106-20002-FIN - 41 PROBLELI(l(17'| points A solid...

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Unformatted text preview: 41 PROBLELI (l) (17'| points} A solid noneonducting spherical shell, of inner radius R and Wu outer radius 35'. carries a uniformlyr distributed positive charge. / The volume charge density of the shell is p. lClive your ensurers . , . . ., interrnsofso.R,p.msndq. [s16 pts.) find the magnitude of the electric field at point P which is at a distance 2!? from the center of the shell [point 0). Gmee' lee-N": al-1": pu- n spherical Seattle's-t Wf‘fflu of rallies Y": 19.: If -*11(t“5—P\3 t... t (menu-m 3 ’i _+ as" W ad Sigrl subsidised-v.19 'r- ': ZR. 'HK E: 1: a {bl-{7 pts.) Find the electric potential difference {Vp— Val between points P and G. r P t r u. org = - IE. I; e _ fessmo'=-Jeas=-;j£ulr=;fctr;, are” fir 4'5"“ o '5 G I... I I Easement,“ hunt. em: If an =%,(r-%) fir egress. “gr!- I "til" “alert-stern} g}. «lessee-ease; [c)(5 pts.) A particle of mass tn and positive charge or is projected from a large distance toward the shell with an initial speed v directed radially inward. What value of v is required for the particle to just reach the shell before reversing direction? a a . I I ‘ I _ I L l Clo-sacrum“ {mmml we” .flLd-KL— Lil-l- + qi-MII omega-3: {3: gm BaajL Hills = in [H941]; I “mafia .5 t 1 t “I weak"; :2; t! __a U. 5:. R = P. {51.1 EM“. 1' unit 3% FT it t to... '5' m Phys I06 Final Eran Page 2!? Mrs} 3!. 2m} 4 2 PROBLEM {2) {15 points) Two metoi spheres in the figure are separated by a distance that is much greater than their radii. They are to be connected by a conducting wire of total resistance R. The sphere of radius a is uncharged and the sphere of radius 2:: has a total charge Q on it. Give your answers in terms of Q, R, a, and k= NM. 3 2 Q [a)[4 pts.) Find the current through the wire immediater after the switch 3 is closed. (h) Find the electrostatic potential energy of the two-sphere system: (i]{5 pts.) Before 5' is closed. u=u1+sf°'=..;:.cu‘=%__i when Cetifliaflxllflfilet]: saga '- 1. t. Lil. I: a = i9. = k 5‘! mm _’ ” mm W (ii)(6 pts.) After Sis closed and siecrrnsratic equilibrium is reached. Compare (i) and (ii) and discuss. (Jfirrt: Treat the spheres as capacitors.) Wm “ha. emmgfific afiuflhwbuet Pia-.0144, his arm MM‘M. 51M Wfifll» .fl. 6'" ...—'p 3:; = 51 (aged atoms, fimldm-gu.mp¢d~'vtly.) L Gwaefiecenfifl-rfld: q.stl+st _..;. (953-31 _._, %.q-qi.sg'=¥ 13 I 1* 1- Q:— Mfimlwzu:flt_+§h l. 3 ae,’ 1;, fat 1 w “3" 5 mi #39:. = famine-r 1%: W* “‘"fi “‘“V '72 a II b at. = 6,2. u" "surm- k '6‘: I; we compare (£1 Ms fit),we set. int uyu'. ‘l'lww due/cu} a nurse-t5 WM E’s-LU = gal-:— L‘g; :Efi?‘ ThiLNI‘ESI'“q W to lostm Luci“ Wm via M mmfinfl “Jim 1+5. f'E-WMLL Phys 1455 FindEmm Friars3i?"r Mayifjflflf 4 3 PROBLEM {3) (19 points) Consider the current-carrying loop shown in the figure. The curved segments are use of circles of radii R and ER with the common center 0. The straight segments are along radii. Give your answers in terms of 1!, yo, i, R. and 3.. (given in part b}. sinso°=fiaanacosec°=ua (aNS pts.) Find the magnetic field (in unit vector notation} at point 0. E=E+K+E§+flfa=fi+ga I difltheuiercfs cit-subar- ML: Br: 43% * éfliq—t) = east) El " I 1 ' tints.“ This it a.“ at In“ a -e In”. A I I A = —— —— = -—II—' E - NHEEL (4.3;): it"; ['k}+lzflt )-—) El 2"”. k- 3 ' Lina IZR (h) Suppose the loop is subjected to an external magnetic field §=Bn{2?+?) where fin is a positive constant. (iKS pts.) Find the forces (in unit vector notation) acting on the Wm the loop. .1; F15: t:th —-) 513M 2. : §=ikfce5£n'€+hhio'j)n Built-H.) E a. l out [Jr (at)- —— (jot +1591 —I. 3‘ i- - ‘21 +8 5 LIL-(viii: oust. Steam Li '. E; = {fit—'3]; fioila‘i'a)”. ——+ EH: {5.35.3 (ii}(5 pts.) What torque (in unit vector notation} acts on the loop? —s _.. -'iI , | t l ' l‘. A ' L A _ .._ ._ l1 a mi - Tit—R gfl .. “CH/Lao -—i/u Med ii}{1j[_‘Ti_l_TJ-T—i/a at J --*_ TIL L 4' a 3,113+li 1 NULL“ flats: (iiiJIE-fl pts.) How much work is required to turn the loop from the position shown in the figure to the position in which the magnetic dipole moment vector ii is at right angles to the external magnetic field E? W=bUa off—U; = (-5763; _ (:HE); = (FEM: ga‘{_tfl.