MAGNETIC EFFECT OF CURRENT

Transcription

1 J-hyscs NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65 The bnch of physcs whch dels wth the gnets due to electc cuent o ovng chge (.e. electc cuent s equvlent to the chges o electons n oton) s clled electognets. OSTD' S DSCOVY The elton between electcty nd gnets ws dscoveed by Oested n 8. Oested showed tht the electc cuent though the conductng we deflects the gnetc needle held below the we. When the decton of cuent n conducto s evesed then deflecton of gnetc needle s lso evesed On ncesng the cuent n conducto o bngng the needle close to the conducto the deflecton of gnetc needle nceses. Oested dscoveed gnetc feld ound conducto cyng electc cuent. Othe elted fcts e s follows: () (b) (c) (d) (e) A gnet t est poduces gnetc feld ound t whle n electc chge t est poduce n electc feld ound t. A cuent cyng conducto hs gnetc feld nd not n electc feld ound t. On the othe hnd, chge ovng wth unfo velocty hs n electc s well s gnetc feld ound t. An electc feld cnnot be poduced wthout chge whees gnetc feld cn be poduced wthout gnet. No poles e poduced n col cyng cuent but such col shows noth nd south poltes. All osclltng o n cceleted chge poduces.m. wves lso n ddtons to electc nd gnetc felds. S S + N N Noth N Oested's epeent. Cuent n the we deflects the copss needle Cuent leent d A vey sll eleent b of length d of thn conducto cyng cuent clled cuent eleent. Cuent eleent s vecto quntty whose gntude s equl to the poduct of cuent nd length of sll eleent hvng the decton of the flow of cuent. ot Svt' s Lw d b d Wth the help of epeentl esults, ot nd Svt ved t thetcl epesson tht gves the gnetc feld t soe pont n spce n tes of the cuent tht poduces the feld. Tht epesson s bsed on the followng epeentl obsevtons fo the gnetc feld d t pont ssocted wth length eleent d of we cyng stedy cuent. d sn d, d d, d snnd d d Vecto fo of ot- Sv t' s lw d sn d nˆ 4 d d 3 4 MAGNTC FFCT OF CUNT d dsn 4 n unt vecto pependcul to the plne of ( d ) nd ( ) [ d (d) ()sn ˆn ]

2 J-hyscs Accodng to d d 3 4 GOLDN KY ONTS, decton of gnetc feld vecto (d) vectos d nd ( ), whee plne of d nd ( ) s the plne of we. Mgnetc feld on the s of cuent cyng conducto s lwys zeo ( o 8 ) Mgnetc feld on the peete of ccul loop o col s lwys nu. s lwys pependcul to the plne of MAGNTC FLD LNS (y Mchl Fdy) n ode to vsulse gnetc feld gphclly, Mchl fdy ntoduced the concept of feld lnes. Feld lnes of gnetc feld e gny lnes whch epesents decton of gnetc feld contnuously. GOLDN KY ONTS Mgnetc feld lnes e closed cuves. Tngent dwn t ny pont on feld lne epesents decton of the feld t tht pont. Feld lnes neve ntesects to ech othe. At ny plce cowded lnes epesent stonge feld whle dstnt lnes epesents weke feld. n ny egon, f feld lnes e equdstnt nd stght the feld s unfo othewse not. Non-unfo Feld Unfo Feld Mgntude s not constnt Decton s not constnt oth gntude nd decton e not constnt oth gntude nd decton e constnt Mgnetc feld lnes ente fo o entes n the sufce of gnetc tel t ny ngle. Mgnetc feld lnes est nsde evey gnetsed tel. Mgnetc feld lnes cn be pped by usng on dust o usng copss needle. GHT HAND THUM UL Ths ule gves the ptten of gnetc feld lnes due to cuent cyng we. () Stght cuent () Ccul cuent Thub n the decton of cuent Culng fnges Gves feld lne ptten Cse : we n the plne of the ppe Mgnetc feld lnes Culng fnges n the decton of cuent, Thub Gves feld lne ptten Cse : we n the plne of the ppe ACW Towds obseve o pependcul out-wds CW Awy fo the obseve o pependcul nwds NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65

3 J-hyscs Cse : We s to the plne of the ppe. Cse : We s to the plne of the ppe ACW CW S N N S ACW concentc & ccul feld lnes CW concentc & ccul feld lnes Towds obseve Awy fo the obseve GOLDN KY ONTS When cuent s stght, feld s ccul When cuent s ccul, feld s stght (long s) When we s n the plne of ppe, the feld s pependcul to the plne of the ppe. When we s pependcul to the plne of ppe, the feld s n the plne of the ppe. ALCATON OF OT- SAVAT LAW : A Mgnet c f eld suound ng thn stght cuent cyng conducto A s stght conducto cyng cuent fo to A. At pont, whose pependcul dstnce fo A s O, the decton of feld s pependcul to the plne of ppe, nwds (epesented by coss) tn dl sec d...() d O 9 & sec y ot- Svt s lw d sn d (due to cuent eleent d t pont ) 4 d d sn 4 (due to we A) cos d 4 Tkng lts of ntegton s to NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65 cos d sn sn sn 4 (nwds) 4 4 Mgnetc feld due to nfnte length we t pont '' [sn9 + sn9 ] 4 d M 9 d d

4 J-hyscs Mgnetc feld due to se nfnte length we t pont '' Sol. 4 d [sn + sn9 ] M 9 9 [sn + ] 4 d L d Mgnetc feld due to specl se nfnte length we t pont '' 4 d [sn + sn9 ] 4d M 9 9 d N Mgnetc feld due to specl fnte length we t pont '' 9 M d 4 d [sn + sn] ; 4d sn f pont les out sde the lne of we then gnetc feld t pont : d sn 9 sn 9 (cos cos ) 4d 4d 4 NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65

5 J-hyscs Mgnetc f eld due to loop of cuent Mgnetc feld lnes due to loop of we e shown n the fgue The decton of gnetc feld on the s of cuent loop cn be detened by ght hnd thub ule. f fnges of ght hnd e culed n the decton of cuent, the stetched thub s n the decton of gnetc feld. Clcult on of gnetc feld z-s Consde cuent loop plced n y-z plne cyng cuent n ntclockwse sense s seen fo postve -s. Due to sll cuent eleent d shown n the fgue, the gnetc feld t s gven by d d sn 9 4. The ngle between d nd s 9 becuse d s long y- s, whle les n -z plne. The decton of d s pependcul d O + d y-s -s to s shown. The vecto d cn be esolved nto two coponents, d cos long z-s nd d sn long -s. Fo ny two detclly opposte cuent eleents, the coponents long -s dd up, whle the othe two coponents cncel out. Theefoe, the feld t s due to -coponent of feld only. Hence, we hve NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65 d sn 3 4 d sn 4 4 d 4 3 / () At the cente,, cente 5 4 (b) At ponts vey close to cente, << (c) At ponts f off fo the cente, >> (d) The esult n pont (c) s lso epessed s 4 whee M d 3 d 3 / 3 4, s clled gnetc dpole oent. M 3 3 z-s dcos d dsn -s

