CHAPTER 35 MAGNETIC FIELD DUE TO CURRENT
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1 HTER 3 MGNETI FIEL UE T URRENT F F N. F q o, q T.sec. / sec. o,., m m N m 7 6 T T ong +ve Y ecton mm So,.8 mm.8 m 7 8., 8 m 7. T 8. 7 T-m/ 3 T mt N m N cm. m,, T We know: Mgnetc fe ue to ong stght we cyng cuent 7 t T upw. net 7 T T t Q T ownws Hence net 6. ( The mmum mgnetc fe s whch e ong the eft keepng the sense ong the ecton of tveng cuent. (bthe mnmum If net < net > net 7. 7 T-m/, 3,. T e to cuent. T ue to woe t pt. cm T. net fe 3 T 3 Z s Q cm cm m X s 8 m 3.
2 8.. ( Kˆ 3 T South to Noth ( Ĵ 3. Mgnetc Fe ue to uent To cnce the mgnetc fe the pont shou be choosen so tht the net mgnetc fe s ong - Ĵ ecton. The pont s ong - î ecton o ong west of the we m mm Let the tow wes be postone t & R, (. (. ( ue to Q, t ue to, t net T 7.88 m T ( tows up the ne.33 T ( tows own the ne (b ue to t T own the ne. 7 ue to t.67 T own the ne.3 net t T (c t 3 ue to T t 3 ue to T Net t 3 T 7 tows own the ne tows own the ne ( t ue to.7 T tows SE.88 t ue to.7 T Net tows SW. os ½, 6 & 6 7 T So net s [( + ( + ( 8 os 6 ] /.989 T [ + + ½ ] / - 3 T.73 T. ( fo X fo Y oth e oppostey ecte hence net (b ue to X ue to X both ecte ong Z s 7 Net 6 T T (c ue to X ue to Y both ecte opposte to ech othe. Hence Net ( ue to X ue to Y 6 T both ecte ong ( ve Z s Hence Net. 6 T (, 3 cm cm cm cm (, (, (,
3 Mgnetc Fe ue to uent. ( Fo ech of the we Mgntue of mgnetc fe (Sn Sn / Fo fo Fo n fo. The two n fes cnce ech othe. Thus net (b t pont Q ue to ( ue to ( ue to (3 ue to (. ( / ( / (/3 7 (/3 Q 3 3 Q Q / cm Q net [ + + (/3 + (/3] T t pont Q ue to ( ue to ( ue to (3 ue to ( net t pont Q 3 ue to ( ue to ( ue to (3 ue to ( o (. o ( / o (. o ( / 7 ( / 7 ( / 7 ( / 7 ( / /3 /3 net [ + + (/3 + (/3] T Fo Q ue to ( /3 ue to ( ue to (3 /3 ue to ( net 3.3
4 Mgnetc Fe ue to uent 3. Snce the ponts e ong cce wth us Hence R & Q both t stnce fom the we. R So, mgnetc fe ue to e sme n mgntue. s the wes cn be tete s sem nfnte stght cuent cyng conuctos. Hence mgnetc fe t ue to s t Q ue to s ue to s ue to s t R ue to s t S ue to s ue to s ue to s. Sn ( When >> Negectng w..t. S / Q (b When >>, negectng w..t. /., cm. m 3. m (Sn Sn T. T Q cm 3 3 Q 3.
5 Mgnetc Fe ue to uent 6., ( Sn s esstnces vy s & Hence uent ong 3 Now, 8. ue to 3 ue to 3 Now & ong Mgnetc fe ue to (Sn (9 + Sn (9 / / os ( / Mgnetc fe ue to Sn (9 3 / os 3 3 ( / 3 / The mgnetc fe ue to & e equ n ppopte hence cnce ech othe. Hence, net mgnetc fe s /3 /3 / / / 3/ / 3.
