Questions. denotes answer available in Student Solutions Manual/Study Guide; O denotes objective question

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1 Qustions 95 Qustions dnots nswr vill in tudnt olutions Mnul/tudy Guid; O dnots ojctiv qustion. Th currnt in circuit contining coil, rsistor, nd ttry hs rchd constnt vlu. Dos th coil hv n inductnc? Dos th coil ffct th vlu of th currnt? 2. Wht prmtrs ffct th inductnc of coil? Dos th inductnc of coil dpnd on th currnt in th coil? 3. O nitilly, n inductor with no rsistnc crris constnt currnt. Thn th currnt is rought to nw constnt vlu twic s lrg. Aftr this chng, wht hs hppnd to th mf in th inductor? () t is lrgr thn for th chng y fctor of 4. () t is lrgr y fctor of 2. (c) t hs th sm nonzro vlu. (d) t continus to zro. () t hs dcrsd. 4. O A long, fin wir is wound into coil with inductnc 5 mh. Th coil is connctd cross th trminls of ttry, nd th currnt is msurd fw sconds ftr th connction is md. Th wir is unwound nd wound gin into diffrnt coil with 0 mh. This scond coil is connctd cross th sm ttry, nd th currnt is msurd in th sm wy. Comprd with th currnt in th first coil, is th currnt in th scond coil () four tims s lrg, () twic s lrg, (c) unchngd, (d) hlf s lrg, or () on-fourth s lrg? 5. O Two solnoidl coils, A nd B, r wound using qul lngths of th sm kind of wir. Th lngth of th xis of ch coil is lrg comprd with its dimtr. Th xil lngth of coil A is twic s lrg s tht of coil B, nd coil A hs twic s mny turns s coil B. Wht is th rtio of th inductnc of coil A to tht of coil B? () 8 () (c) 2 (d) () (f) (g) 6. A switch controls th currnt in circuit tht hs lrg inductnc. s sprk (Fig. Q32.6) mor likly to producd t th switch whn th switch is ing closd, whn it is ing opnd, or dosn t it mttr? Th lctric rc cn mlt nd oxidiz th contct surfcs, rsulting in high rsistivity of th contcts nd vntul dstruction of th switch. Bfor lctronic ignitions wr invntd, distriutor contct points in utomoils hd to rplcd rgulrly. witchs in powr distriution ntworks nd switchs controlling lrg motors, gnrtors, nd lctromgnts cn suffr from rcing nd cn vry dngrous to oprt. Alxndr Hédr Figur Q O n Figur Q32.7, th switch is lft in position for long tim intrvl nd is thn quickly thrown to position. nk th mgnituds of th voltgs cross th four cir- 8 cuit lmnts short tim thrftr from th lrgst to th smllst. 2.0 V Figur Q H 8. Considr th four circuits shown in Figur Q32.8, ch consisting of ttry, switch, lightul, rsistor, nd ithr cpcitor or n inductor. Assum th cpcitor hs lrg cpcitnc nd th inductor hs lrg inductnc ut no rsistnc. Th lightul hs high fficincy, glowing whnvr it crris lctric currnt. (i) Dscri wht th lightul dos in ch of circuits (), (), (c), nd (d) ftr th switch is thrown closd. (ii) Dscri wht th lightul dos in ch circuit ftr, hving n closd for long tim intrvl, th switch is thrown opn. () (c) Figur Q O Don t do this; it s dngrous nd illgl. uppos criminl wnts to stl nrgy from th lctric compny y plcing flt, rctngulr coil of wir clos to, ut not touching, on long, stright, horizontl wir in trnsmission lin. Th long, stright wir crris sinusoidlly vrying currnt. Which of th following sttmnts is tru? () Th mthod works st if th coil is in vrticl pln surrounding th stright wir. () Th mthod works st if th coil is in vrticl pln with th two long sids of th rctngl prlll to th long wir nd qully fr from it. (c) Th mthod works st if th coil nd th long wir r in th sm horizontl pln with on long sid of th rctngl clos to th wir. (d) Th mthod works for ny orinttion of th coil. () Th mthod cnnot work without contct twn th coil nd th long wir. 0. Considr this thsis: Josph Hnry, Amric s first profssionl physicist, cusd th most rcnt sic chng in () (d)