6 J-hyscs Fnd the gnetc feld t the cente of cuent cyng conducto bent n the fo of n c subtendng ngle t ts cente. dus of the c s. Let the c le n -y plne wth ts cente t the ogn. Consde sll cuent eleent d s shown. The feld due to ths eleent t the cente s d 4 Now d d d sn 9 d nd e pependcul d d 4 d d 4 The decton of feld s outwd pependcul to plne of ppe Totl gnetc feld d 4 d 4 4 Fnd the gnetc feld t the cente of cuent cyng conducto bent n the fo of n c subtendng ngle nd t the cente. Mgnetc feld t the cente of c bc nd dc we of ccut loop b bc c length bc nd dc ngle 4 4 dc dus V bc dc A ) d d O d y-s c -s HLMHOLT' Z COL S A ANGMNT Ths ngeent s used to poduce unfo gnetc feld of shot nge. t conssts :- Two dentcl co l cols (N,, se) lced t dstnce (cente to cente) equl to dus ('') of cols lnes of both cols e pllel to ech othe. Cuent decton s se n both cols (obseved fo se sde) othewse ths ngeent s not clled "Helholtz col ngeent". 6 (N,, ) ACW A p of sttony nd nfntely long bent wes e plced n the -y plne s shown n fg. The wes cy cuents of pee ech s shown. The segents L nd M e long the -s. The segents nd Q e pllel to the y-s such tht OS O.. Fnd the gntude nd decton of the gnetc nducton t the ogn O. O O M S O M O / / L (N,, ) ACW (unfo gnetc feld of shot nge HC) Q O Q S M NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65

7 J-hyscs As pont O s long the length of segents L nd M so the feld t O due to these segents wll be zeo. Futhe, ˆ s the pont O s ne one end of long we, Q (k) + (k) ˆ [s O SO d] 4 d 4 d so, (k) ˆ 4 d 4 T nd n (+z) decton. Substtutng the gven dt, 7 (k) ˆ. Wb ˆ 4 (k) Clculte the feld t the cente of se-ccul we of dus n stutons depcted n fgue (), () nd () f the stght we s of nfnte length. b O () c b O c () O b () c The gnetc feld due to stght cuent cng we of nfnte length, fo pont t dstnce fo one of ts ends s zeo f the pont s long ts length nd cente of seccul col s () f the pont s on lne pependcul to ts length whle t the so net gnetc feld t the cente of seccul we s b c 4 ( nto the pge) () [ + ] (out of the pge) () [ ](n to the pge) NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65 Clculte the gnetc nducton t the pont O, f the cuent cyng we s n the shpe shown n fgue. The dus of the cuved pt of the we s nd lne pts e ssued to be vey long nd pllel. Mgnetc nducton t the pont O due to ccul poton of the we µ 4 3 (out of the pge) ( 3 ) 4 Mgnetc nducton t O due to we cd wll be zeo snce O les on the lne cd tself when etended bckwd. Mgnetc nducton t O due to nfntely long stght we e s µ [sn sn ] 4 whee,, 7 µ sn sn 4 µ 4 ecuse both the felds e n se decton.e. pependcul to plne of ppe nd dected upwds, hence the esultnt gnetc nducton t O s b c d e

8 J-hyscs n the fe wok of wes shown n fgue, cuent s llowed to flow. Clculte the gnetc nducton t the cente O. f ngle s equl to 9, then wht wll be the vlue of gnetc nducton t O? Mgnetc nducton t O due to the segent C s 4 Slly, the gnetc nducton t O due to ccul segent AD s 4 A O ( ) Mgnetc feld due to segents A nd CD s zeo, becuse pont 'O' les on s of these pts. Hence esultnt gnetc nducton t O s + f 9, then , 4 Two concentc ccul cols X nd Y of d 6 c nd c espectvely le n the se vetcl plne contnng the noth-south decton. Col X hs tuns nd ces cuent of 6 A; col Y hs 5 tuns nd ces cuent of 8 A. The sense of the cuent n X s ntclockwse, nd n Y clockwse, fo n obseve lookng t the cols fcng the west. Wht s the gntude nd decton of the gnetc feld t the coon cente () Due to col X lone? () Due to col Y lone? () Due to both the cols? Accodng to the fgue the gntude of the gnetc feld t the cente of col X s D C 7 N T Snce the cuent n col X s ntclockwse, the decton of s towds the est s shown n fgue. The gntude of gnetc feld t the cente of the col Y W y N y Col X Col Y s gven by Y YN Y Y T snce the cuent n col Y s clockwse, the decton of feld Y s towds the west (see fg.). Snce the two felds e collne nd oppostely dected. The gntude of the esultnt feld dffeence between the two felds nd ts decton s tht of the bgge feld. Hence the net gnetc feld t the coon cente s 5 4 T nd s dected towds the west. A long we bent s shown n the fgue ces cuent. f the dus of the se-ccul poton s "" then fnd the gnetc nducton t the cente C. Due to se ccul pt ˆ 4 due to pllel pts of cuents ˆ ( k), net C 4 gntude of esultnt feld 4 4 X Z O ( ˆ) + 4 S C ( k) ˆ Y NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65

9 NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65 9 J-hyscs A pece of we cyng cuent of 6 A s bent n the fo of ccul c of dus. c, nd t subtends n ngle of t the cente. Fnd the gnetc feld due to ths pece of we t the cente. µ Mgnetc feld t cente of c 4, d T 6.57 µt An nfntely long conducto s shown n fg. cyng cuent wth seccul loop on X-Y plne nd two stght pts, one pllel to -s nd nothe concdng wth Z-s. Wht s the gnetc feld nducton t the cente C of the se-ccul loop. The gnetc feld nducton t C due to cuent though stght pt of the conducto pllel to X-s s Z sn sn 4 / ctng long + Z decton..e. ˆk The gnetc feld nducton t C due to cuent though the se-ccul loop n X-Y plne s 4 / ctng long + Z-decton.e. The gnetc feld nducton t C due to cuent though the stght pt of the conducto concdng wth Z-s s 3 sn sn 4 / ˆk ctng long ( X)-s.e. 3 ˆ Totl gnetc feld nducton t C s 3 ˆk + ˆk î Y C O kˆ ˆ A conducto cyng cuent s bented s shown n fgue. Fnd the gntude of gnetc feld t the ogn Feld t O due to pt ˆ ˆ Feld t O due to pt k 4 We 3 psses though ogn when t s etended bckwds 3 3 ˆ ˆ k A conducto of length.4 s tngentlly connected to ccul 4A loop of dus.3 pependcul to ts plne. Fnd the gnetc feld nducton t the cente of the loop f 4 pee cuent s pssed though the conducto s shown n fg. Mgnetc feld nducton t the cente of the loop due to the stght cuent-cyng conducto, sn sn sn T z.5 y Mgnetc felds due to the two hlves of the loop e equl n gntude nd opposte n decton. So, the gnetc feld nducton due to the loop t the cente of the loop s zeo. So, the gnetc feld nducton t the cente of the loop s.7 5 T. O 3 X

10 ACW cculton J-hyscs Fgue shows ght-ngled sosceles tngle Q hvng ts bse equl to. A cuent of pee s pssng downwds long thn stght we cuttng the plne of the ppe nolly s shown t Q. Lkewse sl we ces n equl cuent pssng nolly upwds t. Fnd the gntude nd decton Q of the gnetc nducton t. Assue the wes to be nfntely long. Let Q nd + o Mgnetc nducton t due to conducto t Q s 45 (long ) 9 Mgnetc nducton t due to conducto t s (long Q) Now, esultnt of these two s The decton of s towds the d-pont of the lne Q. AM'S CCUTAL L AW Apee's ccutl lw stte tht lne ntegl of the gnetc feld ound ny closed pth n fee spce o vcuu s equl to tes of net cuent o totl cuent whch cossng though the e bounded by the closed pth. Mthetclly. d ostve Negtve ( + 3) Ths lw ndependent of sze nd shpe of the closed pth. Any cuent outsde the closed pth s not ncluded n wtng the ght hnd sde of lw Note : Ths lw sutble fo nfnte long nd syetcl cuent dstbuton. dus of coss secton of thck cylndecl conducto nd cuent densty ust be gven to pply ths lw. MAGNTOMOTV FOC (M.M.F.). d, whee H, H. d H. d The lne ntegl of gnetsng feld ound ny closed pth s equl to net cuent cossng though the e bounded by the closed pth, lso clled 'gnetootve foce'. Mgnetootve foce (M.M.F.) H. d ALCATON OF AM'S CCUTAL L AW Mgnetc feld due to nfnte long thn cuent cyng stght conducto Consde ccle of dus ''. Let XY be the sll eleent of length d. nd d e n the se decton becuse decton of long the tngent of the ccle. y A.C.L.. d, d cos (whee ) d cos () d (whee d ) ACW O y d NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65

