Campo Magnético de Un Solenoide

 

Kfhn`nðl hfg @ckpe Kcilîtn`e hf ulc Bebnlc Pegflenhf R.H. Qfrc 3, D.P. Zfrheke @cn`fhe0  Aulhckfltes hf Fgf`trn`nhch y Kcilftnske, Hfpte. Hf Nliflnfrëc, Vlnvfrsnhch Lc`nelcg hf @egekbnc,  Beietã  Flfre 3> hf 2:2 2:2: :

Rfsukfl Fl fstf gcbercterne sf knhnð gc g c kcilntuh hfg `ckpe kcilîtn`e prehu`nhe per ulc bebnlc segflenhf kfhncltf gc hftfrknlc`nðl hf gc `errnfltf quf `nr`ugc per fggc. Xckbnîl sf hftfrknlð gc aufrzc hfg `ckpe kcilîtn`e oc`nflhe use hf ul cgckbrf `elhu`ter (Fspnrc).

Nltrehu``nðl  Fg `ckpe kcilîtn`e ‗B‛ fs ulc kcilntuh vf`terncg vf`terncg quf p ufhf fstcr prehu`nhe per ulc `cric pultucg fl kevnknflte e per ul `eldulte hf `crics fl kevnknflte, fs hf`nr, per ulc `errnfltf fgî`trn`c. Fg `ckpe kcilîtn`e sf knhf fl Xfsgcs ‗X‛, ul tfsgc sf hfanlf `eke fg `ckpe kcilîtn`e quf fdfr`f ulc aufrzc hf 3 L (lfwtel) sebrf ulc `cric hf 3 @ (`ugekbne) quf sf kufvf c vfge`nhch hf 3 k/s hfltre hfg `ckpe y pfrpflhn`ugcrkfltf c gcs gëlfcs hf `ckpe. @uclhe ulc `cric q  sf kufvf c

`nfrtc vfge`nhch, `rfc ul `ckpe kcilîtn`e fl tehe fg fspc`ne, hn`oe `ckpe vnflf hche per gc Gfy Bnet-Pcvcrt quf rfgc`nelc ges `ckpes kcilîtn`es `el gcs `errnfltfs quf ges `rfcl y sf fs`rnbf hf fstc kclfrc4 ⃙  ⃙  ⃙ ; ¶    (3)    

Helhf   fs gc `cric ⃙ fs gc vfge`nhch hf hn`oc `cric   fs gc hnstcl`nc hfshf fg pulte helhf sf fl`ufltrc gc `cric ocstc fg pulte helhf sf fstã `cg`ugclhe fg `ckpe⃙  fs ul vf`ter ulntcrne quf vc hfshf fg pulte helhf sf fl`ufltrc gc `cric oc`nc fg pulte helhf sf `cg`ugc fg `ckpe ¶  fs ulc `elstcltf hfleknlchc pfrkfcbngnhch hfg fspc`ne gnbrf. Zer etrc pcrtf sn sf vc c rfcgnzcr gc kfhn`nðl hfg `ckpe kcilîtn`e `el fg use hf ulc bcgclzc hf brczes niucgfs (Fspnrc) quf pesff ul trcke hf cgckbrf `elhu`ter hf gelintuh G, sf pufhf hftfrknlcr gc aufrzc quf fdfr`f fg `ckpe kcilîtn`e sebrf fstf, tflnflhe fl `ufltc quf gc `errnfltf `errn fltf N  hfbf fxprfscrsf fl Ckpfrnes, gc gelintuh G hfg cgckbrf fl kftres, gc nltflsnhch hfg `ckpe kcilîtn`e B fl (Lfwtel/Ckpfrne Ù kftre). @el ge cltfrner, gc fxprfsnðl quf vc c hftfrknlcr fg `ekpertcknflte hf gc aufrzc A sebrf fg cgckbrf fstã hchc per4

 ;    (2)  Helhf fg cgckbrf tnflf quf sfr snfkprf pfrpflhn`ugcr c gc hnrf``nðl hfg `ckpe, hf kehe quf fg `ckpe B, pufhf hftfrknlcrsf `el gc fxprfsnðl4 fx prfsnðl4

 ;  /  (0) 

 

Xcbgcs   Nln`ncgkfltf sf hftfrknlð gc aufrzc sebrf ul cgckbrf e Fspnrc hf gelintuh G ( G ; :,:2? k) usclhe ulc bcgclzc, fg brcze hf gc bcgclzc sf nltrehude fl fg nltfrner hf gc bebnlc hf tcg kclfrc quf gc Fspnrc qufhe pfrpflhn`ugcr cg `ckpe kcilîtn`e iflfrche cg nltfrner hf gc bebnlc. Zcrc kfhnr gc aufrzc sebrf gc Fspnrc, sf fqungnbrð gc bcgclzc `ege`clhe trezes hf onge `el ulc gelintuh hf 2: ³ :,2 `k. Xflnflhe fl `ufltc gc hflsnhch  σ hfg onge ( σ ; 0: ki/k ; 0Ù3: -9 Mi/`k) y fg vcger hf gc ircvfhch (>,? k/s2) sf ebtuve fg pfse e aufrzc lf`fscrnc pcrc fqungnbrcr gc bcgclzc. @el ge cltfrner sf puhe `cg`ugcr gc Aufrzc quf hfagf`tc oc`nc crrnbc fg fxtrfke hf gc bcgclzc y oc`nflhe use hf gc aerkugc (0)  auf pesnbgf `cg`ugcr fg `ckpe kcilîtn`e pcrc `chc ulc hf gcs `errnfltfs. Fstes hctes sf rfinstrcrel fl gc Xcbgc 3, helhf sf kcltuve gc `errnfltf hf gc bebnlc `elstcltf (8 ³ :,3 C) knfltrcs quf sf vcrncrel ges vcgerfs hf gc `errnfltf hf gc Fspnrc.

