Ex2_F03_with_solutions

# Ex2_F03_with_solutions - Exam 2 Physigsj'zaéil November 1...

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Unformatted text preview: Exam 2 . . __ . Physigsj'zaéil . November 1. Please print yourname onthetop edgeofthe op-scsn sheet. SsIUm“ ‘ Can‘tﬁﬁ" 2. Use a #2 pencil to ﬁll in your full name. your student identiﬁcation number, your recitation division number, and ﬁnally the answers for problems 1—12. 3. One (both sides) 3 112" x 11“ one sheet is allowed. It must he hand-written. Useﬁil equations and constants: slimy—W3" Jﬁ-ﬁ=ﬂ.fm qusxﬁ F=f§xﬁ s=sxﬁ p=NiA £=”°"‘= ds=-Bvdf N¢,=L: E 211:! .. d9 d¢ i! ‘5" m 3 d! at HE =_;_CV2 V=£ﬂ_e~rue} =%e+use q=qﬂe use 1 - s _ 1 mint V=s(1—e M) =Ec e M) me: E , i 1 R‘ 1 m = Eﬂ=iﬂz z: R1+(XL_XC)1 XL=ﬂ1L XE=E main—i—EX 'X "=1 3-? met hi 3-? R 2 Z poo 2 ' . C1 p0 =4srx10" T-mi'A so =8.85x10'" 2 Ntm e=1.6x10'“c mP=L67>t1lTﬂkg Mammal“ manomm" “mama-n Fat-MA 13 pages total 1 A circuit for charging a capacth is shown below. The awitch is thmwn to position A at H). The circuit has BIEIIIEHIS a=12V, R=lﬂﬂ ﬂ and C=IUﬂF. How long does it take for the capacitor to ha chargad to 99.9 percant afita ﬁnal charga'? EﬁﬂMR—L [:29 aim-32 on mpqrutm‘ La fit-1' L¢+ {:1th than}! on :upucmar L: f": C at: w t «r w u -I- I, is; 3m - =7 w as w = we * “Fr-J (a) m3 tYuwHﬂpl 4-wa- \$115] Hf”? a caracl‘hﬂf‘ a) = I“ E-tXT¢ é a'tm - :—,qq°f=,aul 3; H4711: In LON) =9 1; : _ an Int-am) = —Rr.ln(.nol) r'e'r. = '(m £2)(tano“F) “two = . a? [E 13 pages total 2 A particle of unknown :11ng q and unhicam mass m moves at a speed F4.8><106 mfa in the +x-direetien inte a region cf'eenstant magnetic ﬁeld. The ﬁeld has magnitude B=EL5 T and is orientated in the +y~directicn. The particle is deﬂected in the 42- direetien and traces cut a fragment of a circle of radius R=i}.ln1. What is the sign of the charge and what is its ratio of grin? {a} Neutral, qu=D A d!- .. A -B-- {h} Nasaﬁvejquﬁﬁxm-BCIKE JUNE lama-H m ft?! in F I it”; {c} Positive, q!m=1.4x10’3C!Kg 1? m“ 9'” "'1: In“' " 2 mm In M {a} Negative, qhn=9.ﬁxli}"' (3ng - "‘ n = ? {53' Far 1: urfitle mom «1* mum? {e} Poalttve,qu 9.6x10 (3ng {feed f; m it ML} of Mm El 1' a teamreral ﬁtte’ahd‘i‘lﬂh It '1‘: 1)" This 1].: manure“! 'Forlc" 1i FL: Mac: mug“ . R ._.. The eel; {one antic) on 'Ile. reﬁt]: a 1L me "he. farm F in “"5 mast- Inav'ﬁ _- ' -- f B) 5:: [FBI-.- I1unﬂlf'131‘F’: WEE-Jim \$9- milr“ w B ' T1“ :1, I a; ﬂ .. I * Er= t' 3“ "a ' e R 7W3 "P m “ as t: m](.5T} “ loom”! 13 pages total 3 A leap of wire carrying :1 went has a magnetic dipole moment y. =5x10’4 A-mz. Itﬁtially, the vector pt makes an angle efﬁﬂ” with a [1.5 T magnetic. ﬁeld. As it turns te heeeme aligned with the ﬁeld, the work done by the ﬁeld is: 3 ft}!- h “I E. I-‘l‘I g u 'I'I'IH I'lﬁ'HL J; I; It]. "I u n"; hfhr, £9 h Ir 'l'l y 1 Pa .1 3 A F “I!” E u! a Eur:de i1: my}! 