2 96 Chptr 32 nductnc th humn viw of th Univrs whn h discovrd slfinduction during school vction t th Alny Acdmy out 830. Bfor tht tim, on could think of th Univrs s composd of only on thing: mttr. Th nrgy tht tmporrily mintins th currnt ftr ttry is rmovd from coil, on th othr hnd, is not nrgy tht longs to ny chunk of mttr. t is nrgy in th msslss mgntic fild surrounding th coil. With Hnry s discovry, Ntur forcd us to dmit tht th Univrs consists of filds s wll s mttr. Argu for or ginst th sttmnt. n your viw, wht mks up th Univrs?. O f th currnt in n inductor is dould, y wht fctor is th stord nrgy multiplid? () 4 () 2 (c) (d) 2 () 4 2. O A solnoidl inductor for printd circuit ord is ing rdsignd. To sv wight, th numr of turns is rducd y on-hlf with th gomtric dimnsions kpt th sm. By how much must th currnt chng if th nrgy stord in th inductor is to rmin th sm? () t must four tims lrgr () t must two tims lrgr (c) t must lrgr y fctor of 2. (d) t should lft th sm. () t should on-hlf s lrg. (f) No chng in th currnt cn compnst for th rduction in th numr of turns. 3. Discuss th similritis twn th nrgy stord in th lctric fild of chrgd cpcitor nd th nrgy stord in th mgntic fild of currnt-crrying coil. 4. Th opn switch in Figur Q32.4 is thrown closd t t 0. Bfor th switch is closd, th cpcitor is unchrgd nd ll currnts r zro. Dtrmin th currnts in, C, nd nd th potntil diffrncs cross, C, nd () t th instnt ftr th switch is closd nd () long ftr it is closd. C 5. O Th cntrs of two circulr loops r sprtd y fixd distnc. (i) For wht rltiv orinttion of th loops is thir mutul inductnc mximum? () coxil nd lying in prlll plns () lying in th sm pln (c) lying in prpndiculr plns, with th cntr of on on th xis of th othr (d) Th orinttion mks no diffrnc. (ii) For wht rltiv orinttion is thir mutul inductnc minimum? Choos from th sm possiilitis. 6. n th C circuit shown in Figur 32.0, th chrg on th cpcitor is somtims zro, ut t such instnts th currnt in th circuit is not zro. How is this hvior possil? 7. How cn you tll whthr n C circuit is ovrdmpd or undrdmpd? 8. Cn n ojct xrt forc on itslf? Whn coil inducs n mf in itslf, dos it xrt forc on itslf? Figur Q Prolms Th Prolms from this chptr my ssignd onlin in WAssign. ign in t nd go to ThomsonNOW to ssss your undrstnding of this chptr s topics with dditionl quizzing nd concptul qustions., 2, 3 dnots strightforwrd, intrmdit, chllnging; dnots full solution vill in tudnt olutions Mnul/tudy Guid; dnots cochd solution with hints vill t dnots dvloping symolic rsoning; dnots sking for qulittiv rsoning; dnots computr usful in solving prolm ction 32. lf-nduction nd nductnc. A 2.00-H inductor crris stdy currnt of A. Whn th switch in th circuit is opnd, th currnt is ffctivly zro ftr 0.0 ms. Wht is th vrg inducd mf in th inductor during this tim intrvl? 2. A coild tlphon cord forms spirl hving 70 turns, dimtr of.30 cm nd n unstrtchd lngth of 60.0 cm. Dtrmin th inductnc of on conductor in th unstrtchd cord. 3. A 0.0-mH inductor crris currnt mx sin vt, with mx 5.00 A nd v/2p 60.0 Hz. Wht is th slfinducd mf s function of tim? 4. An mf of 24.0 mv is inducd in 500-turn coil t n instnt whn th currnt is 4.00 A nd is chnging t th rt of 0.0 A/s. Wht is th mgntic flux through ch turn of th coil? 5. An inductor in th form of solnoid contins 420 turns, is 6.0 cm in lngth, nd hs cross-sctionl r of 3.00 cm 2. Wht uniform rt of dcrs of currnt through th inductor inducs n mf of 75 mv? 6. Th currnt in 90.0-mH inductor chngs with tim s.00t t (in units). Find th mgnitud of th inducd mf t () t.00 s nd () t 4.00 s. (c) At wht tim is th mf zro? 7. A 40.0-mA currnt is crrid y uniformly wound ircor solnoid with 450 turns, 5.0-mm dimtr, nd 2.0-cm lngth. Comput () th mgntic fild insid th solnoid, () th mgntic flux through ch turn, nd (c) th inductnc of th solnoid. (d) Wht f? f th currnt wr diffrnt, which of ths quntitis would chng? 8. A toroid hs mjor rdius nd minor rdius r nd is tightly wound with N turns of wir s shown in Figur P32.8. f r, th mgntic fild in th rgion nclosd y th wir of th torus, of cross-sctionl r A pr 2, is ssntilly th sm s th mgntic fild of 2 = intrmdit; 3 = chllnging; = M/G; = ThomsonNOW; = symolic rsoning; = qulittiv rsoning