Xcbgc 3. Kfhn`nðl hf gc Aufrzc aul`nðl hf gc `errnfltf hf gc Fspnrc cpgn`clhe ulc `errnfltf hf 8 C sebrf gc Bebnlc.

Zestfrner c fste, sf rfcgnzð fg knske pre`fhnknflte pfre `el vcgerfs hnafrfltfs pcrc gc `errnfltf hf gc bebnlc, helhf sf gf puse `errnfltfs hf 0C y 2C, ges hctes ebtflnhes sf kufstrcl fl gc Xcbgc 2 y Xcbgc 0.

Xcbgc 2. Kfhn`nðl hf gc Aufrzc aul`nðl hf gc `errnfltf hf gc Fspnrc cpgn`clhe ulc `errnfltf hf 0 C sebrf gc Bebnlc.

 

Xcbgc 0. Kfhn`nðl hf gc Aufrzc aul`nðl hf gc `errnfltf hf gc Fspnrc cpgn`clhe ulc `errnfltf hf 2 C sebrf gc Bebnlc.

Irãan`cs @el ges hcres cltfrnerfs sf rfcgnzð gc irãan`c hf aufrzc fl aul`nðl hf gc `errnfltf hf gc Fspnrc pcrc `chc ule hf ges hnafrfltfs vegtcdfs quf sf gf cpgn`crel c gc bebnlc.

 

Xflnflhe fl `ucltc gcs irãan`cs cltfrnerfs y gc f`uc`nðl (2) pehfkes hf`nr quf gc pflhnfltf k  hf `chc ulc hf gcs irãan`cs rfprfsfltc fg prehu`te fltrf fg `ckpe kcilîtn`e B y gc gelintuh hf gc  Fspnrc G,  ‗

‛

 ;    ;     Hf kehe quf pehfkes `cg`ugcr gc kcilntuh hfg `ckpe kcilîtn`e yc quf `ele`fkes fg vcger cprexnkche hf gc pflhnfltf k hf gcs irãan`cs y gc gelintuh G hf gc Fspnrc (G ; :,:2? k).

 ;    ;

   

Hclhe ges rfsugtches kestrches fl gc Xcbgc 8 helhf sf kufstrc ul vcger cprexnkche cg vcger hfg `ckpe kcilîtn`e.

Xcbgc 8. Kfhn`nðl hfg `ckpe Kcilîtn`e c pcrtnr hfg vcger hf gc pflhnfltf hf gcs Irãan`cs hf Aufrzc vs @errnfltf (Fspnrc).

Hfspuîs sf vcrnð gc `errnfltf hf gc bebnlc y sf kcltuve `elstcltf gc `errnfltf hf gc Fspnrc (3,6 C) hf kclfrc quf sf ebtuvnfrel ges hcres kestrches fl gc Xcbgc 6.

Xcbgc 6. Kfhn`nðl hf gc Aufrzc aul`nðl hf gc `errnfltf hf gc Bebnlc cpgn`clhe ulc `errnfltf hf 3,6 C sebrf gc Fspnrc.

C pcrtnr hf fstes hctes sf rfcgnzð gc sniunfltf irãan`c hf gc Aufrzc fl aul`nðl hf gc `errnfltf hf gc Bebnlc.

 

C pcrtnr hf gc irãan`c cltfrner, sf rfcgnzc fg knske pre`fhnknflte cltfs fdf`utche pcrc `cg`ugcr fg `ckpe kcilîtn`e B, tflnflhe fl `ufltc quf gc gelintuh G hf gc Bebnlc les hne ul vcger cprexnkche hf G ; :,38 k, y quf gc pflhnfltf k hf gc irãan`c hf Aufrzc vs @errnfltf (Bebnlc) les hne ul vcger hf k ; :,:::3.

 Ù  ;  ; :,:::3  ;



; :,:::9382?1 X



@el ges hctes `elsnilches fl gc Xcbgc 6 sf puhe rfcgnzcr gc irãan`c hfg vcger hfg `ckpe kcilîtn`e fl aul`nðl hf gc `errnfltf hf gc Bebnlc.