9 ktwnn M and B It Ufﬂ}=-Faiﬁ= - eel E (c) 4.5mm] eu - LLF- ut. = utw- my): (a 4135313“) - (‘413 w JP»? ﬂ {1 1.0Xlﬂ'4l F, ' E E3; 4.0).:1041 Let hinge” he 111: Hart Jun k1§incui W =ﬁKE=‘ﬂPE=-ﬁu=" {-“B)=#B 529'“ 1‘ ’\ ‘= {Ella-tr ﬂ~in‘)(.5 T): NHL- EJHE'HL Co “ﬂrw‘huu 5F “a?! “WWII; 9197/: dkﬁdﬁgga 5"? E 13 pages tetal 4 Calculate the magnitude of the magnetic ﬁeld at the point C=(ﬂ,ﬂ) for the current loop show below. The loop eonsiete of tore straight portions and a eireular are of radius R, which euhtends an angle ﬂ=11f2 at the center of the are. Ignore the contribution of the current in the short ares near the origin (Ml). Ne coma-livva +n E-{Ielcl #1" C clue +9 «H5 do“ '15on Jule-:11; maul or am; 'From C103. ®,51me (if: F :0 ‘1 “IF E Etﬂ-Squlr'l' Lit-F D 5 IE: 4:51 em .5 r “I? Mr I” ‘ D .,. I - q J ' i - i ﬁ i - --F C x {a} Hammett} Only an Ci) camel-M +v '34:“ a" f (b) Home) . "I I n {e} B=MtBRJ A? 45.1.; wield?! “a?” (:1) Batman) (e) Emma) 13 pages total 5 Two parallel inﬁnite wires ItI cm apart carry currents cf 2A and 4A tresptcctivelyr in the same direction. The force per unit length in Him cf one wire on the ether is: \ “we- (a / WWI (I) l _ . g. 6. “a {a} 1 x1ﬂ‘3 Ntttt tepulstve 11" r ‘1 t-—-—t *- (b) lxlﬂ‘3 term attractive l J / (c) 4x 10'5 Nfrn repulsive \ / {cl} 4xlﬂ'5 Nt'm attractive "t a“ .__ ...-r" (e) Ncne cf these u i Lek-ii 1,: q sec-Hen 9i: wire In fit: same Ditﬂl‘l‘m’l “1 1"" wwcnit ﬂ.” semen It“ icv‘hlt Iflﬁf, Tine Fat-ts cut via: tunes I5 EHIEHFB‘. Slut-c T PM” cut oi +1.1 pure anti tit: E-ielJ Justu- mrc (D Peru“ «intent tn Ilse Pallf’ﬂh a": we @1 in? ram“ {to 11¢ ﬂying se a: \$1313. Pom-n “HI tile. “'71.? anal Lame +iut {am t5ﬂ'l'l'1‘src'l‘WE. IE]:- fflfggi= £1 Irv. .3. mill}? “’5': # 1N attains W I" n F uni, it; ~ ' '1Il‘ 2t Ft: mutt! 4 cs! F in t H? _ I .L: - _ ‘IFKM L2 mats) r5 N ‘5? if :l‘dt " 1 t Q—slﬂ Tn J, 2“- lL-u‘ n‘H‘qufl'ﬂ'ﬁ 13 pages total 6 A long straight wire {radius 11- 3mm) carries a constant current distributed uniformly over a cross section perpendicular to the axis of the wire. If the current density is j===lIllllil'llll'rn2 in the —s direction, what is the magnitude and direction of the magnetic ﬁeld B at the point P located 2 mm from the axis of the wire along the x-axis? (Note that the +2 axis points out of the page). F? Deﬁne an grocer-Inn leaf C. Forum] flat”. I the ran-Ir of" WI'HLL we want? 7'9 “my”: F3 t'm leer I...“ I‘m . Molt“ Patron. 3" (a) 2x lﬂ" T in the +y-direction (b) 2x111?3 T in the —3r-dircction {c} l.3:~<lt:r1r T in the +y~direction (d) 1.3xltlt'1f T in the —y—direction T L (e) None of these :- tta-nan!“ Eht‘mJ I-L: “ﬁn-“ﬂy. I} rim, =j (ares elitism. 3mm“ Inf) . "1. I‘ = J11?“ Bf Hmperéi L'W "" - ' ~ :3“ [Qt-cl ties = “(E = tar“ ' 1 ‘—-w--" a, Bus-Mar: “‘st , u o em: ﬂail?" - {a}: = lam!!!” WNW 5-.“ Karl's) B or!