ELECTROMAGNETIC INDUCTION

Transcription

1 esson-3 EECTOMAGNETIC INDUCTION Mgnetc Flux : Mgnetc flux () through n re s n mgnetc fel s efne s = s () Physclly t represents totl lnes of nucton pssng through gen re Equton () cn be wrtten s A s = s cos () where s ngle between n re ector. Accorng to equton () flux cn chnge not only ue to mgnetc fel n re but lso ue to orentton of re w.r.t.. Dmensonl formul of flux s [M T A ] SI unt of mgnetc flux s olt-sec. whch s lso known s weber. As olt = 8 emu of potentl, the C.G.S. unt of flux, mxwell (Mx) s relte to weber through relton wb = V s = 8 emu of potentl s = 8 Mx. Electromgnetc Inucton If mgnet psses through col n close crcut contnng glnometer, n electrc current s prouce n the crcut. The recton of the current so nuce n the crcut s reerse when the mgnet recees wy from the col. The current so prouce lsts so long s there s relte moton between the mgnet n the col. It s shown tht wheneer the mgnetc flux lnke wth close crcut chnges, n nuce e.m.f. s prouce n the crcut n lsts s long s the flux chnges. Such currents re prouce ue to nuce electromote force n the phenomenon s clle electromgnetc nucton. The mgntue n recton of nuce electromgnetc force s gen by the followng Fry s n enz s lws respectely. Fry s Frst w : Wheneer the mgnetc flux lnke wth close crcut chnges, n nuce electomote force s prouce whch prouces n nuce current n the crcut whch lsts s long s the chnge lsts. Fry s Secon w: The nuce e.m.f. s equl to negte rte of chnge of flux through the crcut. e = G S N

2 The negte sgn shows tht the nuce e.m.f. opposes the chnges n the mgnetc flux. If the col hs N number of turns, then e N. enz s w : The recton of nuce electromote force s such tht t opposes the cuse tht prouces the electromgnetc nucton. If the mgnetc flux chnges from to n tme t, the erge nuce e.m.f. s gen by e (g) N( ). t When the mgnetc flux through close crcut of known resstnce chnges, the quntty of nuce chrge q cn be foun s below: As e N, t e N t q = t = N t t N Totl chnge of flux esstnce Inucton ue to Moton of Strght o n the Mgnetc Fel : Conser strght conuctng ro CD mong wth elocty towrs rght long U shpe conuctor n unform mgnetc fel recte nto the pge. The moton of the conuctor CD results n chngng the re from CDEF to C DEF. It results n chnge of re CDD C n the mgnetc flux proucng n ncrese n the mgnetc flux s =.A If l s the length of ro CD, whch moes wth elocty n tme, chnge n re perpenculr to the fel = CDDC = l = l F C C The mgntue of nuce e.m.f., e = = l l If s the resstnce of loop, the nuce current s E D D l I The recton of the nuce current s gen by Flemng s ght hn rule. [Flemng s ght Hn ule: It sttes tht f the thumb n the frst two fngers of the rght hn re stretche mutully perpenculr to ech other n f the forefnger ges the recton of the mgnetc fel n the thumb ges the recton of moton of the conuctor, then the centrl fnger ges the recton of the nuce current.] The current n the boe mentone loop s n the ntclockwse recton. If the loop CDEF s moe towrs rght wth elocty, the nuce current I wll be flowng n the clock wse recton n ths current wll prouce forces F n F on rms CF n DE respectely whch beng equl n opposte wll cncel. Force F 3 on rm CD = Il where CD = l l C F F 3 D F F E

3 l F 3 = l l where s the resstnce of close loop. Power to pull the loop = F 3 = l. Ths work s completely conerte to het ue to current flowng n the loop. Therefore het prouce n the loop per sec = I = l. Thus, mechncl energy neee to moe the rm CD s conerte nto electrcl energy n then to therml energy. E.M.F. Inuce ue to otton n Mgnetc Fel : () o rottng n mgnetc fel : If lnerly conuctng ro of length l moes wth elocty perpenculr to mgnetc fel, the nuce e.m.f. = E = l. If the ro of length l s rottng n mgnetc fel wth ngulr elocty, Velocty of fferent prts s fferent n ncreses mong from O A. Velocty of element t stnce x from O s x. Inuce emf cross element of length x. e = (x) (x) = (x x) e = x x O A x x = e = recton of emf s gen by rght hn thumb rule. () Col rottng n mgnetc fel : Conser rectngulr conuctng col of re A n N turns s rotte n unform mgnetc fel wth ngulr elocty, s shown n the fgure. As the col rottes, n nuce e.m.f., E s prouce ue to chnge of flux. At ny nstnt re ector of col mkes n ngle wth mgnetc fel, flux lnke wth col s = A cos where = t = A cos t or = A sn t usng Fry s lw e = A sn t e = e sn t

4 The nuce e.m.f. hs snusol rton wth tme n hs mxmum lue of e = NA. Such col conerts mechncl energy nto electrcl energy. It proes the bsc prncple on whch n lterntng current (A.C.) genertor s bse. () Chnge of re nse mgnetc fel chnges : et rectngulr col of wh n length x () nse the mgnetc fel, flux lnke wth col, = A = ( x) x = = () Accorng to Fry s lw e = or e = the recton of nuce emf s gen by enz s lw. x A D Flux lnke wth col lso chnges when mgnetc fel oer col chnge wth tme. INDUCTANCE Self Inuctnce : A mgnetc flux s lnke wth col when constnt current s psse through t. Howeer, when the current s ncrese or reuce n the col, t results n chnge of mgnetc flux ue to whch n e.m.f. s nuce n the col n s clle self nuce e.m.f. ue to the phenomenon of self nucton. The phenomenon of proucton of opposng nuce emf n col s result of ryng current n the col tself s clle self nucton. If current I s flowng n col, mgnetc flux s lnke to the col whch s rectly proportonl to the current I or = I Where s constnt of proportonlty n s clle the self nuctnce of the col or smply nuctnce of the col I e.m.f., nuce n the col, e. The self nuctnce of col s the e.m.f. nuce n t when the rte of chnge of current s unty. The unt of nuctnce s Henry. One Henry s efne s the nuctnce of col n whch n e.m.f. of olt s prouce when the current n the col s chngng t the rte of one mpere per secon. If soleno hs n number of turns per meter n l s ts length wth totl number of turns N = nl n re of cross secton A, ts nuctnce s C = I = N IA = l I N l A. Energy Store n n Inuctor The energy of cpctor s store n the electrc fel between ts pltes. Smlrly n nuctor hs the cpblty of storng energy n ts mgnetc fel.