3 Prolms 97 solnoid tht hs n nt into lrg circl of rdius. Modling th fild s th uniform fild of long solnoid, show tht th inductnc of such toroid is pproximtly m 0N 2 A 2p (An xct xprssion of th inductnc of toroid with rctngulr cross sction is drivd in Prolm 57.) r 9. A slf-inducd mf in solnoid of inductnc chngs in tim s 0 kt. Find th totl chrg tht psss through th solnoid, ssuming th chrg is finit. ction 32.2 Circuits 0. how tht i t/t is solution of th diffrntil qution d dt 0 whr i is th currnt t t 0 nd t /.. A 2.0-V ttry is connctd into sris circuit contining 0.0- rsistor nd 2.00-H inductor. n wht tim intrvl will th currnt rch () 50.0% nd () 90.0% of its finl vlu? 2. n th circuit digrmmd in Figur P32.2, tk 2.0 V nd Assum th switch is opn for t 0 nd is closd t t 0. On singl st of xs, sktch grphs of th currnt in th circuit s function of tim for t 0, ssuming () th inductnc in th circuit is ssntilly zro, () th inductnc hs n intrmdit vlu, nd (c) th inductnc hs vry lrg vlu. l th initil nd finl vlus of th currnt. Figur P32.8 Ar A 4. n th circuit shown in Figur P32.2, lt 7.00 H, 9.00, nd 20 V. Wht is th slf-inducd mf s ftr th switch is closd? 5. For th circuit shown in Figur P32.2, lt th inductnc 3.00 H, th rsistnc 8.00, nd th ttry mf 36.0 V. () Clcult th rtio of th potntil diffrnc cross th rsistor to th mf cross th inductor whn th currnt is 2.00 A. () Clcult th mf cross th inductor whn th currnt is 4.50 A. 6. A 2.0-V ttry is connctd in sris with rsistor nd n inductor. Th circuit hs tim constnt of 500 ms, nd th mximum currnt is 200 ma. Wht is th vlu of th inductnc of th inductor? 7. An inductor tht hs n inductnc of 5.0 H nd rsistnc of 30.0 is connctd cross 00-V ttry. Wht is th rt of incrs of th currnt () t t 0 nd () t t.50 s? 8. Th switch in Figur P32.8 is opn for t 0 nd is thn thrown closd t tim t 0. Find th currnt in th inductor nd th currnt in th switch s functions of tim thrftr. 0.0 V Figur P32.8 Prolms 8 nd H 9. A sris circuit with 3.00 H nd sris C circuit with C 3.00 mf hv qul tim constnts. f th two circuits contin th sm rsistnc, () wht is th vlu of nd () wht is th tim constnt? 20. A currnt puls is fd to th prtil circuit shown in Figur P Th currnt gins t zro, coms 0.0 A twn t 0 nd t 200 ms, nd thn is zro onc gin. Dtrmin th currnt in th inductor s function of tim. (t ) 0.0 A 200 ms (t ) mh Figur P32.2 Prolms 2, 3, 4, nd 5. Figur P Considr th circuit in Figur P32.2, tking 6.00 V, 8.00 mh, nd () Wht is th inductiv tim constnt of th circuit? () Clcult th currnt in th circuit 250 ms ftr th switch is closd. (c) Wht is th vlu of th finl stdy-stt currnt? (d) Aftr wht tim intrvl dos th currnt rch 80.0% of its mximum vlu? 2. A 40-mH inductor nd rsistor r connctd with switch to 6.00-V ttry s shown in Figur P32.2. () Aftr th switch is thrown to (conncting th ttry), wht tim intrvl lpss for th currnt rchs 220 ma? () Wht is th currnt in th inductor 0.0 s ftr th switch is closd? (c) Now th switch is 2 = intrmdit; 3 = chllnging; = M/G; = ThomsonNOW; = symolic rsoning; = qulittiv rsoning