11 Mgnetc feld due to nfnte long sold cylndecl conducto Fo pont nsde the cylnde <, Cuent fo e s J-hyscs so cuent fo e s ( ) y Apee ccutl lw fo ccul pth of dus 3 n () ' n n Coss-sectonl vew s Fo pont on the s of the cylnde ( ); s Fo pont on the sufce of cylnde ( ) y Apee ccutl lw fo ccul pth of dus 3 s ( ) s (t s u) Fo pont outsde the cylnde ( > ) :- y Apee ccutl lw fo ccul pth 3 of dus out ( ) out out Mgnetc feld outsde the cylndecl conducto does not depend upon ntue (thck/thn o sold/hollow) of the conducto s well s ts dus of coss secton. out < > Mgnetc feld due to nfnte long hollow cylndecl conducto NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65 Fo pont t dstnce such tht < < b Fo pont t dstnce such tht < < b () ' () b b Fo pont t dstnce such tht > b >, 3 () Fo pont t the s of cylnde s Mgnetc feld t specfc postons fo thn hollow cylndecl conducto At pont At pont At pont 3 3 (u) [oute sufce] nd (nu) [nne sufce] (fo the pont on s s ) 3 b 3 As Sde Vew 3 b Coss sectonl vew out O 3

12 J-hyscs Mgnetc feld due to n nfnte plne sheet of cuent dsn y -z d d dcos dcos -s dsn An nfnte sheet of cuent les n -z plne, cyng cuent long-z s. The feld t ny pont on y s long lne pllel to -z plne. We cn tke ectngul pen loop s shown. f you tvese the loop n clockwse decton, nwd cuent wll be postve. y Apee ccutl lw, QS.d enclosed Let epesents cuent pe unt length. The cuent enclosed s gven by enclosed.d.d.d.d.d Now, QS Q Q S S Now, Also, Q Q.d.d s d S S...().d.d s d A long stght sold conducto of dus 5 c ces cuent of 3A, whch s unfoly dstbuted ove ts ccul coss-secton. Fnd the gnetc feld nducton t dstnce 4 c fo the s of the conducto. eltve peeblty of the conducto. gne ccul pth of dus whose cente les on the s of 3A sold conducto such tht the pont les on t. the cuent thedng ths closed pth ' Mgnetc feld cts tngentl to the pen ccul pth t nd s se n gntude t evey pont on ccul pth. Usng Apee ccutl lw.d µ µ ' () T. A cuent flows long thn wlled tube of dus wth long longtudnl slt of wdth b (<<). Wht s the gnetc feld nducton t dstnce (< )? Usng pncple of supeposton, feld due to stp n plce of slt + feld due to tube wth slt so feld due to stp n plce of slt b ( b) S Q b b -s 5c NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65

13 J-hyscs MAGNTC FLD DU TO SOLNOD t s col whch hs length nd used to poduce unfo gnetc feld of long nge. t conssts conductng we whch s tghtly wound ove cylndecl fe n the fo of hel. All the djcent tuns e electclly nsulted to ech othe. The gnetc feld t pont on the s of solenod cn be obtned by supeposton of feld due to lge nube of dentcl ccul tuns hvng the centes on the s of solenod. Mgnetc feld due to long solenod A solenod s tghtly wound helcl col of we. f length of solenod s lge, s coped to ts dus, then n the centl egon of the solenod, esonbly unfo gnetc feld s pesent. Fgue shows pt of long solenod wth nube of tuns/length n.we cn fnd the feld by usng Apee ccutl lw. Consde ectngul loop ACD. Fo ths loop ACD.d enc Now.d.d.d.d.d ACD A C CD DA Ths s becuse And, DA A.d.d, d. CD.d ( outsde the solenod s neglgble A D C b Now, enc n s n n (Mgnetc feld lnes) Fnte length solenod : ts length nd dete e copble. M ' (unfo) nd- nd- NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65 y the concept of SL gnetc feld t the l pont '' obtned s : 3 n (cos cos ) Angle nd both esued n se sense fo the s of the solenod to end vectos. nfnte length solenod : ts length vey lge s coped to ts dete.e. ends of solenod tends to nfnty. ( ) Mgnetc feld t l pont whch s well nsde the solenod nd 8 n [cos cos 8 ] ( b ) Mgnetc feld t both l end ponts of solenod 9 nd 8 n [cos 9 cos 8 ] n n [() ( )] n [() ( )] n

14 J-hyscs The length of solenod s.. nd ts dete s vey sll. A we s wound ove t n two lyes. The nube of tuns n nne lye s 5 nd tht of oute lye s 4. The stength of cuent flowng n two lyes n opposte decton s 3A. Then fnd gnetc nducton t the ddle of the solenod. Decton of gnetc feld due to both lyes s opposte, s decton of cuent s opposte so N net n n N ( ) (N N ) (5 4) 5 T A closely wound, solenod 8 c. long hs 5 lyes of wndng of 4 tuns ech. The dete of the solenod s.8 c. f the cuent ced s 8.A. stte the gnetc feld () nsde the solenod () Mgnetc feld nsde the solenod n n N (b) Al end ponts of the solenod 7 4 8, (N4 5 ) (8 ) (b) Mgnetc feld t l end ponts of solenod ends n T T A stght long solenod s poduced gnetc feld '' t ts cente. f t cut nto two equl pts nd se nube of tuns wound on one pt n double lye. Fnd gnetc feld poduced by new solenod t ts cente. Mgnetc feld poduced by long solenod s n, whee n N/ Se nube of tuns wound ove hlf length Mgnetc feld poduced by new solenod s ' 4 N / N Fnd out gnetc feld t l pont of solenod shown n fgue (whee tun densty n nd cuent though t s ) Mgnetc feld t pont due to fnte length solenod 3 n [cos cos ], whee 3 (CW), (8 6 ) (CW) n [cos 3 cos ] n 3 n ( ) end end NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65

15 J-hyscs A unfo gnetc feld ˆ k ests n egon. A cuent cyng we s plced n -y plne s shown. Fnd the foce ctng on pt A of the we. y k A The conducto conssts of 5 stght sectons vz AC, CD, D, F nd F s shown. As the feld s unfo, foce on the sectons s gven by F ˆ F ˆ kˆ j ˆ. Thus, AC ˆ ˆ, ˆ ˆ ˆ ˆ F j ˆ k CD F j ˆ k j F F k j ˆ D, ˆ ˆ F j k ˆ F Net foce, F F ˆ AC FCD FD FF FF 3 j CUNT CAYNG CONDUCTO N MAGNTC FLD When cuent cyng conducto plced n gnetc feld, gnetc foce eets on ech fee electon whch e pesent nsde the conducto. The esultnt of these foces on ll the fee electons s clled gnetc foce on conducto. Mgnetc foce on cuent eleent Though epeents Apee estblshed tht when cuent eleent d s plced n gnetc feld, t epeences gnetc foce df (d ) NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65 df d (Cw) 5 (etenl) Cuent eleent n gnetc feld does not epeence ny foce f the cuent n t s pllel o nt pllel wth the feld o 8 df (n.) Cuent eleent n gnetc feld epeences u foce f the cuent n t s pependcul wth the feld 9 df d (.) Mgnetc foce on cuent eleent s lwys pependcul to the cuent eleent vecto nd gnetc feld vecto. df d nd df (lwys) Totl gnetc foce on stght cuent cyng conducto n unfo gnetc feld gven s f d F f f d, df L L F (L ) Whee L, vecto su of ll length eleents fo ntl to fnl pont, whch s n ccodnce wth the lw of vecto ddton nd L length of the conduto. f N