5 A chngng current n n nuctor cuses n emf between ts termnls The work one per unt tme s power. P = W = e = From W = U or W U = we he, or U U = The totl energy U supple whle the current ncreses from zero to fnl lue s U = U = Ths s the expresson for the energy store n the mgnetc fel of n nuctor when current flows through t. The source of ths energy s the externl source of emf tht supples the current. Mutul Inuctnce If n nuctor s plce close to nother nuctor, n ncrese or ecrese of the current n the frst nuctor prouces mgnetc flux lnke wth ths col whch prouces n nuce e.m.f. n the secon col n s clle s mutul nucton. The phenomenon of proucton of nuce e.m.f. n one col ue to the ryng current n the neghbourng col s clle mutul nucton. If current I P s flowng t ny tme n prmry col P, then the mgnetc flux lnke wth the seconry col S s s whch s rectly proportonl to I P. s I P, s = MI P Where M s constnt clle the mutul nuctnce of two cols. Inuce e.m.f. n the seconry col = e I P e M. The mutul nuctnce M of two cols or crcuts hng self nuctnce n s gen by s I P P S M = K () where K s constnt clle co-effcent of couplng. If cols re woune oer ech other, the couplng s s to be tght otherwse loose. For tght couplng K = so M = whle for other couplng < K <, so M <. Furthermore, from expresson () t s cler tht f =, M wll be zero. Whch mens system cn t he mutul nuctnce wthout hng self nuctnces, howeer conerse my not be true,.e., mutul nuctnce of cols s zero when there s no couplng.

6 Cols n seres n Prllel: () Cols n seres:- Usng Kshchoff s secon lw n the loop E I I E ( + ) I = = e e or I E = E where s equlent self nuctnce of the crcut, n () = + Cols n prllel:- Usng Krchoff s secon lw n the loop I E I I or E = lso E = I = (usng Krchoff s secon lw n loop II) I I I E I II or E = (I + I ) E I where s equlent nuctnce n. Incse of seres groupng of two nuctors, the mutul nuctnce s lso tken nto ccount wth K = then, = + ± M = + + M = + M = + M C Osclltons : If n nuctor of nuctnce s connecte to cpctor of cpctnce C s shown n the crcut there s current I flowng through the crcut t ny tme urng the schrge of the cpctor. The potentl fference cross the cpctor t tht tme = t ny tme t t =. Usng Krchoff s lw n the loop Q I = C Q C I Q, where Q s chrge on the cpctor C C + I

7 Q Q Q As I =, C Q Q C Q Q, Soluton of ths fferentl equton ges rton of Q snusoly s Q = Q cos t. (ssumng tht cpctor hs chrge Q t t = ) Here,. C Q Now, I = = Q sn t or I = Q sn(t) = I sn(t) where, I = wq Energy store n cpctor t ny tme t s U = q C Q C cos t or U = Q 4 C ( + cos t) Whch shows tht energy n cpctor lso chnges snusoly wth ngulr frequency. Energy store n nuctor t ny tme t. U = I = I sn t = I 4 ( cos t) = I 4 [( + cos(t /))] U lso chnges snusoly wth ngulr frequency but legs by / wth U. GOWTH AND DECAY OF CUENT IN CICUIT Conser n nuctor of nuctnce connecte n seres wth resstor whch s connecte n seres to bttery of e.m.f. E n seres through two wy key A,, S s shown n the crcut grm. When the swtch S s connecte to A, the current s the crcut grows from zero lue. When the current strts growng through the nuctnce, bck e.m.f. s nuce n the col ue to self nucton whch opposes the rte of growth of current n the crcut. Smlrly, when the swtch S s connecte to by sconnectng the bttery, the current begns to fll. The current, howeer, oes not fll to zero nstntneously ue to the e.m.f. nuce n the col ue to self nucton whch opposes n reuces the rte of ecy of current n the crcut.

8 Growth of Current : If S s connecte to A urng the growth of current, let I be nstntneous current t ny tme n the crcut. I A bck e.m.f. equl to wll eelop n the crcut so tht I effecte e.m.f n the crcut s E whch s equl to potentl rop of I cross resstor. E or I I E I I Integrtng ths equton between the lmts when the current s zero t tme t = to the nstntneous current I t tme t, I, I I E I t E If I s mxmum current, so tht I = E I = I when [ e t t exp = or t = ] Thus current I pproches lue I symptotclly n grows exponentlly to lue equl to E/. The cure for growth of current n crcut s shown s the fgure. when t =, I = I e e = I = I e e = I.78 =.63 I.78 E = I o.63i o I The current reches lue whch s equl to 63% of the mxmum lue I fter tme of from the begnnng. t secon Tme constnt of the crcut =. The tme constnt of crcut s the tme urng whch the current rses from zero to 63% of ts mxmum lue. I I e t

9 Decy of Current : If swtch S s connecte to, the bttery s sconnecte. The current oes not fll nstntneously from I to zero but ecys slowly ue to the current nuce n the col n the recton I opposte to tht of the fllng current. The nuce e.m.f. n the nuctnce wll be equl to corresponng to the nstntneous current I n resstor t tht tme I I te of ecy of current = I I or I I When t =, The current, I s mxmum n the current t tme t s I. I I I I t t I = I e = I e t Where s the tme constnt of the crcut. When t I I, I I e.37 I e.78 The tme constnt s efne s the tme nterl urng whch the current ecys to 37% of the mxmum current urng the ecy. The rte of ecy of the current shows n exponentl ecy behour s shown n the fgure. The energy store n n nuctor of nuctnce, when the current I s pssng through t, s equl to I whch s n the mgnetc form. Such n C crcut prouces hrmonc oscllton n n electrcl crcut n whch the energy chnges from the electrcl to mgnetc n ce ers. Such osclltons cn be sustne n n electrcl crcut n cn contnue for long tme wth the sme mpltue f there s neglgble resstnce n the crcut.

10 SOVED EXAMPES Ex. Sol.: A squre loop ACDE of re cm n resstnce 5 W s rotte n mgnetc fel = T through 8 () n. s n n. s. Fn the mgntue of e, n q n both the cses. et us tke the re ector S perpenculr to plne of loop nwrs. So ntlly, S n when t s rotte by 8, S. Hence, ntl flux pssng through the loop, = S cos ()( 4 )() = 4. 3 Wb Flux pssng through the loop when t s rotte by 8, f = S cos 8 = () ( 4 )( ) = 4. 3 Wb Therefore, chnge n flux, = f = 8. 3 Wb () Gen t =. s, = 5 e = 8. t. = =.8 olt e =.6 A n q = t =.6. =.6 3 C t =. s e = 8. t. 3 =.4 olt = e.4 5 =.8 A n q = t = (.8)(.) =.6 3 C

11 Ex. A col of re m s plce n mgnetc fel of whch res s = (t + ) T wth re ector n the recton of. Wht s the mgntue of nuce emf t t = sec. Sol.: Angle between re ector n mgnetc fel s = = A cos A e = A = A(4t) e = 8t (Accorng to Fry s lw) At t = sec, e = 8V Ex.3 Sol.: A current = 3.36 ( + t) A ncreses t stey rte n long strght wre. A smll crculr loop of rus 3 m hs ts plne prllel to the wre n s plce t stnce of m from the wre. The resstnce of the loop s Fn the mgntue n the recton of the nuce current n the loop. The stuton s shown n fgure. The fel ue to strght wre t the centre of loop; = 4 I = 7 I m So the flux lnke wth the loop wre = S = r = 7 I ( 3 ) (Are of col s ery smll so oer t cn be tken to be constnt) So emf nuce n the loop ue to chnge of current e = = 3 I Wre oop I = 3.36( + t) so, I A = 6.7 s An hence e = = V An so the nuce current n the loop e 3.44 = = 6 A As ue to ncrese n current n the wre the flux lnke wth the loop wll ncrese, so n ccornce wth enz s lw the recton of current nuce n the loop wll be nerse of tht n wre,.e., ntclockwse.