4 98 Chptr 32 nductnc quickly thrown from to. Wht tim intrvl lpss for th currnt flls to 60 ma? Figur P Two idl inductors, nd 2, hv zro intrnl rsistnc nd r fr prt, so thir mgntic filds do not influnc ch othr. () Assuming ths inductors r connctd in sris, show tht thy r quivlnt to singl idl inductor hving q 2. () Assuming ths sm two inductors r connctd in prlll, show tht thy r quivlnt to singl idl inductor hving / q / / 2. (c) Wht f? Now considr two inductors nd 2 tht hv nonzro intrnl rsistncs nd 2, rspctivly. Assum thy r still fr prt so tht thir mutul inductnc is zro. Assuming ths inductors r connctd in sris, show tht thy r quivlnt to singl inductor hving q 2 nd q 2. (d) f ths sm inductors r now connctd in prlll, is it ncssrily tru tht thy r quivlnt to singl idl inductor hving / q / / 2 nd / q / / 2? Explin your nswr. ction 32.3 Enrgy in Mgntic Fild 23. An ir-cor solnoid with 68 turns is 8.00 cm long nd hs dimtr of.20 cm. How much nrgy is stord in its mgntic fild whn it crris currnt of A? 24. Th mgntic fild insid suprconducting solnoid is 4.50 T. Th solnoid hs n innr dimtr of 6.20 cm nd lngth of 26.0 cm. Dtrmin () th mgntic nrgy dnsity in th fild nd () th nrgy stord in th mgntic fild within th solnoid. 25. On clr dy t crtin loction, 00-V/m vrticl lctric fild xists nr th Erth s surfc. At th sm plc, th Erth s mgntic fild hs mgnitud of T. Comput th nrgy dnsitis of th two filds. 26. Complt th clcultion in Exmpl 32.3 y proving tht 2t> dt A flt coil of wir hs n inductnc of 40.0 mh nd rsistnc of t is connctd to 22.0-V ttry t th instnt t 0. Considr th momnt whn th currnt is 3.00 A. () At wht rt is nrgy ing dlivrd y th ttry? () Wht is th powr ing dlivrd to th rsistor? (c) At wht rt is nrgy ing stord in th mgntic fild of th coil? (d) Wht is th rltionship mong ths thr powr vlus? s this rltionship tru t othr instnts s wll? Explin th rltionship t th momnt immditly ftr t 0 nd t momnt svrl sconds ltr. 28. A 0.0-V ttry, rsistor, nd 0.0-H inductor r connctd in sris. Aftr th currnt in th circuit hs rchd its mximum vlu, clcult () th powr ing supplid y th ttry, () th powr ing dlivrd to th rsistor, (c) th powr ing dlivrd to th inductor, nd (d) th nrgy stord in th mgntic fild of th inductor. 29. Assum th mgnitud of th mgntic fild outsid sphr of rdius is B B 0 (/r) 2, whr B 0 is constnt. Dtrmin th totl nrgy stord in th mgntic fild outsid th sphr nd vlut your rsult for B T nd m, vlus pproprit for th Erth s mgntic fild. ction 32.4 Mutul nductnc 30. Two coils r clos to ch othr. Th first coil crris currnt givn y (t) (5.00 A) t sin (377t). At t s, th mf msurd cross th scond coil is 3.20 V. Wht is th mutul inductnc of th coils? 3. Two coils, hld in fixd positions, hv mutul inductnc of 00 mh. Wht is th pk mf in on coil whn sinusoidl currnt givn y (t) (0.0 A) sin ( 000t) is in th othr coil? 32. On printd circuit ord, rltivly long, stright conductor nd conducting rctngulr loop li in th sm pln s shown in Figur P3.8 in Chptr 3. Tking h mm, w.30 mm, nd 2.70 mm, find thir mutul inductnc. 33. Two solnoids A nd B, spcd clos to ch othr nd shring th sm cylindricl xis, hv 400 nd 700 turns, rspctivly. A currnt of 3.50 A in coil A producs n vrg flux of 300 mw through ch turn of A nd flux of 90.0 mw through ch turn of B. () Clcult th mutul inductnc of th two solnoids. () Wht is th inductnc of A? (c) Wht mf is inducd in B whn th currnt in A incrss t th rt of A/s? 34. A solnoid hs N turns, rdius, nd lngth. t is so long tht its mgntic fild is uniform nrly vrywhr insid it nd is nrly zro outsid. A scond solnoid hs N 2 turns, rdius 2, nd th sm lngth. t lis insid th first solnoid, with thir xs prlll. () Assum solnoid crris vril currnt. Comput th mutul inductnc chrctrizing th mf inducd in solnoid 2. () Now ssum solnoid 2 crris currnt. Comput th mutul inductnc to which th mf in solnoid is proportionl. (c) tt how th rsults of prts () nd () compr with ch othr. 35. A lrg coil of rdius nd hving N turns is coxil