16 J-hyscs Totl gnetc foce on bty shpe cuent cyng conducto n unfo gnetc feld s f f, df d F (L ) (L b) ntl pont L b Fnl pont Whee L f d, vecto su of ll length eleents fo ntl to fnl pont o dsplceent between fee ends of n bty conducte fo ntl to fnl pont. GOLDN KY ONT A cuent cyng closed loop (o col) of ny shpe plced n unfo gnetc feld then no net gnetc foce ct on t (Toque y o y not be zeo) L f d o d So net gnetc foce ctng on cuent cyng closed loop F (lwys) When cuent cyng closed loop (o col) of ny shpe plced n non unfo gnetc feld then net gnetc foce s lwys cts on t (Toque y o y not be zeo) A we bent s shown n fg ces cuent nd s plced n unfo feld of gnetc nducton tht eeges fo the plne of the fgue. Clculte the foce ctng on the we. f The totl foce on the whole we s F L ( + + ) 4 A sque of sde. s plced n unfo gnetc feld. T 6 n decton pependcul to the plne of the sque nwds. qul cuent 3. A s flowng n the dectons shown n fgue. Fnd the gntude of gnetc foce on the loop. Net foce on the loop 3 ( F AD C A D ) Foce on we ACD Foce on AD Foce on AD F net 3() (AD) () (3) (3.) ( )(.) N 36 N. Decton of ths foce s towds C. NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65

17 J-hyscs A etl od of ss g nd length 5 c s suspended on two spngs s shown n fgue. The spngs e etended by 4 c. When pee cuent psses though the od t ses by c. Detene the gnetc feld ssung cceleton due to gvty to be /s. k T Fbl Mg k T Sol. Let tenson n ech spng s T ntlly the od wll be n equlbu f T Mg then T k...() Now when the cuent s pssed though the od t wll epeence foce F L vetclly up; so n ths stuton fo ts equlbu, T + L Mg wth T k...() ( 4 3c) So fo eq. () nd eq.() T Mg L T Mg L Mg Mg L T Two conductng ls e connected to souce of e..f. nd fo n nclne s shown n fg. A b of ss 5 g sldes wthout fcton down the nclne though vetcl gnetc feld. f the length of the b s 5 c nd cuent of.5 A s povded by the bttey, fo wht vlue of wll the b slde t constnt velocty? [g /s ] vconst NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65 Foce on cuent cyng we F L The od wll ove down the plne wth constnt velocty only f F cos g sn L cos g sn o, g tn L T A we Q of ss g s t est on two pllel etl ls. The septon between the ls s 4.9 c. A gnetc feld of.8 tesl s ppled pependcul to the plne of the ls, dected downwds. The esstnce of the ccut s slowly decesed. When the esstnce deceses to below oh, the we Q begns to slde on the ls. Clculte the coeffcent of fcton between the we nd the ls. 4.9c Q 7 6V F cos F g gsn

18 J-hyscs We Q begns to slde when gnetc foce s just equl to the foce of fcton,.e., µ g sn ( 9 ) so 6.3 A so µ g A we bcdef wth ech sde of length '' bent s shown n fgue nd cyng cuent s plced n unfo gnetc feld pllel to +y decton.wht s the foce epeenced by the we. Z c Mgnetc foce on we bcdef n unfo gnetc feld s F (L ), L s dsplceent between fee ends of the conducto fo ntl to d e X fnl pont. L () î nd () ĵ ; F L b f Y L ( ˆ ˆj) (k) ˆ, long +z decton MAGNTC FOC T WN T WO A ALLL CUNT CAYNG CONDUCTOS Lke cuents unlke cuents epulson df df df df d d The net gnetc foce cts on cuent cyng conducto due to ts own feld s zeo. So consde two nfnte long pllel conductos septed by dstence 'd' cyng cuents nd. Mgnetc feld t ech pont on conducto () due to cuent s d Mgnetc feld t ech pont on conducto () due to cuent s 8 d [unfo feld fo conducto ()] [Unfo feld fo conducto ()] consde sll eleent of length 'd' on ech conducto. These eleents e ght ngle to the etenl gnetc feld, so gnetc foce epeenced by eleents of ech conducto gven s df d d d...() (Whee d ) df d d d... () (Whee d ) Whee df s gnetc foce on eleent of conducto (), due feld of conducto () nd df s gnetc foce on eleent of conducto (), due to feld of conducto (). df df Mgnetc foce pe unt length of ech conducto s d d d f d N/ (n S..) f d dyne/c (n C.G.S.) NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65

19 J-hyscs Defnton of pee : Mgnetc foce/unt length fo both nfnte length conducto gves s f d 7 (4 ) () () () 7 N/ 'Apee' s the cuent whch, when pssed though ech of two pllel nfnte long stght conductos plced n fee spce t dstnce of fo ech othe, poduces between the foce of 7 N/ L Foce scle f s pplcble when t lest one conducto ust be of nfnte d length so t behves lke souce of unfo gnetc feld fo othe conducto. Mgnetc foce on conducto 'LN' s F LN f FLN d d (souce) N qullbu of fee we Cse : Uppe we s fee : Consde long hozontl we whch s gdly fed nothe we s plced dectly bove nd pllel to fed we. A A (Stble (fee) qulbu) f g Fnte length (,) h (fed) (Souce) nfnte length + Mgnetc foce pe unt length of fee we f, nd t s epulsve n ntue becuse cuents e unlke. h Fee we y ens suspended f the gnetc foce pe unt length s equl to weght of ts unt length At blnced condton f W'. Weght pe unt length of fee we g (stble equllbu condton) h f fee we s slghtly pluked nd elesed then t wll eecutes S.H.M. n vetcl plne. The te peod of oton s T h g Cse : Lowe we s fee : Consde long hozontl we whch s gdly fed. Anothe we s plced dectly below nd pllel to the fed we. NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65 (fed) (Unstble (fee) qulbu) d (depht) Mgnetc foce pe unt length of fee we s f (Souce) f g d 9 nfnte length + Fnte length (,), nd t s ttctve n ntue becuse cuents e lke. Fee we y ens suspended f the gnetc foce pe unt length s equl to weght of ts unt length At blnced condton f W' Weght pe unt length of fee we d g (unstble equllbu condton)

20 J-hyscs Two hozontl pllel stght conductos, ech c long, e nged one vetclly bove the othe nd cy equl cuents n opposte dectons. The lowe conducto s fed whle the othe s fee to ove n gudes enng pllel to the lowe. f the uppe conducto weghts. g, wht s the ppote cuent tht wll ntn the conductos t dstnce.75 c pt. n equlbu gnetc foce F wll blnce weght g. So g F g d d F g Q gd A S MAGNTC DOL MOMNT A gnetc dpole conssts of p of gnetc poles of equl nd opposte stength septed by sll dstnce.. Mgnetc needle, b gnet, solenod, col o loop. Mgnetc oent of gnet Mgnetc s - Neutl pont + A S N Coss sectonl vew The gnetc oent of b gnet s defned s vecto quntty hvng gntude equl to the poduct of pole stength () wth effectve length () nd dected long the s of the gnet fo south pole to noth pole. M t s n l vecto S.. unt : - A. GOLDN KY ONTS Attctve popety : A b gnet ttcts cetn gnetc substnces (eg. on dust). The ttctng powe of the b gnet s u t two ponts ne the ends clled poles. So the ttctng powe of b gnet t ts poles clled 'pole stength' The 'pole stength' of noth nd south pole of b gnet s conventonlly epesented by + nd espectvely. The 'pole stength' s scl quntty wth S.. unt A. The 'pole stength' of b gnet s dectly popotonl to ts e of coss secton. A The ttctng powe of b gnet t ts cente pont s zeo, so t s clled 'neutl pont'. Mgnetc poles e lwys ests n ps.e. ono pole does not est n gnets. So Guss lw n gnets gven s ds ffectve length o gnetc length : t s dstnce between two poles long the s of b gnet. As pole e not ectly t the ends, the effectve length () s less thn the geoetcl length ( ) of the b gnet. ~ 9 nvese sque lw (Coulob lw) : The gnetc foce between two solted gnetc poles of stength nd lyng t dstnce '' s dectly popotonl to the poduct of pole stength nd nvesely popotonl to the sque of dstnce between the centes. The gnetc foce between the poles cn be ttctve o epulsve ccodng to the ntue of the poles. NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65