12 Ex.4 A squre metl wre loop of se cm n resstnce s moe wth constnt elocty n unform mgnetc fel of nucton = Wb m. The mgnetc fel lnes re perpenculr to the plne of the loop recte nto the pper. The loop s connecte to net work of resstors ech of 3. The resstnces of le wres OS n PQ re neglgble. Wht shoul be the spee of the loop so s to he stey current of m A n the loop? Ge the recton of current n the loop. Sol.: o S O A C P Q Gen network of resstnces of 3 s blnce whet stone brge, so A n C re t sme potentl, no current flows through A C. If s effecte resstnce, or = esstnce of loop = 3 + = 4 et spee of loop s e.m.f. = e = l o =. =. Usng Ohm s w e l o. 4 o O P A S Q C 3 3, ms. A 4 4. Drecton of nuce current n the loop s n clockwse recton., Ex.5 In the fgure shown, = e t A, = 4 A n V c (potentl fference cross cpctor) = 3 e t V. Determne b C = F + V C = O = 3 + c V = 4H () n V V c, V b n V c.

13 Sol.: () For cpctor q = CV = 3 e t = 6e t C current through cpctor, c = e t A usng Krchoff s frst lw t juncton o b + = c + = 4 e t + V = = 4 4 e t = 6 e t V Usng Krchoff s secon lw n brnch oc C o c V e t = V c V V c = V c = ( e t )V Now, usng Krchoffs secon lw n brnch ob V e t + 3e t = V V V b = V b = 7 e t V Now, usng Krchoff s secon lw n brnch co V c e t = V V c V = V c = ( + 6 e t )V Ex.6 Sol.: A strght soleno hs 5 turns per cm n prmry n turns n the seconry. The re of cross secton of the soleno s 4 cm. Clculte the mutul nuctnce. Mgnetc fel nse ny pont of soleno = n where n no of turns n prmry n s current n prmry Flux through seconry hng turns n s n = n (A) = n n A M = n = n n S 4 7 = = 5 4 H Ex.7 Wht nuctnce woul be neee to store. kwh of energy n col crryng A current. ( kwh = J) Sol.: V = V = 3.6 = () 6 = 8 H

14 Ex.8 Sol.: A col of resstnce n nuctnce.5 henry s swtche to c olt supply. Clculte the rte of ncrese of current: () t the nstnt of closng the swtch n fter one tme constnt. (c) Fn the stey stte current n the crcut. () Current t ny tme s gen by = e t V e t V t t =, t t = I E.5 = 4 A/S Ex.9 Sol.: = 4 e = 48 A/S (c) Snce stey current s t t = n stey current = 4 A The two rls of rlwy trck nsulte from ech other n the groun, re connecte to mlloltmeter. Wht s the reng of the oltmeter when trn trels t spee of 8 kmh long the trck? Gen the ertcl component of erth s mgnetc fel = 4 Tesl & seprton between the rls = m. As the xle of the trn moes forwr, t cuts the lnes of force of ertcl component of erth s mgnetc fel. The nuce e.m.f ue to chnge of flux s gen by e A A where A s re n s ertcl components of erth s mgnetc fel. If s spee of trn, A l, e l where l = m., =. x 4 T 8 5 m s 66 e =. 4 5 = 3 mlloltmeter wll re m V. Ex. A col of 5 turns n cm meter s me of wre of resstty 6 ohm cm. The col s connecte to source of e.m.f. V n hng neglgble nternl resstnce () Fn the current through the col wht must be the potentl fference cross the col so s to nullfy the erth s mgnetc fel, (H=.34 Guss) t the centre of the col. How shoul the col be plce?

15 Sol.: () us of col = = 5 cm. length of wre = l = r 5 = 5 5 = 5 cm. rus of wre =. cm. re of cross-secton of the wre = (.)² = 4 cm² 6 l 5 4 A usng Ohm s lw, E. A. Mgnetc nucton t the centre of the crculr col, n 4 r 7 5 = 5 Mgnetc nucton ue to erth s mgnetc fel =.34 x 4 T P.D. cross col = = 5 =.5 V. Plne of the col shoul be perpenculr to the mgnetc mern. Ex. An ron core s nserte nto soleno.5 m long wth 4 turns per unt length. The re of cross secton of the soleno s. m. () Fn the relte permeblty of the core when current of 5A flowng through the soleno wnng cretes the mgnetc flux through the cross secton of the soleno equl to.6 3 Wb fn the nuctnce of the soleno. Sol.: Mgnetc nucton t the xs of soleno s = ( r ni), where n re number of turns/unt length. A ().6 3 A m 3.6 Wb m As = µ µ r n I.6 = µ r Totl no. of turns = n l = 4.5 =. nke flux through soleno = N=.6 3 =.3 Wb Nφ.3 =. 64 H = 64 mh. I 5

16 N A Alterntely, = n l A l = (4).5 3 = 64 m H. Ex. The spce s e by the lne A D nto two regons. egon I s fel free n the regon II hs unform mgnetc fel recte nto the plne of pper. ACDA s semcrculr conuctng loop of rus r wth centre t O, the plne of the loop beng n the plne of the pper. The loop s now me to rotte wth constnt ngulr elocty bout n xs pssng through O n the plne of the pper. The effecte resstnce of loop s. () (c) obtn n expresson for the mgntue of nuce current n the loop show the recton of the current when loop s enterng regon II. plot grph between the nuce e.m.f. n tme for two peros of rotton. Sol.: () et t t = loop strts enterng n regon II n t tme t, loop rottes by ngle t tme t flux lnke wth loop, = r. Accorng to Fry s lw e = = r e = r n I = r. Accorng to enz s lw, the recton of current nuce s to oppose the chnge n mgnetc (c) flux. So current nuce n the wre must crete n outwr mgnetc fel. For ong so the recton of current s ntclock wse. When the loop enters the mgnetc fel, the mgnetc flux lnke wth the loop ncreses n e.m.f. s r n one recton. when the loop comes out of the fel, the flux ecreses n e.m.f. s nuce of sme mgntue but n opposte sense. The grph between e.m.f. n tme of rotton for two peros s shown s the fgure

17 Ex.3 A power trnsformer s use to step up n lterntng e.m.f. from V to 4.4 KV to trnsmt 6.6 KW of power. If prmry col hs turns, fn () no. of turns n the seconry the current rtng of the seconry col. Sol.: () es 4.4 N S NP, ep If p s current n prmry, p e p = W 6.6 p 3 A 3 s p N N p s s 3 p. 5 A current rtng of the seconry col s.5 A Ex.4 A long strght wre crres current. At stnces n b from t there re two other wres, prllel to the former one, whch re nterconnecte by resstnce. A connector sles wthout frcton long the wres wth constnt elocty. Assumng the resstnces of the wres, the connector, the slng contcts n the self nuctnce of the frme to be neglgble, fn () the mgntue n the recton of current nuce n the connectors the force requre to mntn the connector s elocty constnt. Sol.: () Mgnetc fel ue to strght current crryng conuctor t stnce r s gen by r Voltge nuce cross r length of slng wre, e = r(usng e = ) Where s spee of slng wre. For nuce emf cross slng wre. e b b r e r r Usng Ohm s lw e log e e b log e b Mgnetc force ctng on slng wre F F r F + r b