with smll coil of rdius 2 nd hving N 2 turns. Th cntrs of th coils r sprtd y distnc x tht is much lrgr thn 2. Wht is th mutul inductnc of th coils? uggstion: John von Numnn provd tht th sm nswr must rsult from considring th flux through th first coil of th mgntic fild producd y th scond coil or from considring th flux through th scond coil of th mgntic fild producd y th first coil. n this prolm, it is sy to clcult th flux through th smll coil, ut it is difficult to clcult th flux through th lrg coil cus to do so, you would hv to know th mgntic fild wy from th xis. 36. Two inductors hving inductncs nd 2 r connctd in prlll s shown in Figur P Th mutul inductnc twn th two inductors is M. Dtr- 2 = intrmdit; 3 = chllnging; = M/G; = ThomsonNOW; = symolic rsoning; = qulittiv rsoning

5 Prolms 99 min th quivlnt inductnc q for th systm (Fig. P32.36). (t ) () M 2 Figur P32.36 (t ) q ction 32.5 Oscilltions in n C Circuit 37. A.00-mF cpcitor is chrgd y 40.0-V powr supply. Th fully chrgd cpcitor is thn dischrgd through 0.0-mH inductor. Find th mximum currnt in th rsulting oscilltions. 38. An C circuit consists of 20.0-mH inductor nd mF cpcitor. f th mximum instntnous currnt is 0.00 A, wht is th grtst potntil diffrnc cross th cpcitor? 39. n th circuit of Figur P32.39, th ttry mf is 50.0 V, th rsistnc is 250, nd th cpcitnc is mf. Th switch is closd for long tim intrvl, nd zro potntil diffrnc is msurd cross th cpcitor. Aftr th switch is opnd, th potntil diffrnc cross th cpcitor rchs mximum vlu of 50 V. Wht is th vlu of th inductnc? Figur P An C circuit lik th on in Figur 32.0 contins n 82.0-mH inductor nd 7.0-mF cpcitor tht initilly crris 80-mC chrg. Th switch is opn for t 0 nd thn thrown closd t t 0. () Find th frquncy (in hrtz) of th rsulting oscilltions. At t.00 ms, find () th chrg on th cpcitor nd (c) th currnt in th circuit. 4. A fixd inductnc.05 mh is usd in sris with vril cpcitor in th tuning sction of rdiotlphon on ship. Wht cpcitnc tuns th circuit to th signl from trnsmittr rodcsting t 6.30 MHz? 42. Th switch in Figur P32.42 is connctd to point for long tim intrvl. Aftr th switch is thrown to point, wht r () th frquncy of oscilltion of th C circuit, () th mximum chrg tht pprs on th cpcitor, V Figur P mf C () 0.00 H (c) th mximum currnt in th inductor, nd (d) th totl nrgy th circuit posssss t t 3.00 s? 43. An C circuit lik tht in Figur 32.0 consists of 3.30-H inductor nd n 840-pF cpcitor tht initilly crris 05-mC chrg. Th switch is opn for t 0 nd thn thrown closd t t 0. Comput th following quntitis t t 2.00 ms: () th nrgy stord in th cpcitor, () th nrgy stord in th inductor, nd (c) th totl nrgy in th circuit. ction 32.6 Th C Circuit 44. n Activ Figur 32.5, lt 7.60, 2.20 mh, nd C.80 mf. () Clcult th frquncy of th dmpd oscilltion of th circuit. () Wht is th criticl rsistnc? 45. Considr n C circuit in which 500 mh nd C 0.00 mf. () Wht is th rsonnc frquncy v 0? () f rsistnc of.00 k is introducd into this circuit, wht is th frquncy of th (dmpd) oscilltions? (c) Wht is th prcnt diffrnc twn th two frquncis? 46. how tht Eqution in th txt is Kirchhoff s loop rul s pplid to th circuit in Activ Figur Elctricl oscilltions r inititd in sris circuit contining cpcitnc C, inductnc, nd rsistnc. () f V 4>C (wk dmping), wht tim intrvl lpss for th mplitud of th currnt oscilltion flls to 50.0% of its initil vlu? () Ovr wht tim intrvl dos th nrgy dcrs to 50.0% of its initil vlu? Additionl Prolms 48. viw prolm. This prolm xtnds th rsoning of ction 26.4, Prolm 29 in Chptr 26, Prolm 33 in Chptr 30, nd ction () Considr cpcitor with vcuum twn its lrg, closly spcd, oppositly chrgd prlll plts. how tht th forc on on plt cn ccountd for y thinking of th lctric fild twn th plts s xrting