21 J-hyscs F F F k whee k µ 4 (S..) (C.G.S.) nvese sque lw of Coulob n gnets s pplcble only fo two long b gents becsue solted poles cnnot est. f gnet s cut nto two equl pts long the length then pole stength s educed to hlf nd length ens unchnged. New gnetc dpole oent M''() M. The new gnetc dpole oent of ech pt becoes hlf of ognl vlue. - S ' (/), ' + S N M N S N M M' (/) ' M/ ' ' / S N S N M M' f gnet s cut nto two equl pts tnsvese to the length then pole stength ens unchnged nd length s educed to hlf. New gnetc dpole oent M M '. The new gnetc dpole oent of ech pt becoes hlf of ognl vlue. The gnetc dpole oent of gnet s equl to poduct of pole stength nd dstnce between poles. M N S N S N S NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65 As gnetc oent s vecto, n cse of two gnets hvng gnetc oents M nd M wth ngle between the, the esultng gnetc oent. / M M M MM cos wth tn M M sn M cos The foce between two gnetc poles n s 9.64 N. f one pole s tes stonge thn the othe, clculte the pole stength of ech f dstnce between two poles s.? Foce between poles 7 µ 3 F o 9.64 o 96.4 N T 9.8N/T 4.. So stength of othe pole s N/T A steel we of length L hs gnetc oent M. t s then bent nto seccul c. Wht s the new gnetc oent?

22 J-hyscs M f s the pole stength then M.L L f t s bent nto seccul c then L So new gnetc oent M L M M ' L L Two dentcl b gnets ech of length L nd pole stength e plced t ght ngles to ech othe wth the noth pole of one touchng the south pole of othe. vlute the gnetc oent of the syste. M M L nd M sn 9 tn M M cos9 M M M M M cos L.e. tn 45 M S N S M N M M M MAGNTC MOMNT OF CUNT CAYNG COL ( LOO) Cuent cyng col (o loop) behves lke gnetc dpole. The fce of col n whch cuent ppes to flow nt clock wse cts s noth pole whle fce of col n whch cuent ppes to flow clock wse cts s south pole. A loop of geoetcl e 'A', ces cuent '' then gentc oent of col M A A col of tuns 'N', geoetcl e 'A', ces cuent '' then gentc oent M N A Mgnetc oent of cuent cyng col s n l vecto M NA whee A s e vecto pependcul to the plne of the col nd long ts s. S UNT : A- o J/T ACW M CW M M Decton of M fnd out by ght hnd thub ule Culng fnges n the decton of cuent Thub Gves the decton of M Fo cuent cyng col, ts gnetc oent nd gnetc feld vectos both e pllel l vectos. Fnd the gntude of gnetc oent of the cuent cyng loop ACDFA. ch sde of the loop s c long nd cuent n the loop s. A A C F D NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65

23 J-hyscs y ssung two equl nd opposte cuents n, two cuent cyng loops (AFA nd CD) e foed. The gnetc oents e equl n gntude but pependcul to ech othe. C D A F Hence, M net M M M whee M A (.)(.)(.). A- M net ( )(.) A-.8 A- The we loop QS foed by jonng two seccul wes of d nd ces cuent s shown n fg. Wht s the gnetc nducton t the cente O nd gnetc oent of the loop n cses (A) nd ()? (A) S O Q S () O Q As the pont O s long the length of the stght wes, so the feld t O due to the wll be zeo nd hence. (A).e., 4 4 & M NS () Followng s n cse (A), n ths stuton, nd, 4 MAGNTC DOL N MAGNTC FLD Toque on gnet c dpole M NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65 CW S F - 3 N + ( ) gnet foce pependcul dstnce between foce couple () (sn), whee M Msn ( b ) Col o Loop M NAsn 9 M (u) o 8 N A (nu) 9 NA (u) o 8 (nu) F CW (unfo) Vecto fo M O lne of col M CW (unfo)

24 J-hyscs GOLDN KY ONTS Toque on dpole s n l vecto nd t s dected long s of otton of dpole. Tendency of toque on dpole s ty to lgn the M n the decton of o tes to kes the s of dpole pllel to o kes the plne of col (o loop) pependcul to. Dpole n unfo gnetc feld Dpole n non unfo gnetc feld F (no tnsltoy oton) net y o y not be zeo (decdes by ) F net (tnsltoy oton) y o y not be zeo (decdes by ) When cuent cyng col (o loop) s plced n longtudenl gnetc feld then u toque cts on t. 9 M M NA When cuent cyng col (o loop) s plced n tnsvese gnetc feld the no toque cts on t. M o 8 M nt n WOK DON N OTATNG A M AGNTC DOL Wok done n ottng dpole n unfo gnetc feld though sll ngle 'd' dw.d Msnd So wok done n ottng dpole fo ngul poston to wth espect to the Mgnetc feld decton W dw M sn d M(cos cos ) f gnetc dpole s otted fo feld decton.e. to poston then wok done s W M ( cos) M sn / n one otton o 36 W n /4 otton 9 W M n hlf otton 8 W M n 3/4 otton 7 W M Wok done to otte dpole n gnetc feld s stoed n the fo of potentl enegy of gnetc dpole. OTNTAL NGY OF MAGNTC DOL The potentl enegy of dpole defned s wok done n ottng the dpole fo decton pependcul to the gven decton. U W W 9 U M ( cos) M M cosn vecto fo U M. When M nd When M nd GOLDN KY ONTS e pllel ( ), the dpole hs nu potentl enegy nd t s n stble equllbu. U M (nu) e nt pllel ( 8 ), the dpole hs u potentl enegy nd t s n unstble equllbu. U M (u) When M nd e ppendcul to ech othe ( 9 ), the dpole hs potentl enegy U nd n ths stuton u toque cts on t hence no equllbu. 4 NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65

25 J-hyscs A ccul col of 5 tuns nd dus 6. c, cyng cuent of A, s suspended vetclly n unfo gnetc feld of gntude. T. The feld lnes un hozontlly n the plne of the col. Clculte the foce nd toque on col due to the gnetc feld. n whch decton should blncng toque be ppled to pevent the col fo tunng? Mgnetc foce F d d so F Fo col o close loop The toque on col of ny shpe hvng N tuns nd cuent n gnetc feld s gven by NAsn sn N The decton of s vetclly upwds. To pevent the col fo tunng, n equl nd opposte toque ust be ppled. A unfo gnetc feld of 5 guss s estblshed long the postve z-decton. A ectngul loop of sde c nd 5 c ces cuent of A s suspended n ths gnetc feld. Wht s the toque on the loop n the dffeent cses shown n the followng fgues? Wht s the foce n ech cse? Whch cse coesponds to stble equlbu? Z Z Z O Y O Y O Y X () X (b) X (c) Z Z Z X O 3 (d) Y O (e) Y O (f) Y NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65 () Toque on loop, A sn Hee, 9 ; 5 guss5 4 tesl.5 tesl pee, A 5c 4 Now,.5 5 N t s dected long y-s (b) Se s (). (c) 5 N long -decton (d) 5 N t n ngle of 4 wth + decton. (e) s zeo. [Angle between plne of loop nd decton of gnetc feld s 9 ] (f) s zeo. esultnt foce s zeo n ech cse. Cse (e) coesponds to stble equlbu. A ccul col of tuns nd hvng dus of.5 ces cuent of. A. Clculte the wok equed to tun the col n n etenl feld of.5 T though 8 bout n s pependcul to the gnetc feld? The plne of col s ntlly t ght ngles to gnetc feld. Wok done W M (cos cos ) NA (cos cos ) W N (cos cos ). 3.4 (.5).5 (cos cos).355j 5