18 = r r b e b. log log log b b e e log b e To mntn elocty, force F n mgntue but opposte n the recton of elocty shoul be pple. Ex.5 Two long prllel horzontl rls, stnce prt n ech hng resstnce per unt length, re jone t one en by resstnce. A perfectly conuctng ro MN of mss m s free to sle rls wthout frcton. There s unform mgnetc fel of nucton norml to the plne of the pper n recte nto the pper. A rble force F s pple to the ro MN such tht, s the ro moes, constnt current flows through. () Fn the elocty of the ro n the pple force M N x F s functon of the stnce x of the ro from. Wht frcton of the workone per secon by F s conerte nto het? Sol.: et F be the nstntneous force ctng on the ro MN t ny nstnt t when the ro s t stnce x. The nstntneous flux s gen by = x The nstntneous nuce emf s gen by x e The nstntneous totl resstnce of the crcut = + x Current n the crcut s x x e ) ( esstnce x x ) (.e., elocty x ) ( The nstntneous ccelerton x x x ( ) ( x Instntneous pple force F = m m x ) ( From ths equton ) ( F x m

19 F Het prouce per secon = ² ( + x) m ( x) Power W = F. = F Therefore, Het prouce work one H W F m F( x) 3 3 m ( x ) Ex.6 A metl ro of mss m cn rotte bout horzontl xs O, slng long crculr conuctor of rus. The rrngement s locte n horzontl n unform mgnetc fel of nucton recte to the rng plne. The xs n the rng re connecte to n e.m.f. source to form crcut of resstnce. Deuce the relton ccorng to whch the source e.m.f. must ry to mke the ro rotte wth constnt ngulr elocty. Neglect the frcton, crcut nuctnce n rng resstnce. E t O mg X x Sol.: Inuce e.m.f. cross the ens of the ro e = e x x = Force on the ro f current I flow through It: F = I If the ngulr elocty s constnt so tht torque bout O must nsh. Hence mg sn t = I Current requre through the ro I = mg sn t Ths must be equl to the current ue to totl e.m.f. n the crcut I = E mg sn t E = ( m g sn t + ² ²) Ex.7 Two long wres re plce on pr of prllel rls perpenculr to the wres. The spcng between the rls s lrge compre wth x, the stnce between the wres. oth wres n rls re me of mterl of resstty per unt length. A mgnetc flux ensty s pple perpenculr to the

20 rectngle me by the wres n rls. One wre s moe long the rls wth unform spee whle the other s hel sttonry. Determne how the force on the sttonry wre res wth x n show tht t nshes for lue of x pproxmtely equl to (µ /4) Sol.: et t ny nstnt t, urng the moton of secon wre, the secon wre s t stnce x. The re of the rectngle between the two wres s x. te of chnge of mgnetc flux through the rectngle x ( x ) = = Inuce e.m.f., e I x l l So, the current nuce n the rectngle I s gen by I e.m.f resstnce ( x) The force between the two wres ue to current flow F = x = I 4 x 4 x ( x) The force F, ue to mgnetc fel on the sttonry wres F = I = ( x) ( x) The former force on sttonry wre wll be recte towrs left hn se becuse opposte currents repel ech other whle the force ue to mgnetc fel wll be recte towrs rght hn se ccorng to rght hn rule. F resultnt = F F ( x) 4 x ( x) ( x) 4 ( x) The force wll be zero, when 4( x) or x ~ 4 (neglectng x n comprson wth ) Ex.8 A metl ro OA of mss m n length l s kept rottng wth constnt ngulr spee n ertcl

21 plne bout horzontl xs pssng through the en O. The free en A s rrnge to sle wthout frcton long fxe conuctng crculr rng plce n the sme plne s tht of rotton. A unform n constnt mgnetc fel nucton s pple perpenculr n nto n plne of rotton s shown n fgure. An nuctor n n externl resstnce re connecte through swtch S between the pont O n pont C on the rng to form n electrcl crcut. Neglect the resstnce of the rng n the ro. Intlly, the swtch s open. () Wht s the nuce e.m.f. cross the termnls of the swtch? If the swtch s s close t tme t =, obtn n S expresson for () the current s functon of tme. () torque requre to mntn the constnt ngulr spee, gen tht the ro OA ws long the poste X-xs t t =. Sol.: () The flux enclose by re of sector OA P t the gen nstnt of tme Y O A P C =. r r r The nuce e.m.f. eelope between two ens O n A of the ro, ccorng to Fry s lw e r r r² The negte sgn nctes the recton of e.m.f. whch woul be from A towrs O so s to resst the moton n ntclockwse recton. () Here we cn replce the ro by bttery of e.m.f. r² wth poste termnl pontng towrs O. Now swtch, resstnce n nuctnce re connecte n seres s shown n fgure. At t =, the swtch s close. et current I flows through the crcut. When the current ncreses n the crcut, self nuce e.m.f. y Krchoff s lw, we he or I I s eelope n the nuctnce. I E I = = E I or I E I E + I X or or I I E I t E I [ e t/ ]

22 r I ( e t/ ) () The force ctng on ro ue to nuce current I s gen by F = I ( ) F = r ( e t/ ) r or 3 r F ( e t/ ) y symmetry, ths force my be regre s ctng on the mle pont of ro OA. The torque prouce s gen by r r F. 4 4 ( e t/ ) The torque cts n clockwse recton. To mntn constnt ngulr spee, n externl torque s neee to be pple n ntclockwse recton wth sme tme epenence. Ex.9 A mgnetc fel = ( y/)k s nto the pper n the +Z recton. n re poste constnts. A squre loop EFGH of se, mss m n resstnce, s ntlly locte n X Y plne. It strt fllng uner the nfluence of grty. Note the rectons of X n Y xes s shown n fgure. Fn. () (c) the nuce current n the loop n ncte ts recton, the totl lorentz force ctng on the loop n ncte ts recton n expresson for the spee of the loop, (t) n ts termnl elocty. O Y E H F G X g Sol.: () et be the elocty of the loop t ny tme t. Inuce e.m.f. n HG s gen by e HG ( y ) = (y + ), ( = )...() (nuce emf n wre mong wth spee s equl to l sn ) The potentl of G wll be hgher thn the potentl of H (usng flemng s rght hn rule) Smlrly, y = y, ( = )...() eef Here F s t hgher potentl. e EH n e FG = so, the current n the crcut ( y ) y The current wll be n ntclock wse recton s shown n fgure. The lorentz forces on EF n HG re gen s E H ( y) ( y + ) F G