ngtiv prssur qul to th nrgy dnsity of th lctric fild. () Considr two infinit pln shts crrying lctric currnts in opposit dirctions with qul linr currnt dnsitis J s. Clcult th forc pr r cting on on sht du to th mgntic fild, of mgnitud m 0 J s /2, crtd y th othr sht. (c) Clcult th nt mgntic fild twn th shts nd th fild outsid of th volum twn thm. (d) Clcult th nrgy dnsity in th mgntic fild twn th shts. () how tht th forc on on sht cn ccountd for y thinking of th mgntic fild twn th shts s xrting positiv prssur qul to its nrgy dnsity. This rsult for mgntic prssur pplis to ll currnt configurtions, not only to shts of currnt. 49. A.00-mH inductor nd.00-mf cpcitor r connctd in sris. Th currnt in th circuit is dscrid y 20.0t, whr t is in sconds nd is in mprs. Th cpcitor initilly hs no chrg. Dtrmin () th voltg cross th inductor s function of tim, () th voltg cross th cpcitor s function of tim, nd (c) th tim whn th nrgy stord in th cpcitor first xcds tht in th inductor. 50. An inductor hving inductnc nd cpcitor hving cpcitnc C r connctd in sris. Th currnt in th circuit incrss linrly in tim s dscrid y Kt, 2 = intrmdit; 3 = chllnging; = M/G; = ThomsonNOW; = symolic rsoning; = qulittiv rsoning

6 920 Chptr 32 nductnc whr K is constnt. Th cpcitor is initilly unchrgd. Dtrmin () th voltg cross th inductor s function of tim, () th voltg cross th cpcitor s function of tim, nd (c) th tim whn th nrgy stord in th cpcitor first xcds tht in th inductor. 5. A cpcitor in sris C circuit hs n initil chrg Q nd is ing dischrgd. Find, in trms of nd C, th flux through ch of th N turns in th coil whn th chrg on th cpcitor is Q / n th circuit digrmmd in Figur P32.8, ssum tht th switch hs n closd for long tim intrvl nd is opnd t t 0. () Bfor th switch is opnd, dos th inductor hv s n opn circuit, short circuit, rsistor of som prticulr rsistnc, or non of ths choics? Wht currnt dos th inductor crry? () How much nrgy is stord in th inductor for t 0? (c) Aftr th switch is opnd, wht hppns to th nrgy prviously stord in th inductor? (d) ktch grph of th currnt in th inductor for t 0. l th initil nd finl vlus nd th tim constnt. 53. At th momnt t 0, 24.0-V ttry is connctd to 5.00-mH coil nd rsistor. () mmditly thrftr, how dos th potntil diffrnc cross th rsistor compr to th mf cross th coil? () Answr th sm qustion out th circuit svrl sconds ltr. (c) s thr n instnt t which ths two voltgs r qul in mgnitud? f so, whn? s thr mor thn on such instnt? (d) Aftr 4.00-A currnt is stlishd in th rsistor nd coil, th ttry is suddnly rplcd y short circuit. Answr qustions (), (), nd (c) gin with rfrnc to this nw circuit. 54. Whn th currnt in th portion of th circuit shown in Figur P32.54 is 2.00 A nd incrss t rt of A/s, th msurd potntil diffrnc is V 9.00 V. Whn th currnt is 2.00 A nd dcrss t th rt of A/s, th msurd potntil diffrnc is V 5.00 V. Clcult th vlus of nd. Figur P A tim-vrying currnt is snt through 50.0-mH inductor s shown in Figur P Mk grph of th potntil t point rltiv to th potntil t point. lr frquncy to th xprimntlly msurl ngulr frquncy. 57. Th toroid in Figur P32.57 consists of N turns nd hs rctngulr cross sction. ts innr nd outr rdii r nd, rspctivly. () how tht th inductnc of th toroid is m 0N 2 h 2p ln () Using this rsult, comput th inductnc of 500-turn toroid for which 0.0 cm, 2.0 cm, nd h.00 cm. (c) Wht f? n Prolm 8, n pproximt qution for th inductnc of toroid with W r ws drivd. To gt fl for th ccurcy of tht rsult, us th xprssion in Prolm 8 to comput th pproximt inductnc of th toroid dscrid in prt (). How dos tht rsult compr with th nswr to prt ()? Figur P () A flt, circulr coil dos not ctully produc uniform mgntic fild in th r it ncloss. Nvrthlss, stimt th inductnc of flt, compct, circulr coil, with rdius nd N turns, y ssuming th fild t its cntr is uniform ovr its r. () A circuit on lortory tl consists of.5-volt ttry, 270- rsistor, switch, nd thr 30-cm-long ptch cords conncting thm. uppos th circuit is rrngd to circulr. Think of it s flt coil with on turn. Comput th ordr of mgnitud of its inductnc nd (c) of th tim constnt dscriing how fst th currnt incrss whn you clos th switch. 