26 J-hyscs A b gnet of gnetc oent.5 JT les lgned wth the decton of unfo gnetc feld of. T. () Wht s the ount of wok equed to tun the gnet so s to lgn ts gnetc oent. () Nol to the feld decton? () Opposte to the feld decton? (b) Wht s the toque on the gnet n cse () nd ()? Hee, M.5 JT,. T. ().. wth gnetc oent lgned to feld M.. wth gnetc oent nol to feld.. wth gnetc oent ntpllel to feld + M () Wok done ncese n.. ( M) M J. () Wok done ncese n.. M ( M) M J. (b) We hve Msn () M sn J. (9 sn) Ths toque wll tend to lgn M wth. () M sn.5. ( 8 sn) A shot b gnet of gnetc oent.3 J/T s plced n unfo feld of.5 T. f the b s fee to otte n plne of feld then whch oentton would coespond to ts () stble nd () unstble equlbu? Wht s potentl enegy of gnet n ech cse? () f M s pllel to then. So potentl enegy U U n M U n M.3.5 J 4.8 J (stble equlbu) () f M s ntpllel to then So potentl enegy U U + M J (unstble equlbu.) ATOMC MAGNTSM An toc obtl electon, whch dong bounded unfo ccul oton ound nucleus. A cuent consttues wth ths obtl oton nd hence obt behves lke cuent cyng loop. Due to ths gnets poduces t nucleus poston. Ths phenoenon clled s 'toc gnets. oh' s postultes : v v kze h () () L v n, whee n,,3... ACW +Ze sc eleents of toc gnets : e Fe e ev e () Obtl cuent :- ef (cuent) T (b) Mgnetc nducton t nucleus poston :- As ccul obt behves lke cuent (c) cyng loop, so gnetc nducton t nucleus poston N ef e ev e N T 4 4 Mgnetc oent of ccul obt :- Mgnetc dpole oent of ccul obt e ev e T elton between gnetc oent nd ngul oentu of obtl electon M A whee A s e of ccul obt. M ef Mgnetc oent M ev el (ngul oentu L v) el Vecto fo M Fo obtl electon ts M nd L both e ntpllel l vectos. 6 e M (cuent) NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65

27 J-hyscs OH MAGNTON ( ) Accodng of oh's theoy, ngul oentu of obtl electon s gven by L nh, whee n,, 3... nd h s plnk's constnt. Mgnetc oent of obtl electon s gven by M el eh n 4 f n then M Defnton of : eh 4, whch s oh gneton denoted by oh gneton cn be defned s the gnetc oent of obtl electon whch evolves n fst obt of n to. eh A.. sc eleents of toc gnets fo fst obt of H- to (n, z ) () Accute fo :- (v.8 6 /sec, f cy/sec..59å) (b) Obtl cuent.96 A Mgnetc nducton t nucleus poston N.8 T Mgnetc oent of obtl electon M.93 3 A. Sple fo :- (v 6 /sec, f 6 5 cy/sec,.5å) Obtl cuent A Mgnetc nducton t nucleus poston N 4T Mgnetc oent of obtl electon M µ A. NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65 A NONCONDUCTNG CHAGD ODY S OTATD WTH SOM ANGUL A SD. n ths cse the to of gnetc oent nd ngul oentu s constnt whch s equl to hee q chge nd the ss of the body. n cse of ng, of ss, dus nd chge q dstbuted on t ccufeence. Angul oentu L ( )()... () Mgnetc oent M A (qf) ( ) f M (q) Fo qs. () nd () F HG K J ( ) q M L q 7...() q q Although ths epesson s deved fo sple cse of ng, t holds good fo othe bodes lso. Fo eple, fo dsc o sphee. M ql b g M q, whee L gd body n g D s c Sold sphee Sphecl shell Moent of net () Mgnetc oent q q q q 5 q 3

28 J-hyscs FOC ON A CHAGD ATCL N A MAGNTC FLD Foce epeenced by cuent eleent d n gnetc feld s gven by df d...() Now f the cuent eleent d s due to the oton of chge ptcles, ech ptcle hvng chge q ovng wth velocty v though coss-secton A, d nqav d nqdv v [wth volue dva d] Fo eq n () we cn wte df ndv q (v ) ndvthe totl nube of chged ptcles n volue dv (nnube of chged ptcles pe unt volue), foce on chged ptcle F n GOLDN KY ONT The foce F s lwys pependcul to both the velocty v nd the feld A chged ptcle t est n stedy gnetc feld does not epeence ny foce. f the chged ptcle s t est then v, so v d F dv q (v ) A ovng chged ptcle does not epeence ny foce n gnetc feld f ts oton s pllel o ntpllel to the feld. q v q v q 8 F (A) F O q v F vsn () F O 9 q F qv (C) v f the ptcle s ovng pependcul to the feld. n ths stuton ll the thee vectos F, v nd e utully pependcul to ech othe. Then sn,.e., 9, The foce wll be u F q v Wok done by foce due to gnetc feld n oton of chged ptcle s lwys zeo. When chged ptcle ove n gnetc feld, then foce cts on t s lwys pependcul to dsplceent, so the wok done,w F.ds Fds cos 9 (s 9 ), And s by wok-enegy theoe W K, the knetc enegy hence speed of chged ptcle v ens constnt. 8 v ens unchnged nd Howeve, n ths stuton the foce chnges the decton of oton, so the decton of velocty v of the chged ptcle chnges contnuously. MOTON OF A CHAGD ATCL N A MAGNTC FLD Moton of chged ptcle when t s ovng collne wth the feld gnetc feld s not ffected by the feld (.e. f oton s just long o opposte to gnetc feld) ( F ) Only the followng two cses e possble : Cse : When the chged ptcle s ovng pependcul to the feld. The ngle between nd v s 9. So the foce wll be u ( qv) nd lwys pependcul to oton (nd lso feld); Hence the chged ptcle wll ove long ccul pth (wth ts plne pependcul to the feld). Centpetl foce s povded by the foce qv, So Angul fequency of ccul oton, clled cycloton o gyo-fequency. v q v qv v q NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65