6 Mgnetc Fe ue to uent 9. ue t & ue to t t e equ oe pposte Hence net Smy, ue to & t The net t the ente of the sque oop zeo.. Fo s ong (Sn6 Sn6 Fo (Sn6 Sn6 Fo (Sn6 Fo (Sn6 Net. ( s Equte /3 uent So, M s M : M : Q 6 M 6 ue to t <. (Sn Sn net (b ue to 8 Net 8. Sn (/ /8 Sn (/ Mgnetc fe ue to R Sn(8 (9 ( / [Sn(9 ( / ] Sn( / (os( / Sn( / os ( / ot( / Sn( / os( / The mgnetc fe ue to both the we. ot( / ot( / 3.6
7 3. Sn Sn b b Sn ( +b b b Sn b b Net b b Sn Sn + b b., n n n ( b / ( / / (b / b b b b / / b Mgnetc Fe ue to uent b b b b Tn Tn n (Sn Sn ( Tn( / nsn( / nn Tn Sn ntn( / nsn( / n ntn( / nsn( / n Fo n ses, net. Net cuent n ccut Hence the mgnetc fe t pont [wng to whet stone bge pncpe] 6. Foce ctng on cm of we s N F 7-3. m cm 7. Mgnetc foce ue to two pe uent yng wes. F So, F o F by + F by N tows me we cm 3 3.7
8 8. ( cm The th we shou be pce cm fom the we n 8 cm fom we. 9. F F + F EF ownw. E F F + F EF s F & F EF e equ n oppostey ecte hence F 3. mg (Fo poton of we of ength m F Q 3 F on F 3 Q 3 7 [og] 7 [og 3 og ] Smy foce of F RS 7 [og 3 og ] So, F Q F S F RS 6 F RQ N (Tows ght N 3 Net foce tows own ( N 3.. mt,, n,? n n Mgnetc Fe ue to uent 3. 3 m.7 3 m.7 cm.7 cm 3. I S I cm ( F F mg R Q cm
9 Mgnetc Fe ue to uent n 33. n, 6 T cm. m n evoutons n sec. evoutons n sec 3 q.6 t m / n ech semcce ( / ownws ( / upws Net 36. cm cm n n n n ( n n (b 37. ute ce n, m. m n. Inne ce cm. m, n T hozonty tows West. n, ownws. Net cm,, V 6 m/s, 3 F e(v ev Sn Sn N mt / / 3.9
10 39. Lge oop R ue to ge oop on the sme oop ( Sn 9. The foce ctng on the sme oop F Sn o R R. mpee, cm. m s the semccu we foms hf of ccu we, 7 So,..7 6 T 6 6 T.6 T. R 3 R t T 3. ue to oop Let the stght cuent cyng we be kept t stnce R fom cente. Gven ue to we R R 3. Mgnetc Fe ue to uent Now, the ue to both w bnce ech othe Hence R R Hence the stght we shou be kept t stnce / fom cente n such wy tht the ecton of cuent n t s opposte to tht n the neest pt of ccu we. s esut the ecton w w be oppose.. n,, cm n n ( 3.. T. mt (b ( n 3 / 7 n ( n 3 / 3 / ( ( + 3/ 3 + ( 3 /3 + ( /3 + /3 ( + /3 ( + /3 ( ( /3 ( ( /3 ( m cm.. t the must be ecte ownws We Know t the ne t & ( 3 / 7.6 ((. 3 / cm. m 3 cm.3 m 6 T ownws n both the cses cm M cm R R 3 cm 3 cm.3 m
11 Mgnetc Fe ue to uent 6. q 3. 6, cm. m, q 3. 6 w 6 /sec.,. t. Q Eectc fe Mgnetc fe / 3 / (. 7. ( Fo nse the tube s, nse the conuctng tube o (b Fo outse the tube 3 6 Q 3 / 3 / / 3 8. ( t pont just nse the tube the cuent encose n the cose sufce. Thus o (b Tkng cync sufce just out se the tube, fom mpee s w. b b 9. s unfomy stbute thoughout. So, fo the pt of us b b Now ccong to mpee s ccut w b b. ( cm m m, n the egon of us cm b b ( ( ( (- 7. (b cm us ( 7.. (c cm ( (
12 . We know,. Theotcy t Mgnetc Fe ue to uent If, cuent s psse though the oop QRS, then w est n ts vcnty. ( b R S Now, s the b t s zeo. So thee be no ntecton Howeve pctcy ths s not tue. s cuent cyng oop, espectve of ts ne bout poston s wys ffecte by n estng mgnetc fe.. ( t pont,, Thus (b t pont R,, (c t pont, ppyng mpee s ue to the bove ectnge K o Q k K o k b k k Snce the ue to the stpes e ong the sme ecton, thus. k net k k 3. hge q, mss m We know us escbe by chge ptce n mgnetc fe m q t K [ccong to mpee s ccut w, whee K s constnt] m q k q k m., 3. T, n? n 3. 7 n n 7. tuns/m.. mm,, n (fo soeno Wth of ech tun mm 3 m No. of tuns n 3 3 So, T 6. R. n m,. cm Tot tuns, cm, T, n tuns/m E E R / ( R E.. n 3.
13 Mgnetc Fe ue to uent 7 E E uent t ue to the ccu oop fo the whoe soeno. V n 3 / n n 3 3 / 3 / n 3 / n / / 8., f 8 ev/sec, n?, m e 9. 3 kg, q e.6 9 c, n n f q m e fm q e e n fme q e tuns/m 9. No. of tuns pe unt ength n, us of cce /, cuent n the soeno, hge of tce q, mss of ptce m n mv gn qv V 6. No. of tuns pe unt ength q m ( s the net mgnetc fe zeo pte Soeno pte k k pte k Equtng both (b k c q n m nq m...( Soeno k k k k k k k n n 6. f, Q V 3, t sec, V V, V 8 V, Q V.8 3, n ( Q Q n tuns/m. t n T c n
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