rc s$%r ##as * C(a!&$ (!a car)a #3ctrica -$r 7m-#$ (! #ctró!J $ (! )r(-$ & car)as #3ctricas m(c$s #ctr$!sJ si)( (!a tra5ct$ria & cami!$ crra&$ -$r 7m-#$ (! circ(#$J> s # -(& asi)!ar a s( m$'imi!t$ (! 'ct$r ##ama&$ m$m!t$ ma)!3tic$ # c(a# s -r$-$rci$!a# a# 9ra !crra&a -$r #a tra5ct$ria 5 a #a '#$ci&a& c$! #a c(a# s m('a &ica car)a* U! %(c# & c$rri!t #3ctrica= (! im9! & %arra= (! #ctró!= (!a m$#3c(#a 5 (! -#a!ta= t$&$s ti!! m$m!t$s ma)!3tic$s* Ta!t$ # m$m!t$ ma)!3tic$ c$m$ # cam-$ ma)!3tic$ -(&! sr c$!si&ra&$s c$m$ 'ct$rs c$! (!a ma)!it(& 5 &ircció!* 8a &ircció! &# m$m!t$ ma)!3tic$ a-(!ta &# -$#$ s(r a# -$#$ !$rt &# im9!* E# cam-$ ma)!3tic$ -r$&(ci&$ -$r (! im9! s -r$-$rci$!a# a s( m$m!t$ ma)!3tic$* 9s -rcisam!t= # t3rmi!$ m$m!t$ ma)!3tic$ s r,ir !$rma#m!t a# m$m!t$ &i-$#ar ma)!3tic$ & (! sistma= .( -r$&(c # -rimr t3rmi!$ ! #a 4-a!sió! m(#ti-$#ar & (! cam-$ ma)!3tic$ ! )!ra#* E# &i-$#$ .( c$m-$! # cam-$ ma)!3tic$ & (! $%7t$ s sim3tric$ rs-ct$ a #a &ircció! & s( m$m!t$ &i-$#ar ma)!3tic$= 5 &ismi!(5 c$! #a i!'rsa &# c(%$ & #a &ista!cia &# $%7t$*
1K
E! -rs!cia & (! cam-$ ma)!3tic$ i!r!tm!t 'ct$ria#J= # m$m!t$ ma)!3tic$ s r#aci$!a c$! # m$m!t$ & ,(r/a & a#i!ació! & am%$s 'ct$rs ! # -(!t$ ! # .( s sita # #m!t$* E# cam-$ ma)!3tic$ s # B= &!$mi!a&$ i!&(cció! ma)!3tica $ &!si&a& & ,#(7$ ma)!3tic$* Si s sita (!a %arra & matria# &iama)!3tic$ ! # i!tri$r & (! cam-$ ma)!3tic$ (!i,$rm i!t!s$= sta s &is-$! tra!s'rsa#m!t rs-ct$ & a.(#*
MOMENTO MAGNÉTICO ATÓMICO
E! #$s matria#s &iama)!3tic$s= #a &is-$sició! & #$s #ctr$!s & ca&a 9t$m$ s ta#= .( s -r$&(c (!a a!(#ació! )#$%a# & #$s ,ct$s ma)!3tic$s* Si! m%ar)$= si # matria# s i!tr$&(c ! (! cam-$ i!&(ci&$= #a s(sta!cia a&.(ir (!a ima!tació! &3%i# 5 ! # s!ti&$ $-(st$ a# cam-$ i!&(ct$r*
8$s matria#s -arama)!3tic$s !$ -rs!ta! #a a!(#ació! )#$%a# & ,ct$s ma)!3tic$s= -$r #$ .( ca&a 9t$m$ .( #$s c$!stit(5 acta c$m$ (! -.($ im9!* Si! m%ar)$= #a $ri!tació! & &ic$s ima!s s= ! )!ra#= ar%itraria= 5 # ,ct$ )#$%a# s a!(#a* Asimism$= si # matria# -arama)!3tic$ s s$mt a #a acció! & (! cam-$ ma)!3tic$ i!&(ct$r= # cam-$ ma)!3tic$ i!&(ci&$ ! &ica s(sta!cia s $ri!ta ! # s!ti&$ &# cam-$ ma)!3tic$ i!&(ct$r* 8$s #ctr$!s 5 m(c$s !c#$s atómic$s tam%i3! ti!! m$m!t$s ma)!3tic$s i!tr!sc$s= c(5a 4-#icació! r.(ira tratami!t$ mca!$c(9!tic$ 5 .( s r#aci$!a .( # m$m!t$ a!)(#ar & #as -artc(#as* S$! st$s m$m!t$s ma)!3tic$s i!tr!sc$s 1