29 J-hyscs nd the te peod, T.e., te peod (o fequency) s ndependent of speed of ptcle q nd dus of the obt. Te peod depends only on the feld nd the ntue of the ptcle,.e., specfc chge (q/) of the ptcle. Ths pncple hs been used n lge nube of devces such s cycloton ( ptcle cceleto), bubble-chbe ( ptcle detecto) o ss-spectoete etc. Cse : The chged ptcle s ovng t n ngle to the feld : (, 9 o 8 ). esolvng the velocty of the ptcle long nd pependcul to the feld.the ptcle oves wth constnt velocty v cos long the feld ( no foce cts on chged ptcle when t oves pllel to the feld). And t the se te t s lso ovng wth velocty v sn pependcul to the feld due to whch t wll descbe ccle (n plne pependcul to the feld) (v sn ) dus of the ccul pth nd Te peod T q v sn q So the esultnt pth wll be hel wth ts s pllel to the feld s shown n fg. v sn Helcl th v cos p NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65 The ptch p of the hel lne dstnce tvelled n one otton pt (vcos) (v cos ) q An electon etted by heted cthode nd cceleted though potentl dffeence of. kv entes egon wth unfo gnetc feld of.5 T. Detene the dus of the tjectoy of the electon f the feld s () Tnsvese to ts ntl velocty(b) Mkes n ngle of 3 wth the ntl velocty [Gven : e 9 3 kg] v ev v () dus v q 9 3 ev (b) dus v sn sn sn3 q b g /s.5 MOTON OF CHAGD ATCL N COMND LCTC AND MAGNTC FLDS Let ovng chged ptcle s subjected sultneously to both electc feld nd gnetc feld. The ovng chged ptcle wll epeence electc foce Fe q nd gnetc foce F q (v ). Net foce on the chge ptcle F q( v ) " Loentz- foce" Dependng on the decton of v, nd vous stuton e possble nd the oton n genel s qute cople. Cse : v, nd ll the thee e collne :

30 J-hyscs v q As the ptcle s ovng pllel o ntpllel to the feld. The gnetc foce on t wll be zeo F q nd only electc foce wll ct So, cceleton of the ptcle Hence, the ptcle wll pss though the feld followng stght lne pth (pllel to the feld) wth chnge n ts speed. n ths stuton speed, velocty, oentu nd knetc enegy ll wll chnge wthout chnge n decton of oton s shown n fgue bove. v' q Cse : v, nd e utully pependcul : q v F e q v F f n ths stuton decton nd gntude of nd e such tht F esultnt foce F Fe F Then s shown n fg., the ptcle wll pss though the feld wth se velocty F e F.e. qqv 3 v A be of potons s deflected sdewys. Could ths deflecton be cused by () gnetc feld () n electc feld? f ethe possble, wht would be the dffeence? Yes, the ovng chged ptcle (e.g. poton, -ptcles etc.) y be deflected sdewy ethe by n electc o by gnetc feld. () () The foce eeted by gnetc feld on the ovng chged ptcle s lwys pependcul to decton of oton, so tht no wok s done on the ptcle by ths gnetc foce. Tht s the gnetc feld sply deflects the ptcle nd does not ncese ts knetc enegy. The foce eeted by electc feld on the chged ptcle t est o n oton s lwys long the decton of feld nd the knetc enegy of the ptcle chnges. A neuton, poton, n electon n -ptcle ente egon of constnt gnetc feld wth equl veloctes. The gnetc feld s long the nwds nol to the plne of the ppe. The tcks of the ptcles e shown n fg. elte the tcks to the ptcles. C A D NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65

31 Sol. Foce on chged ptcle n gnetc feld F q (v ) Fo neuton q, F hence t wll pss undeflected.e., tcks C coesponds to neuton. f the ptcle s negtvely chged,.e. electon. F e( v ) t wll epeence foce to the ght; so tck D coesponds to electon. J-hyscs f the chge on ptcle s postve. t wll epeence foce to the left; so both tcks A nd coesponds to postvely chged ptcles (.e., potons nd -ptcles). When oton of chged ptcle pependcul to the gnetc feld the pth s ccle wth dus v q.e. nd s q 4 q e whle q e p q q p So > p tck to -ptcle nd A coesponds to poton. An electon does not suffe ny deflecton whle pssng though egon. Ae you sue tht thee s no gnetc feld? s the evese defnte? f electon pssng though cetn egon does not suffe ny deflecton, then we e not sue tht thee s no gnetc feld n tht egon. Ths s due to tht electon suffes no foce when t oves pllel o ntpllel to gnetc feld. Thus the gnetc feld y est pllel o ntpllel to the decton of oton of electon. The evese s not tue snce n electon cn lso be deflected by the electc feld. n chbe, unfo gnetc feld of 8 4 T s ntned. An electon wth speed of 4. 6 /s entes the chbe n decton nol to the feld. () (b) (c) Descbe the pth of the electon. Wht s the fequency of evoluton of the electon? Wht hppens to the pth of the electon f t pogessvely loses ts enegy due to collsons wth the tos o olecules of the envonent? NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65 () (b) (c) The pth of the electon s ccle of dus v 3 6 e The sense of otton of the electon n ts obt cn be detened fo the decton of the centpetl foce. F e ( v ). So, f we look long the decton of, the electon evolves clockwse. the fequency of evoluton of the electon n ts ccul obt f eb Hz.4 MHz 9. Due to collson wth the toc consstent of the envonent, the electon pogessvely loses ts speed. f the velocty vecto of the electon ens n the se plne of the ntl ccul obt fte collsons, the dus of the ccul obt wll decese n popoton to the decesng speed. Howeve, n genel, the velocty of the electon wll not en n the plne of the ntl obt fte collson. n tht cse, the coponent of velocty nol to wll detene the dus of the obt, whle the coponent of velocty pllel to ens constnt. Thus, the pth of the electon, between two collsons s, n genel, helcl. ut n potnt fct ust be noted: the fequency of obtl evoluton ens the se, whteve be the speed of the electon. 3

32 J-hyscs A be of potons wth velocty 4 5 /s entes unfo gnetc feld of.3 tesl t n ngle of 6 to the gnetc feld. Fnd the dus of the helcl pth tken by the poton be. Also fnd the ptch of hel. Mss of poton.67 7 kg. dus of hel v sn (coponent of velocty to feld s vsn) q (.67 )(4 ) 9 (.6 ).3 3.c Agn, ptch pvcos T (whee T v sn ) vsn vcos p p v cos v sn cos 6 (. ) c sn 6 The egon betwen nd L s flled wth unfo, stedy gnetc feld k ˆ. A ptcle of ss, postve chge q nd velocty vˆ tvels long X-s nd entes the egon of gnetc feld. Neglect the gvty thoughout the queston. () (b) Fnd the vlue of L f the ptcle eeges fo the egon of gnetc feld wth ts fnl velocty t n ngle 3 to ts ntl velocty. Fnd the fnl velocty of the ptcle nd the te spent by t n the gnetc feld, f the gnetc feld now etends upto. L. () The ptcle s ovng wth velocty ˆ v, pependcul to gnetc feld k ˆ. Hence the ptcle wll ove long L ccul c OA of dus v q Let the ptcle leve the gnetc feld t A. Fo CDA, sn6 AD L L sn3 CA L v q (b) As the gnetc feld etends upto. L.e., L >, so the ptcle copletes hlf cycle befoe levng the gnetc feld, s shown n fgue. The gnetc feld s lwys pependcul to velocty vecto, theefoe the gntude of velocty wll en the se. Fnl velocty v ( ˆ ) v ˆ Te spent n gnetc feld v q 3 D 3 C v y v A 3 NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65

33 J-hyscs A unfo gnetc feld wth slt syste s shown n fg. s to be used s oentu flte fo hgh enegy chged ptcles. Wth feld of tesl t s found tht the flte tnsts -ptcle ech of enegy 5.3 MeV. The gnetc feld s ncesed to.3 tesl nd deuteons e pssed nto the flte. Wht s the enegy of ech deuteon tnstted by the flte? Souce Detecto n cse of ccul oton of chged ptcle n gnetc feld k q So ccodng to the gven poble ( k ) e 4 b g nd ( b g k ) D b e g b. 3 g bg.e. ( ) ( ) k D k b g. 3 4 ( k ) D (5.3) MeV A chged sphee of ss nd chge q stts sldng fo est on vetcl fed ccul tck of dus fo the poston s shown n fgue. Thee ests unfo nd constnt hozontl gnetc feld of nducton. Fnd the u foce eeted by the tck on the sphee. q NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65 Sol. Mgnetc foce on sphee F qv (dected dlly outwd) N g sn qv v N v Hence, t / we get N g + g sn + qv + g + q g 3g + q g 33 gsn An electon gun G ets electons of enegy kev tvellng n the postve -decton. The electons e equed to ht the spot S, whee GS., nd the lne GS kes n ngle of 6 wth the -s, s shown n the fgue. A unfo gnetc feld pllel to GS ests n the egon outsde the electon gun. Fnd the nu vlue of needed to ke the electon ht S. G 6 S F g O N