“ '- 1- 1 It. inmate arsenal C W TL: Jtricfl‘ﬂ'ﬂ 5': it“ P H ‘Fﬁﬂl’l’ y u “710-1th “.19.. It‘ll" For” Jun} u. Jlmtlen oi current [into first), tile-1 Fiver} curl [a direction dF in Particular-1 the. E‘ni“ Punt! Jot-tr- (I.E_ in 1:11 'y dlﬂc'hnn) d? P. M13 13 pages total 'l' Two long solenoids (radii 2t] mm and 3t] mm respectively} entry the earne current I, ﬂowing in opposite directions. The smaller solenoid is mounted inside the larger, along a common axle. It is observed that there is a zero magnetic ﬁeld within the inner solenoid. Therefore the inner solenoid must have X times as many turns per unit length on the outer solenoid, where X is: Let‘ the outer toleneltl Lave: curronf if +urn5 n (a) 1 ""“"‘lfll ' (b) 4!? end lat 1'ch ll‘l'ﬂﬂr‘ “Ln'lJ limit: cur-In“? Ill (a) 233 ’ e 3:: Kim” n‘ e T l‘“ “tilde the Inner solenoid; «the Fired... clue“- +l'¢ "l" solenoids Illﬂ. B.=u.i,h, H ignorant The met qunem {acid It here line, when: .1 u- . llall=lBll J Le. “ehntlwlhna 2;. entrain—gm e, E cm- 15 are ﬁtted (y eirumrﬂen 13 pages total 8 A square loop ofwire measuring 12 cm hy12 cm has a battery ofcmf4 V and a lﬂ Ohm resistor. A uniform magnetic ﬁcld B points out of thc page and is dccrcasing in magnitude at tho ratc of 15!} Tfs . The current in thc circuit is: |, “cinch; “on 1-1:” bile hﬂl n = ﬂﬂ a .. R I .4 Ear; 3.41;: awcsw‘ III “HM cheL '77 "'r W =12 om 1 . HE J E “1'? ac= *ch .) = -5!— ca: -cc T ' r at lit: 1 Incitich when? (s) cc: A, clockwise HM“: lmiumJ cui- E“; (b) \$.22 A, clockwise W; (o) [LE2 A, counterclockwise I (c) 11.22 A, counterclockwise : c N g (c) {1 A ___._R.... {h Finri cilrec'non a? thﬂtﬁJ curfew} “1M! Loaf; [out if! i- Wﬂi- “We 33? ‘ﬁwl‘ J, uni. “Hm Tc c c TL! Elm- e In “can, we mm.- 1'0 Elﬁn Kc NH Jo Jo L), s E”? cit! n? I“ “if JIM ﬂllrecﬁﬂn c5111: erymoi ﬁ‘ﬁe”) 3:22 Riol; languid“ PM" 4mm" in Amman oi imiou E41.” [ﬂu-r J ’1”): cl...“ chm cur} n. «irrerhon a? [mi-:ch curl“!an Lt. ccuoﬁrclocimue. 5 In mum-cm 'ro 11¢ I Haul cuﬁﬂlﬂ,fiwro is «im +II£ current Joe 1'0 ‘4! ~ ~ 'I v I Wm»? lccf eruﬂno‘. t-cﬂtﬂ z”) I=E=h=*‘ﬁi 1" Ir counﬂrdﬂjmut x " + i. 13 pagcc total 9 mi 11. h- corn-11- = .11 ﬂ) mmcrciccimue + it, ﬁlmumnlmmg in n, “chronicle...” '-‘> The ﬁgure below shows a circuit that contains tiuee identical mistors with resistance- R = 9 ﬂ , two identical inductors with inductance L = 2J0 M and an ideal batman-3.:r with omfe -13v. What is the current i through tho battery just after the switch is closed? What is the current i through the batter],Ir a long time after the switch has been closed? just After a longtime after (a) 3 A 2 A (b) *5 A 6 A (c) 2 A 2 A (d) 6 A 2 A (13) 2 A 6 A. 7w: ugh:- (uncle. 1; aiIJEJ} CUFFIH+ 1’th “CL l‘ﬂJl-Ithr' ‘5 *Erﬂ (lltﬂlﬂe tﬂfﬂh‘i’ fiw hob Imiudw we: ﬁne before trite lair}th m1 ﬂuid, and Ihtiuc‘l'll” Jan‘l- ail'm +Le curmf +1.” film in chef Inmntanﬂ-Iy). Thu Me an refine eat]. mtiuetor thL an «arm elrculf; 5mm Eiuffaj if, h ink“! ‘ u the current tbru 1L: Shirk-L. “Him? I Ivor ttﬂlﬁohl E..