[altzi+1}] W=_ Trial!» .3. Phys MISme Page-fl? MSIJOW . ' " 4 4 PROBLEM (4} {16 points} The figure shows a cross section cf a long cylindrical conductor of radius R {= 2 cm}. carrying a uniformly distributed current i{=2A) directed into the page. (than 104 Tmi‘A} [m4 pts.) What is the value of the integral flit-tn along the straight path KL shown in the figure? Amp-42's. imtr fr "M. eluted squeeze inept §Ev dg=fle int-tr. M44 Magmwdh‘lf wt. We: Jag. at 5m = MN , tannai-rixtm K It (hi6 pts.) Find the distance r of an external point P from the axis of the cylinder at 1which the magnitude of the magnetic field is the same as that at r = M, within the conductor. gr point P; M glued-vice! mnduchr Adan; ct lit-«:3 wire . Sc, 3:- % . At MM rung- : 393wg= rim—4 [Bltzn §)=h%n[§f=& {c}(6 pts.) Calculate the magnetic energy per unit length stored within the conductor. . '8‘ 2mm chum-h] -, uh: -——- 29,14. -* ‘ ' t'nr' ég. Refit,“ —-g {mum-h!” fit ut-l __’ Eli-('1': g?— mechmflnlwwilcfhtwnhw:* ‘ 1 uh ‘ jaut .. Su‘tflew .t J'JL. (art-Karim = J;E(%ifi) furl-4r) t. 1/“ t m. fit- ‘u lg gti“ cl" n t‘.‘ rmt‘T-wctm‘ a t; —- e. 1' :__..—-—-——-"' L ‘ Hark-Ir r me “t c 1511 '1” u". it??? s 1 "I / Phys lime Fag-£53? MEL 21301 4 5 PROBLEM (5} (16 points} Consider the IR circuit shown in the figure. (:06 pts.) What is the current through the hatter a long time after the switch Sis closed + A lav-3 nfir ‘fIniL 5wi+cle .5 Cloud 1 Mthducicretehem a. shirt circuit. so] infill: 33..” —--“*"' =34+zA I“; 16- (MG pts.) When the current through the inductor reaches its maximum, steel:ler value, the switch S is opened at time t = fl. Find the initial voltages across each resistor and lite inductor just after t = 0. was... Mswihh ,5 is tome nit-innit. tie, at current etsz MW“ 414:. mildew m4 ellw WM 1-1. were. 114.1 “firm-f a m Wu salty. its) The mere-«t will deeruf ffm 1,: an in: am Where. j-M'i “Hf fto,‘ih.n. colic-5M m: Acme in. the. wear: u. = [1&1C‘IJL)—) Afit‘at-BM'EJL regain-hr ., clanking—l rim‘s‘n M Messier -. a; [wt .4. efvsv io=zfit (c)(fi pts.) Howloug after t = D will the magnetic energy,' stored by the inductor reach half of its initial value at r = fl? _ I hir— i" %LLL=JT-F L». we a — a "" F'z. . -1:I'E._ L 5H 1H s tum“. ufmm. rte?- when. 'Z...= R‘Jfgt‘HJH-IBJL L 1'7 -‘f{'- -‘H:. -‘|'t 4:14: __, TL.” qhtfiyhk ) t L _,iiu,fi,=—'~tt _, “91:15 Phys 106 fine! Eran Page 6:"? May .H'. 200! 46 PROBLEM (6} (11r points) A long (ideal) solenoid with 21100 turnsim and radius 2 cm carries a current i. A single conducting loo of radius 3 cm is held perpendicular to the axis 0 the solenoid. Give your answers in terms of 11:. [3)(5 pts.) What is the mutual inductance M for the loop-solenoid combination? Suzie-mid L949 n..= 1m “if-«t N “l (1. 8 1m {adios} h = 3 m frail“) m -% cfimnd" l. l. M = fqnx1€?fiufn'}fmo wfiytjnlfilfllt i M = ain‘me' H [h)[5 pts.) If the solenoid's current i increases linearly from 2.4 A to 7.2 A in 113 s, what is the induced emf in the hop? What is the direction of the induced current in the loop? :11: 2mm Mmajnl‘l'udl, DEMII-‘ldflfllm‘filfll (l ‘1' ‘ - A ' Tied-(Bret _ 1.2”.”- '1"! 1:-¥'1 a=-——v———-—J'--11QT I t 151'. At = 9-3 5 E: THE-K” '“l' 0.3 5 3‘31”? 2,; a?” a = so. “LEW-i V N: Mflqn'hw lfigrufiufi - flhglfl EM :0 tlfldL-WIH err-Md lep 4:: weatherman Mflmt. (elf? ptsJ While the solenoid's current is changing in the manner ruentioned in part {b}, what is the force (magnitude and direction) acting on a stationary positive point charge q = 1.5 x 10-“ C placed at point P that is 1 cm from the axis of the solenoid {see figure}? I . a I 1 "TL: 5mm Merge-1%; flux mint“ Mn. dWC-‘Fidtl E d pain-1+ P. we arse. s2, ffedsmuh 2364:” Earl-“J cue . . - flax Dmehud muffin 1‘ I I I. | i I = I 5:? i “#4:— ” minim”) ’5“ % 'diP ’ . . ' :5: 50mm“ Etiflru‘fldnp’rafi_ fl m% 5% 19% E - (ll-11x15 Wan utm lf-Hlfilililml in mg) n 1.. E a Music?“ or; fluid-i FWE efi-smigcxtrrmfiltit) —; F: tarma‘luiemnrt Phys ifldFicciEmu Phys?” “0331.200! ...
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106-20002-FIN - 41 PROBLELI(l(17'| points A solid...

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