23 y EF Β F (long + Y xs) y ) ( Β F HG (long Y xs) Dfferent elements wll experence fferent forces s shown n fgure. Net orentz force X O Y E F H G FEF E HG F = (y + ) y = ( long Y xs) j) ( F (c) Net force ctng on the frme F mg or mg m or m mg C / log m t mg Where c s constnt of ntegrton. Applyng the ntl conton.e., t t =, =. Hence C = ) log( mg ) log( log mg m t mg or mg m t mg log log / m t e mg n Termnl elocty termnl = mg (t t = )

24 OJECTIVE QUESTIONS. When the number of turns n the length of the soleno re ouble keepng the re of cross-secton sme, the nuctnce () remns the sme s hle (c) s ouble () becomes four tmes.. A col of cm cm hng 5 turns s mkng 5 r.p.s. n mgnetc fel of nucton tesl. The pek lue of nuce e.m.f. s pproxmtely () olt olt (c) 34 olt () 68 olt 3. Two cols X n Y re plce n crcut such tht current chnges by 3 mpere n col X n the mgnetc flux chnges of. weber occurs n Y. The lue of mutul nuctnce of the col s (). H.4 H (c).6 H () 3.6 H 4. A col of re cm hng 5 turns s perpenculr to mgnetc fel of ntensty. weber/m. The resstnce of the col s. If t s remoe n sec. from the mgnetc fel, the nuce chrge prouce s () 5 C.5 C (c).5 C ().5 C 5. A force of N s requre to moe conuctng loop through non-unform mgnectc fel t m/s. The rte of chnge of nternl energy n wtt n loop s () 5 (c) 5 () 6. A col of conuctng wre of rus r hs 6 turns n self nuctnce of 8 mh. The self nuctnce of smlr col of 5 turns wll be () 75 mh 8 mh (c) 9 mh () 6.5 mh 7. Two pure nuctor cols of self nuctnce ech re connecte n seres, the net nuctnce s () (c) / () /4 8. An eroplne s flyng horzontlly wth elocty of 36 km/hr. The stnce between the tps of wngs s 5 m. If the ertcl component of erth s mgnetc fel s 4 x 4 T, nuce e.m.f. s () zero V (c) mv () V 9. A crculr rng of meter cm hs resstnce. ohm. How much chrge wll flow through the rng f t s rotte from poston perpenculr to the unform mgnetc fel of = T to poston prllel to fel? () 4 C 6.8 C (c) 3.4 C () 5. C. A rectngulr loop wth slng connector of length cm s stute n unform mgnetc fel perpenculr to plne of the loop. The mgnetc nucton s. T n resstnce of connector s ohm. The ses A n C D he resstnces ohm n 3 ohm respectely. Fn the current n the connector urng ts moton wth constnt elocty of one metre/sec. () A A (c) A D 3 C A () A 44 55

25 . Two fferent cols he self nuctnces = 8 mh, = mh. The current n one col s ncrese t constnt rte. The current n the secon col s lso ncrese t the sme constnt rte. At certn nstnt of tme, the power gen to the two cols s the sme. At tht tme the current, the nuce oltge n the energy store n the frst col re, V n W respectely. Corresponng lues for the secon col t the sme nstnt re, V n W respectely. Then whch nswer s not correct () / = /4 / = 4 (c) W /W = 4 () V /V = /4. The rto of seconry to the prmry turns n trnsformer s 5. If the output oltge be P, the nput oltge neglectng ll losses, must be equl to () 5 P 5 P (c) P/5 () P / 5 3. A rectngulr col of turns n sze. m x.5 m s plce perpenculr to mgnetc fel of. T. If the fel rops to.5 T n.5 s, the mgntue of the e.m.f. nuce n the col s ().5 V.75 V (c). V ().5 V 4. A col of re cm, turns n resstnce s plce n mgnetc fel recte perpenculr to the plne of the col n chngng t the rte of 8 guss/secon. The nuce current n the col wll be () 5 A.5 A (c).5 A () 5 A 5. A col of cross-sectonl re 4 cm hng 3 turns s mkng 8 re/mn n mgnetc fel of T. The pek lue of the nuce e.m.f. s () 3 V 6 V (c) 339 V () 45 V 6. A soleno hs turns woun oer length of.3 m. Its cross-sectonl re s. 3 m. Aroun ts centrl secton col of 3 turns s woun. If n ntl current of A flowng n the soleno s reerse n.5 s, the e.m.f nuce n the col wll be () 6. 4 V 6. V (c) V () 4.8 V 7. A squre metl loop of se cm n resstnce ohm s moe wth constnt elocty prtly nse unform mgnetc fel of 5 Wb/m, recte nto the pper, s shown n the fgure. The loop s connecte to network of fe resstors ech of lue. If stey current of. A flows n the loop, n the spee of the loop s m/s, then s equl to () 3 (c) 8 () 9 8. A rectngulr col of sngle turn, hng re A, rottes n unform mgnetc fel wth n ngulr elocty bout n xs perpenculr to the fel. If ntlly the plne of the col s perpenculr to the fel, then the erge nuce e.m.f. when t hs rotte through 9 s () A A (c) A 4 () A

26 9. An e.m.f. of 5 V s pple n crcut contnng 5 H nuctnce n resstnce. The rto of the currents t tme t = n t t = s s () e e e e (c) e () e. An el trnsformer s use to step own n lterntng e.m.f. of V to 4.4 V to trnsmt 6.6 W of power. The current rtng of the seconry s () 3 A 3 A (c).5 A () A. A rectngulr loop of ses 8 cm n cm s lyng n unform mgnetc fel of mgntue.5 T wth ts plne norml to the fel. The fel s now grully reuce t the rte of. T/s. If the resstnce of the loop s.6, then the power sspte by the loop s het s () 6.4 W 3. W (c) W () 3. 5 W. A current of A flowng through col of turns ges rse to mgnetc flux of 5 5 Wb per turn. The mgnetc energy ssocte wth the col s () 5 J.5 J (c).5 J ().5 J 3. The tme constnt of n nuctnce col s. 3 s. When 9 resstnce s jone n seres, the tme constnt becomes.5 3 s. The nuctnce n resstnce of the col re () 3 mh; 3 3 mh;6 (c) 6 mh;3 () 6 mh;6 4. Two resstors of n n n el nuctor of H re connecte to V bttery s shown. The key K s nserte t tme t =. The ntl (t t = ) n fnl (t t = ) currents through the bttery re H K () 5 A; A V A; 5 A (c) 5 A; A () A; 5 5 A 5. A cpctor of F ntlly chrge to V s connecte cross n el nuctor of. mh. The mxmum current n the crcut s ().6 A A (c).5 A () A 6. A long soleno hng turns per cm s crryng lterntng current of one mpere pek lue. A serch col of re of cross-secton 4 m n of turns s plce n the mle of the soleno so tht ts plne s perpenculr to the xs of the soleno. The serch col regsters pek oltge.5 V. The frequency of the current n the soleno s- ().6 per secon.6 per secon (c) 5.9 per secon () 5.85 per secon