¢:R=a 5w MIML u elem}, turner-1' the: en]. I: conflian “J ,1“!ng (Ly EL='1\$)J+L¢ whey! unrest WL Inoioe‘iﬂ‘l’ a earnJ so we Me; a; will Peffgu “cl. Imlue‘tﬂr‘ URL 0: Myth “WE-I .._—I-I-—- g-Lﬂﬂ e a => t”. “*1 fidﬁ 3;: 3 a ET leoP larva-hon: E _,E 861:0 £5": L¢E—=3_£:3!IEI!_ R“! #3 R [Q'@ 13pageetotal 10 1G. 1‘7 A long straight wire is in the plane of a rectangular conducting loop. The straight wire carries a constant current 1', as shown below. While the wire is being moved toward the rectangle, the current in the rectangular loop is: his (3) g; mares”? (a) Zero (h) lClockwise (c) CounterclockwiSe (d) Clockwise on the left side and counterclockwise on the right side (e) Counterclockwise on the left side and clockwise on the right side 8)! 1“?qu haul “.33 (LE. Pour}? fhuml m (.lIPQE'l‘l‘On oi: {omen-r} gmjm turl m Jurﬁchon ol' #1.; E—Elclcl Fom‘I-I mm YLQ Faye w flag rifle oi ﬁle wire, Srnre flu: turpo r5 Lem} mama} 11;.me 11c lump 3 the ﬁ-fttlnl m- Hlle Position cl: ‘lrlne “of IS \$th Stroyer and "rims +1.6 mu/qmrucle J the majnehe l-luit tullm thelu‘aurlriiliii'ﬂllJ LS muemlhju lens's st the induced turns-11- {rlows m a directrori .50 95 M ﬂpfﬂje "Mime elaonjﬂ In Since .5 maturity mil-l: 'Hn'leJ A we. can opyose {LIE Junie weqhemnj 3 “H1 Le wEnlLEHEJ ﬁlmle 1):: IHJJOQJ 3-‘Fielcl Pom? In file ofFonhz elrruf’dq 1‘1:- hlie 04*?an E'ﬁcld, he. our is firth By shawl-3r Hill" limit) Mlle [Pallan jlmmt l" J’Wtfm’l HF '“JME'J E'ﬁfulgnjer‘i Wr‘l m rlie ollrer‘lim 15F '"l't thduceol Wﬂ'r we 'F J 4w L . a” )13 psgdis total l a mural “We” 1“will: 11. Consider hare parallel infinite wins, cne carrying a current cf 5 A cut at” the page, the ether can}ng a current of 5 A late the page. The point P is located such that if a line were drawn from P be each wire, then these lines would subtend an angle ef9ﬂ' degrees, as shown helcw. Furthermore, the point P is at a distance d ﬁ-cm each wire. What is the directicn cf the magnetic ﬁeld at the point P? 5 A, inte- the page 5 A, cut cf the page {a} UP (b) Down (c) Left (a) Right (e) Intc the page her ninja-ch:- {mini Point-r I a IE 13 pages total 1'2 11 A metal rod is forced to move 1saith constant velocity it along two parallel metal rails, connected with a strip of metal at one end, as shown in the ﬁgure below. A magnetic ﬁeld B - {1.5 T points out of the page. If the rails are separated by L = 212} cm and the speed of the rod is v = 10 cmfs, what is the emf generated? If the rod has a resistance of 5 ohms and the rails and comector have negligible resistance, what is the current I in the red“? I I I I I I I I {a} emf=0ﬂ\$ V, Iﬂﬂﬂl A {b} ernf=0.£|2 v.1-o.oo4 A (c) erni'=0.ﬂl V, I=t}.ﬂ A {d} emf=U.DI V, Iﬂﬂﬂm A {e} emﬁﬂ V, I-rﬂ A Let- s- : Jute-ice e? NJ ﬂora Milie- tutti. i. Final manger. {lg}. +Lw leer: EB I“ I §,J]'=1§| [am HIth latest) = 1m Lx * emu. elatiost Ibr- Ll It o-F turns. N1! 1" = -. (.5 The: not.» Mo) = — .0! v ' 3- Moynﬂ‘vdt oi: mJuceJ current '5 = -_ g M .'.." (IIH’ “I'Ifﬂﬂﬁg R S Q “W hop in LE] 13 pages total 13 ...
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