#$s .( &a! #()ar a ,ct$s macr$scó-ic$s & ma)!tism$= 5 a $tr$s ,!óm!$s c$m$ #a rs$!a!cia ma)!3tica !(c#ar*
8$s #ctr$!s a# )irar ! s(s ór%itas -r$&(c! (! cam-$ ma)!3tic$ sm7a!t a# & (! im9!= c$m$ sa%m$s -$r #a t$ra #ctr$ma)!3tica* As= &s& # -(!t$ & 'ista & s(s -r$-i&a&s ma)!3ticas= #$s matria#s st9! ,$rma&$s -$r -.($s ima!s .(= si # matria# !$ ma!i,ista ma)!ti/ació!= !csariam!t st9! $ri!ta&$s a# a/ar* C(a!&$ s s$mt (! matria# a #a acció! & (! cam-$ ma)!3tic$= -(&! &ars &$s mca!ism$s*
E! # -rimr$ #$s ima!s sim-#m!t s a#i!a! ! #a &ircció! &# cam-$ a-#ica&$= c$m$ #as %r7(#as ! #a Tirra* Est ,ct$ s ##ama -arama)!tism$ 5 st a#i!ami!t$ -r$&(c (!a rs(#ta!t ! #a misma &ircció! &# cam-$= &a!&$ c$m$ rs(#ta&$ .( # matria# s c$m-$rt c$m$ (! im9! .( s atra&$ ! # s!ti&$ & s cam-$* E! # s)(!&$ mca!ism$= ##ama&$ &iama)!tism$= # matria# tam%i3! s c$m-$rta c$m$ (! im9!= -r$ .( s $-$! a# cam-$ .( #$ -r$&(c= si!&$ r-#i&$ -$r 3st* A.( # cam-$ 4tr!$ $%#i)a a #$s ima!s atómic$s a -r$csar ! #a &ircció! &# cam-$= )!ra!&$ (! m$m!t$ ma)!3tic$* Tam%i3! -$&m$s a$ra !t!&r # ,ct$ & #a tm-rat(ra ! #$s ,!óm!$s ma)!3tic$s= 5a .( #$s 9t$m$s st9! tam%i3! s(7t$s a m$'imi!t$s t3rmic$s .( s $-$!! a .( s a#i!! ! (!a cirta &ircció!*
1M
E!t!&r # ,rr$ma)!tism$ s m9s &i,ci#* Est$s matria#s -rs!ta! -$rci$!s .( ti!! ma)!ti/ació! c$m-#ta 5 -rma!!t 5 s ##ama! &$mi!i$s ,rr$ma)!3tic$s* F( Pirr iss ! 1M0K .(i! s &i$ c(!ta & .( #$s matria#s ,rr$ma)!3tic$s st9! ,$rma&$s -$r st$s &$mi!i$s= #$s c(a#s -(&! i!c#(si' $ri!tars & ta# ma!ra .( # matria# !$ 4i%a -r$-i&a&s ma)!3ticas*
C$! (! cam-$ ma)!3tic$ 4tr!$ #$s &$mi!i$s s -(&! r$ri!tar $ crcr asta ,$rmar (! im9!* Est -r$cs$ & ma)!ti/ació! s irr'rsi%#* Para 4-#icar #a 4ist!cia & #$s &$mi!i$s tam%i3! s -(& -!sar ! t3rmi!$s & -.($s ima!s= -r$ .( st9! ,$rma&$s -$r #$s -r$-i$s #ctr$!s= #$s c(a#s -$s! (! m$'imi!t$ ma)!3tic$ i!tr!sc$ ##ama&$ s-!* 8a acció! c$!7(!ta & #$s s-i!s &!tr$ & (! &$mi!i$ $%&c a #a ,(r/a & i!trcam%i$ .( s & !at(ra#/a c(9!tica 5 !$ ti! a!9#$)$ ! #a ,sica c#9sica*