27 7. A smll squre loop of wre of se l s plce nse lrge squre loop of wre of se (>> ). The loops re co-plnr n ther centers conce. The mutul nuctnce of the system s proportonl to () / / (c) / () / 8. A col of re 7 cm n of 5 turns s kept wth ts plne norml to mgnetc fel. A resstnce of 3 ohm s connecte to the resstnce-less col. s 75 exp ( t) guss. The current pssng through the resstnce t t = 5 ms wll be- ().64 ma.5 ma (c).75 ma ().6 ma 9. Two nuctnces n re plce fr prt n n prllel. Ther combne nuctnce s () ( ) (c) ( ) () ( ) 3. A conuctor s bent n -shpe n nother conuctor s slng wth constnt elocty recte perpenculr to ts length s shown n the fgure. The slng conuctor lwys mkes equl ngle wth the two rms of the bent conuctor. If resstnce per unt length of ech conuctor s r then current n the loop forme by conuctors s : () V ( )r V ( )r (c) V ( )r () V ( )r MOE THAN ONE COECT CHOICE 3. A conuctng ro of length s hnge t pont O. It s free to rotte n ertcl plne. There exsts unform mgnetc fel n horzontl recton. The ro s relese from the poston shown n the fgure. The potentl fference between the two ens of the ro s proportonl to : O q () 3/ (c) sn () (sn) / 3. A crculr conuctng loop of rus r n hng resstnce per unt length s shown n the fgure s plce n mgnetc fel whch s constnt n spce n tme. The ens of the loop re crosse n pulle n opposte rectons wth elocty V such tht the loop lwys remns crculr n the rus of the loop goes on ecresng, then () (c) () rus of the loop chnges wth r = r t/. EMF nuce n the loop s functon of tme s e = (r t/) Current nuce n the loop s Current nuce n the loop s I I V

28 33. A constnt current s mntne n soleno. Whch of the followng qunttes wll ncrese f n ron ro s nserte n the soleno long ts xs? () mgnetc fel t the centre mgnetc flux lnke wth the soleno (c) self-nuctnce of the soleno () rte of Joule hetng 34. Two fferent cols he self nuctnce = 8 mh, = mh. The current n one col s ncrese t constnt rte. The current n the secon col s lso ncrese t the sme rte. At certn nstnt of tme, the power gen to the two cols s the sme. At tht tme the current the nuce oltge n the energy store n the frst col re, V n W respectely. Corresponng lues for the secon col t the sme nstnt re, V n W respectely. Then () / = /4 / = 4 (c) W /W = 4 () V /V = /4 35. A smll mgnet M s llowe to fll through fxe horzontl conuctng rng. et g be the ccelerton ue to grty. The ccelerton of M wll be : () (c) () < g when t s boe n mong towrs > g when t s boe n mong towrs < g when t s below n mong wy from > g when t s below n mong wy from 36. The mgnetc flux (f) lnke wth col epens on tme t s f = t n, where s constnt. The nuce e.m.f. n the col s e : () If < n <, e = If < n <, e & e ecreses wth tme (c) f n =, e s constnt () If n >, e ncreses wth tme 37. If n E enote nucton of mgnetc fel n energy ensty t the mpont of long soleno crryng current I, then whch of the followng grphs s/re correct? () (c) () 38. A loop s forme by two prllel conuctors connecte by soleno wth nuctnce n conuctng ro of mss M whch cn freely sle oer the conuctors. The conuctors re locte n unform mgnetc fel wth nucton perpenculr to the plne of loop. The stnce between conuctors s l. At t =, the ro s gen elocty recte towrs rght n the current through the nuctor s ntlly zero. M () The mxmum current n crcut urng the moton of ro s The ro moes for some stnce n comes to permnently rest. (c) The elocty of ro when current n the crcut s hlf of mxmum s 3 () The ro osclltes n SHM.

29 39. A metl sheet s plce n front of strong mgnetc pole. A force s neee to : () hol the sheet there f the metl s mgnetc hol the sheet there f the metl s nonmgnetc (c) moe the sheet wy from the pole wth unform elocty f the metl s mgnetc () moe the sheet wy from the pole wth unform elocty f the metl s nonmgnetc Neglect ny effect of prmgnetsm, mgnetsm n grty. 4. A conuctng ro of length s moe t constnt elocty on two prllel, conuctng, smooth, fxe rls, tht re plce n unform constnt mgnetc fel perpenculr to the plne of the rls s shown n fgure. A resstnce s connecte between the two ens of the rl. Then whch of the followng s/re correct x () (c) () The therml power sspte n the resstor s equl to rte of work one by externl f pple externl force s ouble thn prt of externl power ncreses the elocty of ro. enz s lw s not stsfe f the ro s ccelerte by externl force If resstnce s ouble then power requre to mntn the constnt elocty becomes hlf.

30 MISCEANEOUS ASSIGNMENT Comprehenson- Inuctnce of col or crcut cn be efne s properly by rtue of whch, the col or crcut opposes ny chnge n the flux lnke to t. Wheneer one tres to chnge the flux, the col or crcut prouces nuce current or nuce e.m.f., so tht t cn oppose the cuse of the chnge of flux. It s lso clle electromgnetc nert, whch opposes ny chnge n ts electromgnetc stte. Mgnetc flux s proportonl to the current (I) flowng s = I, where s proportonlty constnt, clle self nuctnce. Energy n mgnetc fel nse nuctor cn be ssocte s U = (/)I, where s self nuctnce n I s the current flowng through t. Now nswer the followng. In the shown fgure mgnet s plce long the xs of conuctng col. If mgnet s pushe towrs cols () col get ttrcte towr mgnet col get repelle wy from mgnet S N (c) force on mgnet cts wy from col () col behes lke mgnet. In the shown - crcut swtch s thrown from () to () t tme t = () Just fter closng the swtch current becomes hlf Just fter closng the swtch current wll not chnge (c) ong tme fter closng the swtch current n the crcut s equl to E/ I E S () ong tme fter closng the swtch current s E/ 3. In the shown n the fgure smooth col hng n smooth ron ro, plce s shown n the fgure. Mss of ro s m n self nuctnce of col n resstnce. If force F s pple on the ro (neglectng grty) just fter the force s pple. () ccelerton of ro s F/m F ccelerton of ro s less thn F/m Comprehenson- An nuctor hng self nuctnce wth ts col resstnce s connecte cross bttery of emf. When the crcut s n stey stte t t = n ron ro s nserte nto the nuctor ue to whch ts nuctnce becomes n (n > ). (c) ccelerton of ro s more thn F/m () none of these E

31 4. After nserton of ro whch of the followng qunttes wll chnge wth tme? () Potentl fference cross termnls A n () Inuctnce (3) te of het prouce n col () only () () n (3) (c) only (3) () (), () n (3) 5. After nserton of ro, current n the crcut : () Increses wth tme (c) emns constnt wth tme Decreses wth tme () Frst ecreses wth tme then becomes constnt 6. When gn crcut s n stey stte, the current n t s : () I < / I > / (c) I = / () None of these 7 Tme ryng mgnetc fel s present n crculr regon of rus. Then Column I Column II A. If ro s plce long the meter of the (p) Electrc fel s perpenculr to the length of mgnetc fel the ro.. Inuce electrc fel t pont wthn (q) Constnt long the length of conuctor. mgnetc fel (r < ) C. Inuce electrc fel t pont out se the (r) mgnetc fel (r > ) D. Inuce electrc fel n conuctor hs (s) r r component prllel to length of conuctor 8. Column II ges tme lue for the current to rech A the lues of menton n column I for the crcut. Column I Column II A. (p) 3 ms. 5 (q) 3.8 ms C. 6 (r) 6.45 ms D. (s) 9. When the current n col chnges from 8A to A n 3 s. The emf nuce n the col s V. Then the self-nuctnce of the col s (n) mh. Fn the lue of n. The current (n mpere) n n nuctor s gen by I = t, where t s n secon. The self-nuce emf n t s mv. The self nuctnce s 6.5 n 4 H. Fn the lue of n.