59. At t 0, th opn switch in Figur P32.59 is thrown closd. Using Kirchhoff s ruls for th instntnous currnts nd voltgs in this two-loop circuit, show tht th currnt in th inductor t tim t 0 is t2 3 >2t 4 whr 2 /( 2 ). 56. Considr sris circuit consisting of 500-mF cpcitor, 32.0-mH inductor, nd rsistor. Explin wht you cn sy out th ngulr frquncy of oscilltions for () 0, () 4.00, (c) 5.0, nd (d) 7.0. lt th mthmticl dscription of th nguh (ma) t (ms) Currnt sourc 50.0 mh 2 Figur P32.55 Figur P A wir of nonmgntic mtril, with rdius, crris currnt uniformly distriutd ovr its cross sction. Th totl currnt crrid y th wir is. how tht th mgntic nrgy pr unit lngth insid th wir is m 0 2 /6p. 2 = intrmdit; 3 = chllnging; = M/G; = ThomsonNOW; = symolic rsoning; = qulittiv rsoning

7 Prolms n Figur P32.6, th switch is closd for t 0 nd stdystt conditions r stlishd. Th switch is opnd t t 0. () Find th initil mf 0 cross immditly ftr t 0. Which nd of th coil, or, is t th highr voltg? () Mk frhnd grphs of th currnts in nd in 2 s function of tim, trting th stdy-stt dirctions s positiv. how vlus for nd ftr t 0. (c) At wht momnt ftr t 0 dos th currnt in 2 hv th vlu 2.00 ma? 2.0 V Armtur mh 0.0 V Figur P k 6.00 k H 8.0 V Figur P Th ld-in wirs from tlvision ntnn r oftn constructd in th form of two prlll wirs (Fig. P32.62). Th two wirs crry currnts of qul mgnitud in opposit dirctions. Assum th wirs crry th currnt uniformly distriutd ovr thir surfcs nd no mgntic fild xists insid th wirs. () Why dos this configurtion of conductors hv n inductnc? () Wht constituts th flux loop for this configurtion? (c) how tht th inductnc of lngth x of this typ of ld-in is m 0x p w ln whr w is th cntr-to-cntr sprtion of th wirs nd is thir rdius. TV ntnn Figur P32.62 TV st viw prolms. Prolms 64 through 67 pply ids from this nd rlir chptrs to som proprtis of suprconductors, which wr introducd in ction Th rsistnc of suprconductor. n n xprimnt crrid out y. C. Collins twn 955 nd 958, currnt ws mintind in suprconducting ld ring for 2.50 yr with no osrvd loss. f th inductnc of th ring wr H nd th snsitivity of th xprimnt wr prt in 0 9, wht ws th mximum rsistnc of th ring? uggstion: Trt th ring s n circuit crrying dcying currnt nd rcll tht x x for smll x. 65. A novl mthod of storing nrgy hs n proposd. A hug undrground suprconducting coil,.00 km in dimtr, would frictd. t would crry mximum currnt of 50.0 ka through ch winding of 50-turn N 3 n solnoid. () f th inductnc of this hug coil wr 50.0 H, wht would th totl nrgy stord? () Wht would th comprssiv forc pr mtr lngth cting twn two djcnt windings m prt? 66. uprconducting powr trnsmission. Th us of suprconductors hs n proposd for powr trnsmission lins. A singl coxil cl (Fig. P32.66) could crry MW (th output of lrg powr plnt) t 200 kv, DC, ovr distnc of 000 km without loss. An innr wir of rdius 2.00 cm, md from th suprconductor N 3 n, crris th currnt in on dirction. A surrounding suprconducting cylindr of rdius 5.00 cm would crry th rturn currnt. n such systm, wht is th mgntic fild () t th surfc of th innr conductor nd () t th innr surfc of th outr conductor? (c) How much nrgy would stord in th spc twn th conductors in 000-km suprconducting lin? (d) Wht is th prssur xrtd on th outr conductor? 