APLICACIONES DE LOS IMANES
8$s ima!s ti!! m#ti-#s a-#icaci$!s c$m$ -$r 7m-#$ ! #a ,a%ricació! & %r7(#as 5 & a-arat$s #3ctric$s GA8VANOETROS= APERIETROS= VO8TIETROS= CONTADORES= AGNETOS= tc*J* 8$s ima!s -rma!!ts s m-#a! ! a#t$-ar#a!ts= i!str(m!t$s -ara m&ici$!s #3ctricas= tc* 8$s cam-$s ma)!3tic$s s m-#a! -ara c$!tr$#ar #as tra5ct$rias & -artc(#as car)a&as ! &is-$siti'$s c$m$ #$s ac#ra&$rs & -artc(#as $ #$s s-ctró)ra,$s & masas* 8$s m$t$rs #3ctric$s 5 #$ )!ra&$rs & #ctrici&a&* 20
E! #$s #tim$s 100 a$s a! s(r)i&$ !(mr$sas a-#icaci$!s &# ma)!tism$ 5 & #$s matria#s ma)!3tic$s* P$r 7m-#$" 8$s #ctr$ima!s #a %as &# m$t$r #3ctric$ 5 # tra!s,$rma&$r* 9s rci!tm!t s (ti#i/a -ara # &sarr$##$ & !('$s matria#s ma)!3tic$s a i!,#(i&$ !$ta%#m!t
!
#a
r'$#(ció!
&
#$s
$r&!a&$rs $ c$m-(ta&$ras* Es
-$si%# ,a%ricar
c$m-(ta&$ra %(r%(7a*
mm$rias
(ti#i/a!&$ :Est$s
&
&$mi!i$s
&$mi!i$s
s$!
-.(as r)i$!s & ma)!ti/ació!= -ara##as
$
a!ti-ara##as
a
#a
ma)!ti/ació! )#$%a# &# matria#; 5 :#a %(r%(7a i!&ica (! (!$ $ (! cr$= -$r #$ .( acta c$m$ &)it$ ! # sistma %i!ari$ m-#a&$ -$r #$s $r&!a&$rs;* 8$s matria#s ma)!3tic$s tam%i3! s$! c$m-$!!ts im-$rta!ts & #as ci!tas 5 &isc$s -ara a#mac!ar &at$s* U! 7m-#$ & a#ta tc!$#$)a m$&r!a s #$s tr!s & #'itació! ma)!3tica #$s c(a#s (ti#i/a! -$&r$s$s ima!s -ara #'ars -$r !cima & #$s ra#s 5 'itar # r$/ami!t$* E! #a 4-#$ració! m&ia!t rs$!a!cia ma)!3tica !(c#ar= (!a im-$rta!t rrami!ta & &ia)!óstic$ m-#a&a ! m&ici!a= s (ti#i/a! cam-$s ma)!3tic$s & )ra! i!t!si&a&* 8$s ima!s s(-rc$!&(ct$rs s m-#a! ! #$s ac#ra&$rs & -artc(#as m9s -$t!ts -ara ma!t!r #as -artc(#as ac#ra&as ! (!a tra5ct$ria c(r'a 5 !,$car#as* 8$s ima!s )ra!&s 5 -$t!ts s$! cr(cia#s ! m(cas tc!$#$)as m$&r!as* 8$s ima!s s(-rc$!&(ct$rs s m-#a! ! #$s ac#ra&$rs & -artc(#as 21
m9s -$t!ts -ara ma!t!r #as -artc(#as ac#ra&as ! (!a tra5ct$ria c(r'a 5 !,$car#as*
BIBLIOGRAFÍ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
22