32 . Two conuctng rngs of r r n r moe n opposte rectons wth eloctes n respectely on conuctng surfce S. There s unform mgnetc fel of mgntue perpenculr to the plne of the rngs. The potentl fference between the hghest ponts of the two rngs s n r. Fn the lue of n. r x S. The loop shown moes wth elocty n unform mgnetc fel of mgntue, recte nto the r pper. The potentl fference between P n Q s. Fn the lue of n. n P / x Q 3. A current of A s ncresng t rte of 4 A/s through col of nuctnce H. The energy store n the nuctor per unt tme s 4n J/s (when current ws A). Fn the lue of n. 4. Three nuctnces re connecte s shown below. Assumng no couplng, the resultnt nuctnce s n H. Fn the lue of n..5 H 5. In n nuctor of self-nuctnce = mh, current chnges wth tme ccorng to relton I = t e t then fn the tme n secon when nuce emf s. 6. The current n col res w.r. to tme t s = 3t + t. If the nuctnce of col be mh, the lue of H H nuce e.m.f. t t = s s.7 n V. Fn the lue of n. 7. A crculr col of rus 5 cm hs 5 turns of wre. The pproxmte lue of the coeffcent of selfnucton of the col s 5n mh. Fn the lue of n. 8. A current of A n the prmry col of crcut s reuce to zero t unform rte n 3 secon. If the coeffcent of mutul nuctnce s 3H, the nuce e.m.f. n the seconry col s n kv. Fn the lue of n.

33 PEVIOUS YEA QUESTIONS IIT-JEE/JEE-ADVANCE QUESTIONS. A nonconuctng rng of rus.5 m crres totl chrge of. C strbute non unformly on ts crcumference proucng n electrc fel E eerywhere n spce. The lue of the lne ntegrl l l E l (l = beng centre of the rng) n olt s () + (c) () zero. A crculr loop of rus, crryng current I, les n x- y plne wth ts centre t orgn. The totl mgnetc flux through x-y plne s () rectly proportonl to I rectly proportonl to (c) rectly proportonl to () zero 3. A col of wre hng nuctnce n resstnce hs conuctng rng plce coxlly wthn t. The col s connecte to bttery t tme t =, so tht tme-epenent current I (t) strts flowng through the col. If I (t) s the current nuce n the rng, n (t) s the mgnetc fel t the xs of the col ue to I (t), then s functon of tme (t > ), the prouct I (t) (t) () Increses wth tme ecreses wth tme (c) oes not ry wth tme () psses through mxmum 4. Two entcl crculr loops of metl wres re lyng on tble wthout touchng ech other. oop A crres current whch ncreses wth tme. In response, the loop () remns sttonry s ttrcte by the loop A (c) s repelle by the loop A () rottes bout ts CM, wth CM fxe 5. A col of nuctnce 8.4 mh n resstnce 6 s connecte to V bttery. The current n the col s A t pproxmtely the tme () 5 s ms (c) 35 ms () ms 6. A rectngulr loop of wh, length b s locte t stnce c from long strght wre crryng current I. The wre s prllel to the long se of the loop. The mgnetc flux through the loop s. Ib () = = ln c Ib c (c) = ln () = c I c b ln b 7. A unform but tme-ryng mgnetc fel (t) exsts n crculr regon of rus n s recte nto the plne of the pper, s shown. The mgntue of the nuce electrc fel t pont P t stnce r (r > ) from the centre of the crculr regon () s zero ecreses s (/r) (c) ncreses s r () ecreses s (/r )

34 8. The mtul nuctnce between the rectngulr loop n the long strght wre s shown n the fgure s M. () M = zero M = c ln b b c (c) M = ln b () M = b ln c 9. The network shown n the fgure s prt of complete crcut. At certn nstnt, the current I s 5A n t s ecresng t rte of 3 As. Then V V A equls () V 5 V (c) V () 5 V. A mgnetc fel exsts prllel to the xs of long cylnrcl olume of rus. If t s ncresng t the rte, then electrc fel t stnce r from ts xs s () E = r for r < E = 4 for r < (c) E = r for r > () E = r for r >. The mgnetc flux ensty s chngng n mgntue t constnt rte. A gen mss m of copper, rwn nto wre of rus n forme nto crculr loop of rus r s plce perpenculr to the fel. The nuce current n the loop s. The resstty of copper s n ensty s. () = m 4 = m 4 r (c) = m 4 () = m. Fgure shows lne of the fel whch of the followng fel(s) s(re) not shown by the fgure () electrc fel mgnetc fel (c) nuce electrc fel () grttonl fel Comprehenson Moern trns re bse on Mgle technology n whch trns re mgnetclly lette, whch runs ts EDS Mgle system. There re cols on both ses of wheels. Due to moton of trn current nuces n the col of trck whch lette t. Ths s n ccornce wth lenz.s lw. If trns lower own then ue to lenz.s lw repulse force ncreses ue to whch trn gets uplfte n f t goes much hgh then there s net ownwr force ue to grty. The ntge of mgle trn s tht there s no frcton between the trn n the trck, thereby reucng power consumpton n enblng the trn to ttn ery hgh spees.

35 Dsntge of mgle trn s tht s t slows own the electromgnetc forces ecreses n t becomes ffcult to keep t lette n s t moes forwr ccorng to enz lw there s n electromgnetc rg force. 3. Wht s the ntge of ths system? () No frcton hence no power consumpton No electrc power s use (c) Grtton force s zero () Electrosttc force rws the trn 4. Whch force cuses the trn to elete up? () Electrosttc force Tme ryng electrc fel (c) Mgnetc force () Inuce electrc fel 5. Wht s the sntge of ths system? () Trn experences upwr force ccorng to enz s lw (c) () Frcton force crete rg on the trn etrton y enz s lw trn experence rg 6. A crculr wre loop of rus s plce n the x-y plne centere t the orgn O. A squre loop of se ( << ) hng two turns s plce wth ts centre t z = 3 long z 45 the xs of the crculr wre loop, s shown n fgure. The plne of the squre loop mkes n ngle of 45 wth respect to the z-xs. If the mutul nuctnce between the loops s gen by o p /, then the lue of p s 7. A current crryng nfntely long wre s kept long the meter of crculr wre loop, wthout touchng t. The correct sttement (s) s (re) () (c) () The emf nuce n the loop s zero f the current s constnt The emf nuce n the loop s fnte f the current s constnt The emf nuce n the loop s zero f the current ecreses t stey rte The emf nuce n the loop s fnte f the curent ecreses t stey rte. Prgrph A pont chrge Q s mong n crculr orbt of rus n the x-y plne wth n ngulr elocty. Ths cn be consere s equlent to loop crryng stey current Q. A unform mgnetc fel long the poste z-xs s now swtche on, whch ncreses t constnt rte from to n one secon. Assume tht the rus of the orbt remns constnt. The pplcton of the mgnetc fel nuces n emf n the orbt. The nuce emf s efne s the work one by n nuce electrc fel n x O y