63. To prvnt dmg from rcing in n lctric motor, dischrg rsistor is somtims plcd in prlll with th rmtur. f th motor is suddnly unpluggd whil running, this rsistor limits th voltg tht pprs cross th rmtur coils. Considr 2.0-V DC motor with n rmtur tht hs rsistnc of 7.50 nd n inductnc of 450 mh. Assum th mgnitud of th slfinducd mf in th rmtur coils is 0.0 V whn th motor is running t norml spd. (Th quivlnt circuit for th rmtur is shown in Fig. P32.63.) Clcult th mximum rsistnc tht limits th voltg cross th rmtur to 80.0 V whn th motor is unpluggd. Figur P32.66 = 2.00 cm = 5.00 cm 67. Th Missnr ffct. Compr this prolm with Prolm 57 in Chptr 26, prtining to th forc ttrcting prfct dilctric into strong lctric fild. A fundmntl proprty of typ suprconducting mtril is prfct 2 = intrmdit; 3 = chllnging; = M/G; = ThomsonNOW; = symolic rsoning; = qulittiv rsoning

8 922 Chptr 32 nductnc dimgntism, or dmonstrtion of th Missnr ffct, illustrtd in Figur in ction 30.6 nd dscrid s follows. Th suprconducting mtril hs B 0 vrywhr insid it. f smpl of th mtril is plcd into n xtrnlly producd mgntic fild or is coold to com suprconducting whil it is in mgntic fild, lctric currnts ppr on th surfc of th smpl. Th currnts hv prcisly th strngth nd orinttion rquird to mk th totl mgntic fild zro throughout th intrior of th smpl. This prolm will hlp you to undrstnd th mgntic forc tht cn thn ct on th suprconducting smpl. A vrticl solnoid with lngth of 20 cm nd dimtr of 2.50 cm consists of 400 turns of coppr wir crrying countrclockwis currnt of 2.00 A s shown in Figur P () Find th mgntic fild in th vcuum insid th solnoid. () Find th nrgy dnsity of th mgntic fild, noting tht th units J/m 3 of nrgy dnsity r th sm s th units N/m 2 of prssur. (c) Now suprconducting r 2.20 cm in dimtr is insrtd prtwy into th solnoid. ts uppr nd is fr outsid th solnoid, whr th mgntic fild is ngligil. Th lowr nd of th r is dp insid th solnoid. Explin how you idntify th dirction rquird for th currnt on th curvd surfc of th r so tht th totl mgntic fild is zro within th r. Th fild crtd y th suprcurrnts is sktchd in Figur P32.67, nd th totl fild is sktchd in Figur P32.67c. (d) Th fild of th solnoid xrts forc on th currnt in th suprconductor. Explin how you dtrmin th dirction of th forc on th r. () Clcult th mgnitud of th forc y multiplying th nrgy dnsity of th solnoid fild tims th r of th ottom nd of th suprconducting r. B 0 () () (c) Figur P32.67 B tot Answrs to Quick Quizzs 32. (c), (f). For th constnt currnt in sttmnts () nd (), thr is no voltg cross th rsistnclss inductor. n sttmnt (c), if th currnt incrss, th mf inducd in th inductor is in th opposit dirction, from to, mking highr in potntil thn. imilrly, in sttmnt (f), th dcrsing currnt inducs n mf in th sm dirction s th currnt, from to, gin mking th potntil highr t thn t (i), (). As th switch is closd, thr is no currnt, so thr is no voltg cross th rsistor. (ii), (). Aftr long tim, th currnt hs rchd its finl vlu nd th inductor hs no furthr ffct on th circuit (), (d). Bcus th nrgy dnsity dpnds on th mgnitud of th mgntic fild, you must incrs th mgntic fild to incrs th nrgy dnsity. For solnoid, B m 0 n, whr n is th numr of turns pr unit lngth. n choic (), incrsing n incrss th mgntic fild. n choic (), th chng in cross-sctionl r hs no ffct on th mgntic fild. n choic (c), incrsing th lngth ut kping n fixd hs no ffct on th mgntic fild. ncrsing th currnt in choic (d) incrss th mgntic fild in th solnoid (). M incrss cus th mgntic flux through coil 2 incrss (i), (). f th currnt is t its mximum vlu, th chrg on th cpcitor is zro. (ii), (c). f th currnt is zro, this momnt is th instnt t which th cpcitor is fully chrgd nd th currnt is out to rvrs dirction. 2 = intrmdit; 3 = chllnging; = M/G; = ThomsonNOW; = symolic rsoning; = qulittiv rsoning