Zer ôgtnke, sf `cg`ugð fg vcger tfðrn`e hfg `ckpe kcilîtn`e oc`nflhe use hf gc aerkugc (8) 

 ; ɰ   (8) Helhf  fs gc `elstcltf hf pfrkfcbngnhch pfrk fcbngnhch kcilîtn`c hfg vc`ëe quf tnflf ul vcger hf 8  Ù 3 :− , N fs gc `errnfltf y helhf ɰ     sf `cg`ugc hf fstc kclfrc4

ɰ;

 ?: ; ; 693,8 693,82> 2>   :,38

Helhf L fs fg lôkfre hf fspnrcs y G fs gc gelintuh hf gc fspnrc. Rfcgnzclhe ges rfspf`tnves `ãg`uges sf ebtuve ges sniunfltfs rfsugtches.

Xcbgc 1  . @ekpcrc`nðl hfg @ckpe Kcilîtn`e tfðrn`e y fg @ckpe Kcilîtn`e fxpfrnkfltcg.

   

 

@el`gusnelfs Gc kfhn`nðl hfg `ckpe kcilîtn`e hf ulc bebnlc segflenhf sf pufhf hftfrknlcr kfhncltf gc `errnfltf quf `nr`ugc per fggc, y oc`nflhe use hf ulc bcgclzc e Fspnrc. Fg `ckpe kcilîtn`e les hne hf kclfrc fxpfrnkfltcg :,:23, :,::2?  y :,::01 pcrc 2, 0 y 8 Ckpfrnes rfspf`tnvckfltf `el ul frrer kãxnke hfg 81%. Fstf frrer sf hfbf c quf gc bcgclzc tnflf ulc sflsnbngnhch bcstcltf cgtc rf`nbnflhe `errnfltf, tckbnîl sf hfbf cg frrer hche per fg pfse hfg Onge, yc quf le auf ulc kfhnhc hnrf`tc y tnflf ul frrer `elsnhfrcbgf. Pn sf `elsnhfrcl fstes cspf`te c gc oerc hf rfcgnzcr fg fxpfrnkfltf lufvckfltf, sf pufhf rfhu`nr fg frrer fxpfrnkfltcg.

  Rfcgnzclhe µZehrëc uscr fstc bcgclzc pcrc kfhnr fg `ckpe kcilîtn`e tfrrfstrf (hf vcger

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cprexnkchckfltf 0,2 Ù 3:−6  X)5 Xflnflhe fl `ufltc gc sflsnbngnhch hf gc bcgclzc quf ebsfrvð, `cg`ugf fg erhfl hf kcilntuh hf gc `errnfltf quf hfbfrëc `nr`ugcr per gc fspnrc fl fstf `cse. Fxpgnquf. Gc bcgclzc le sf pehrëc fkpgfcr pcrc rfcgnzcr fg `ãg`uge hfg `ckpe kcilîtn`e tfrrfstrf yc quf pcrc pehfr hftfrknlcr fg ãliuge hf hfagfxnðl sf tflhrëcl quf uscr `errnfltfs kuy cgtcs pcrc pehfr oc`fr ul clãgnsns hf supfrpesn`nðl hf `ckpes, hche c gc sflsnbngnhch hf gc bcgclzc.

  µPf pufhf uscr ulc fspnrc hf onfrre fl gc bcgclzc5

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Le sf pufhf uscr ulc fspnrc of`oc hf fstf kctfrncg yc quf fg onfrre fs ul kctfrncg afrrekcilîtn`e y cg sekftfrge c ul `ckpe kcilîtn`e nltflse, ges heknlnes tnflhfl c cgnlfcrsf `el fg `ckpe kcilîtn`e y cg fgnknlcr fstf, fg heknlne pfrkclf`f hurcltf `nfrte tnfkpe= chn`nelcg c fste ges kctfrncgfs afrrekcilîtn`es pesffl ul c pfrkfcbngnhch kuy cgtc quf caf`tcrëc gc `ekpcrc`nðl hf `ckpes kcilîtn`es.

  µZufhf uscr gc bcgclzc pcrc kfhnr fg `ckpe kcilîtn`e prehu`nhe per ul pfqufóe nkãl

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pfrkclfltf5 Zcrc rfcgnzcr gc kfhn`nðl hfg `ckpe `ckpe kcilîtn`e hf ul nkãl, sf tnflf quf tflfr tflfr fl `ufltc gc aufrzc quf fstf pufhc iflfrcr, hche quf fg `ckpe kcilîtn`e iflfrche per fg nkãl pufhf sfr niucg e kãs cgte quf fg `ckpe kcilîtn`e iflfrche per gc bebnlc.

Rfafrfl`ncs  Dfwf tt, D (2::>) Aësn`c pcrc `nfl`ncs f nliflnfrëc, n liflnfrëc, Qegukfl 2. @flicif Gfcrlnli ]3[ Pfrwcy, R= Dfwftt, Fhnterfs P.C. @cpëtuge 0:. ]2[ Xnpgfr, Z. C. (2:::) Aësn`c pcrc gc @nfl`nc y gc Xf`legeiëc. Rfvfrtî P.C. Pfiulhc fhn`nðl. ]0[ 

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