36 mong unt poste chrge roun close loop. It s known tht, for n orbtng chrge, the mgnetc pole moment s proportonl to the ngulr momentum wth proportonlty constnt. 8. The mgntue of the nuce electrc fel n the orbt t ny nstnt of tme urng the tme nterl of the mgnetc fel chnge s () 4 () 9. The chnge n the mgnetc pole moment ssocte wth the orbt, t the en of the tme nterl of the mgnetc fel chnge s () Q Q (c) DCE QUESTIONS Q () Q. Two cols of self nuctnce n re plce so close together tht effecte flux n one col s completely lnke wth other. If M s mutul nuctnce between them, M = () / (c) ( ) (). Fn out the emf prouce when the current chnges from to A n S, = H () V V (c) mv (). V 3. enz s lw pples to () electrosttcs lenses (c) electromgnetc nucton () cnem sles 4. Fry s secon lw sttes tht mss eposte on the electroe s rectly proportonl to () tomc mss tomc mss lncy (c) tomc mss/lncy () lency 5. Dmensons of Mgnetc flux re () M T M T A (c) M T A () M T I 6. If col s open then n becomes (),, (c), (), 7. In col when current chnges from A to A n tme. sec, nuce emf s 3.8 V. Wht s self nuctnce of col () 4 H.4 H (c).4 H () 5 H 8. Flemng s left n rght hn rule re use n () D.C. motor & A.C. genertor D.C. genertor & A.C. motor (c) D.C. motor & D.C. genertor () both rules re sme, ny one cn be use

37 9. Coeffcent of couplng between two cols of self nuctnces n s unty. If mens () 5% flux of s lnke wth % flux of s lnke wth (c) tme of flux of s lnke wth () none of these MAINS QUESTIONS. A col of nuctnce 3 mh n resstnce s connecte to sources of oltge V. The current reches hlf of ts stey stte lue n ().5 s.3 s (c).5 s (). s. The self nuctnce of the motor of n electrc fn s H. In orer to mprt mxmum power t 5 Hz, t shoul be connecte to cpctnce of () F F (c) 4 F () 8 F 3. The flux lnke wth col t ny nstnt t s gen by = t 5t + 5 The nuce emf t t = 3 s s () 9 V V (c) V () 9 V 4. A long soleno hs turns per cm n crres current. The mgnetc fel t ts centre s 6.8 Weber/m. Another long soleno hs turns per cm n t crres current /3. The lue of the mgnetc fel t ts centre s ().5 Weber/m.5 5 Weber/m (c).5 3 Weber/m ().5 4 Weber/m 5. An nuctor ( = mh), resstor ( = ) n bttery (E = V) re ntlly connecte n seres s shown n the fgure. After long tme the bttery s sconnecte fter short crcutng the ponts A n. The current n the crcut ms fter the short crcut s () /e A (c) () e A. A A A E 6. An nuctor of nuctnce = 4mH n resstors of resstnces = n = re connecte to bttery of emf V s shown n the fgure. The nternl resstnce of the bttery s neglgble. The swtch S s close t t =. The potentl rop cross s functon of tme s () e 3t V t 6 e t V (c) e 5t V () 6 e 5t V E S

38 7. In the crcut shown below, the key K s close t t =. The current through the bttery s () V t t = n V + t t = V K (c) () V( ) V t t = n t t = V V + t t = n t t = V t t = n V( ) t t = 8. A resstor n F cpctor n seres s connecte through swtch to V rect supply. Across the cpctor s neon bulb tht lghts up t V. Clculte the lue of to mke the bulb lght up 5s fter the swtch hs been close. (log.5 =.4) () (c).7 6 () A bot s mong ue est n regon where the erth s mgnetc fel s 5. 5 NA m ue north n horzontl. The bot crres ertcl erl m long. If the spee of the bot s.5 ms, the mgntue of the nuce emf n the wre of erl s () mv.75 mv (c).5 mv ().5 mv. The fgure shows n expermentl plot for schrgng of cpctor n n -C crcut. The tme constnt of ths crcut les between Potentl fference V n olts Tme t s secons () 5 n sec n 5 sec (c) 5 sec n sec () sec & 5 sec. A metllc ro of length I s te to strng of length l n me to rotte wth ngulr spee on horzontl tble wth one en of the strng fxe. If there s ertcl mgnetc fel n the regon, the e.m.f nuce cross the ens of the ro s () 4l 5l (c) l () 3l

39 ASIC POEMS. A copper ro of length.9 m s mong wth unform elocty m/s prllel to long strght wre crryng current of 5. A. The ro tself s perpenculr to the wre wth ts ens t stnces. m n. m from t. Clculte the e.m.f. nuce n the ro. 5A m/s. m. m. A long soleno of meter. m hs 4 turns per metre. At the centre of the soleno turn col of rus. m n resstnce s plce wth ts xs concng wth the soleno xs. The current n the soleno s ecrese t constnt rte from + A to A n.5 s. Fn the e.m.f. nuce n the col. Also fn the totl chrge flowng through the col urng ths tme. 3. A ery smll crculr loop of re 5 4 m, resstnce n neglgble nuctnce s ntlly coplnr n concentrc wth much lrger fxe crculr loop of rus. m. A constnt current of mpere s psse n the bgger loop n the smller loop s rotte wth ngulr elocty r/s bout meter. Clculte s functon of tme () the flux lnke wth the smller loop, nuce e.m.f. (c) nuce current n the smller loop. 4. A close col conssts of 5 turns on rectngulr frme of re 4. cm n hs resstnce of 5. The col s kept wth ts plne perpenculr to unform mgnetc fel of. T. Clculte the mount of chrge flowng through the col f t s turne oer (rotte through 8 ). Wll the nswer epen on the spee wth whch the col s rotte? 5. A long soleno hng turns per cm crres n lterntng current of pek lue mpere. A serch col hng cross-sectonl re of 4 m n turns s kept n the soleno so tht ts plne s perpenculr to the xs of the soleno. The serch col regsters pek oltge of.5 olt. Fn the frequency of the current n the soleno. 6. A col of nuctnce H n resstnce s connecte cross bttery of V long wth key. At tme t =, the key s close. Fn () (c) () tme constnt of the crcut stey-stte current n the crcut current n the crcut t t = s mgnetc energy store n the col n the stey stte. 7. Two long prllel wres of zero resstnce re connecte to ech other by bttery of. olt. The seprton between the wres s.5 m. A metllc br, whch s perpenculr to the wres n of resstnce moes on these wres whle mgnetc fel of. Tesl s ctng perpenculr to the plne contnng the br n the wres. Fn the stey stte elocty of the br. If mss of the br s. kg, fn ts elocty s functon of tme.