34 J-hyscs Sol. The velocty of the electons etted by electon gun long -s, s v K v The velocty of the electon cn be esolved nto two coponents v cos nd v sn, pllel nd pependcul to the gnetc feld espectvely. Due to coponent v cos electon wll ove n the decton of gnetc feld wth constnt speed v cos but due to coponent v sn, t wll ove on ccul pth n the plne to gnetc feld. Hence electon wll ove on spl pth. As electons e equed to ht the spot S, hence dstnce tvelled by electon n one te peod long the decton of gnetc feld ust be just equl to GS. The electons y lso ht the spot S fte two o oe te peods but nu vlue of s equed As pe bove dscusson, G S Dstnce tvelled long the decton of gnetc feld n one te peod (v cos ) T v cos q K cos q b g cos q GS cos T. 6. MOVNG COL GALVANOMT A glvnoete s used to detect the cuent nd hs odete esstnce. N S ncple. When cuent cyng col s plced n gnetc feld, t 34 epeences toque gven by NA sn whee s the ngle between nol to plne of col nd decton of gnetc feld. n ctul ngeent the col s suspended between the cylndcl pole peces of stong gnet. The cylndcl pole peces gve the feld dl such tht sn (lwys). So toque NA f C s tosonl gdty (.e., estong couple pe unt twst of the suspenson we), then fo deflecton of col C. n equlbu we hve etenl couple estong couple.e.cna o NA.e., C n wods the deflecton poduced s dectly popotonl to cuent n the col. The quntty NA C s clled the cuent senstvty of the glvnoete. Obvously fo getee senstvty of glvnoete the nube of tuns N, e of col A nd gnetc feld poduced by pole peces should be lge nd tosonl gdty C should be slle. Tht s why the suspenson we s used of phospho bonze fo whch tosonl gdty C s slle. NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65

35 J-hyscs CON VSON OF GALVANOMT NTO A MMT An ete s low esstnce glvnoete; used to esue cuent dectly n pees nd s lwys connected n sees wth the ccut. To convet glvnoete nto ete, low esstnce, clled shunt, s connected n pllel to the glvnoete s shown n fgue. S g G b Let g be the cuent n glvnoete fo ts full scle deflecton nd G the esstnce of glvnoete. Let s the nge of ete nd s the cuent n shunt S. Then potentl dffeence coss nd b s V b g G S S....() At juncton, S + g.e., S g Theefoe fo () g G ( g )S o g (S+G) S.e., g S...() S G Ths s the wokng equton fo conveson of glvnoete nto ete. Hee g <. Fo () shunt equed S G g g. f g <<, S g G The esstnce of ete A so foed s gven by A G + S SG A S G...() Note: quton () y lso be used to ncese the nge of gven ete. Hee G wll be esstnce of gven ete, S shunt ppled, g ts ntl nge nd the new nge desed. NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65 CON VSON OF GALVANOMT NTO VOLTMT A voltete s hgh esstnce glvnoete nd s connected between two ponts coss whch potentl dffeence, s to be esued.e., voltete s connected n pllel wth the ccut. glvnoete nto voltete, hgh esstnce n sees s connected to the f V s nge of voltete, then g g G V G 35 g V o esstnce n sees G...() Ths s wokng equton fo conveson of glvnoete nto voltete. The esstnce of voltete so foed s V +G...() g To convet glvnoete. Note: quton () y lso be used to ncese the nge of voltete. f V s ntl nge nd V s new nge of voltete, then g V V G G

36 J-hyscs SOM WOKD OUT XAMLS p le# Cuent.5 A flows long the ccle + y 9 c (hee & y n c) s shown. Mgnetc feld t pont (,, 4 c) s 7 (A) 36 T k ˆ 7 () ˆ 36 T k (C) 5 Mgnetc feld on the s of ccul loop p le# 9 7 ˆ T k kˆ 3 / 6 T kˆ 36 T kˆ 4 z ˆ 5 Ans. (A) 7 (D) T k Thee e constnt electc feld ˆ j & gnetc feld k ˆ pesent between pltes nd '. A ptcle of ss s pojected fo plte ' long y s wth velocty v. Afte ovng on the cuved pth, t psses though pont A just gzng the plte wth velocty v. The gntude of pulse (.e. Ft p ) povded by gnetc foce dung the oton of ptcle fo ogn to pont A s : y A v v (A) v v () v v (C) v (D) v Ans. (D) lectc foce s only esponsble fo the chnge n oentu long y s. Theefoe pulse povde by gnetc foce s J v. p le#3 Thee dentcl chge ptcles A, nd C e pojected pependcul to the unfo gnetc feld wth veloctes v, v nd v 3 (v < v < v 3 ) espectvely such tht T, T nd T 3 e the espectve te peod of evoluton nd, nd 3 e espectve d of ccul pth descbed. Then :- (A) 3 T T T 3 () T < T < T 3 (C) 3 T T T 36 ' 3 (D) 3 NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65

37 T q & v q T v J-hyscs Ans. (C) p le#4 An nfntely long stght we s bent s shown n fgue. The ccul poton hs dus of c wth ts cente O t dstnce fo the stght pt. The vlue of such tht the gnetc feld t the cente O of the ccul poton s zeo wll be :- O c (A) Solut on c () c (C) 5 c (D) 5 c Ans. (A) ccul loop we c p le#5 Two cylndcl stght nd vey long non gnetc conductos A nd, nsulted fo ech othe, cy cuent n the postve nd the negtve z decton espectvely. The decton of gnetc feld t ogn s y A (A) î () î (C) ĵ (D) ĵ y Ans. (C) A A NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65 p le#6 The gnetc foce between wes s shown n fgue s :- (A) n L () L n 37 L (C) n L (D) None of these

38 J-hyscs Mgnetc feld t d, L d Foce on sll eleent t dstnce of we of length L s df (d) L d L F n Ans. (C) p le#7 A we cyng cuent of 4A s bent n the fo of pbol + y 6 s shown n fgue, whee nd y e n ete. The we s plced n unfo gnetc feld 5k ˆ tesl. The foce ctng on the we s y (A) 8 ˆj N () 8 ˆj N (C) 6 ˆj N (D) 6 ˆj N F 4 8ˆ 5kˆ 6 ˆj N 38 Ans. (C) p le#8 A conductng col s bent n the fo of equltel tngle of sde 5 c. Cuent flowng though t s. A. The gnetc oent of the tngle s :- (A) 3 A (). 4 A (C). A (D) 3 4 A Ans. () Mgnetc oent of cuent cyng tngul loop M A 3 5 M A- p le#9 A dsc of dus nd cyng postve chge q s ottng wth ngul speed n unfo gnetc feld bout fed s s shown n fgue, such tht ngle de by s of dsc wth gnetc feld s. Toque ppled by s on the dsc s (A) (C) Dsc Fed s q sn, clockwse () q sn, ntclockwse (D) q sn, ntclockwse 4 q sn, clockwse 4 NOD6 ()\Dt\4\Kot\J-Advnced\SM\hy\Unt No-9\Mgnetc ffect of cuent & Mgnets\ng\.Theoy.p65