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test2mwf - V Problem 1a Write down the equation for...

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Unformatted text preview: V? Problem 1a Write down the equation for Gauss” Law for E-field and explain the meaning of each term. (6) H Sta/Ho on Gay Gem/é 742. Q 32m extra fed (JV (:OL/kloc'fll!) _.'. " FEM; .' A F? mac/a"- -, I Hm (e, GCLM 55 L Cue 2‘ , E . A A = l. 2’ 5 Problem 1b A spherical conductor of radius R carries a charge — Q. Under stationary conditions Where does the charge reside? Show that the E-field jumps by — Q 472'6‘0R2 C “”6001, AkCV/Tbo’taa CLCWAOU 7&wa .4 ' a, Cam 4%,?“sz W 1.12 lax/Q 5‘0 m7) Mae/j % “a l. 4 r w , u (“an «Gag/ate Mob. 0“ (£12 “MW Wax/Sl— ,._. GJL SURFACE, fflz 2ezW A; 6 s ' Mira / ., 774;; vab/em \ v . , " ' «SH ELL 41 Ya-éSZ/‘CM gr m Swim/e '37 A ‘Sf'géw’ 60“? ‘ _ Cal-v. - \ a 1A,!” W Flat/2644 {g SPheJrI‘CO/C 3qu X 41/12, A 65 “s OJ) (LL-K; Sf’e’l are. 50 E M 7: Ta , L? A Om €27 an ‘ :9 when you cross the surface. (4, 15) [gm/((1 o‘er/fibée, 09>th MLZ’TM/CMW? ‘ ' ‘ . S” Lac/(H \ (fl/34% V) "Va E; U “/2” 64444357 GM I F’C cl. 5 [Vagina (QMEW—e/GL Om C) A C I h . . ._ . SD —‘ L: i T ’F SUGSiéLL ()2 4(3), 12(4) Lm/L‘L: o 'fyv opt/L .5 '0 A N " 2- ,w E {’4 i - C9 1 23(4) AMT/i " "‘—" $0 a. ‘ 4,;(56’21 ' xz—w’l 12(12):"6? )9 om at; Six/W ‘__::.___. (HQ-”Q1 -—a r ‘ .. 76. ‘ 5‘ _> gag 'fsr/ecl 3M”): 1°21 5M7 0m armswg WV W. 1/} Problem 2a Show that the Coulomb Force: kteQZ i; 2 FE: _. I” . . . ‘ ~ , ‘7' IS a conservat1v::(:cle ’(g-urtx, (/dzJY k CQL VIE: 16 A NDb-PE—MDZI—‘N (EM 6% ‘ WILL i FUV Op ”flak L‘H‘U} Ha a1; 0031 P «If awe! Much GALE} .0“ 5 $12: V }) Com/83%{m‘m [Ar «5 CRQCi/QL Laid/Q“ :5 \A j, 4;& To PVoVe W704“ FE G" (WQWVA'UC 5"“ Q‘ 41/ ’ abkd ’W‘mja QZA {Jam 1 MAL/Q (Q2 db“? inQ-iqus . a ‘29. A76 Wave. 1am o, A wfib, ' 0 ‘ A Q] ‘3' 8415.42; Firs? ”WINK Q'z/KY‘IM ’45; oh Ct‘rcumffaeJAOal Awfifil :: 0 A! 54¢ EELA‘ISI NM?! MWQ (Jam? ‘Y‘w Aig1 (:1 A13 _ H‘Y 'T/Cké/Q/(‘C ch‘ {WK/51.20% J-Q .. AL'JAII‘g’: AWAé . EMA/€543 Awfi’B‘?‘ AM} i ‘i ”(rad-1‘5“] way/b; flaw—a (5 Hepr—a AWHK: FHA " 3’3 LNWEJ>EWDBUT oi Para; ~ Problem 2b FE V; Gauge,“ UGJT'U‘P , — 2 In order to place a charge Q on a capacitor C the battery must do g5 joules of work, where does this energy go? Why? (5) The (M a ,3 me: flag» u s w: c 2T g E ' 512d b é-QmeoM Q; (PL: 12;“ "7 a. Problech Show that an E-field stores £50132 joules/m3 of energy. (10) Ta/‘Q (2x (€43 mSJA—uv 0:}? '1"? ~58 4 gaPmaww ck £223; TWM \ 7Q— sax; Ewe/“(38. Wécfil ‘40 PM i— & O“ P (A 2 ME 3 fl» 2C. LAM/LC Q :: (r; A M 3 thj 22¢} Wary» Q”“ (P) QM) W E (A W)» f\ E, M M \MJK ‘ (n z ,4; 50 NM ’ Q2 '— $23426. VLE “" ,___..———— " 1 fl QC; 260 v 2 , S M 21 A642 ' 72: C" (£0) -: 7 Q- E 2 ”A , E 0 End?" (Ad/U; m: 6— 7L“ M77 f“ (V15 “.21 U5 _ .L éwo E2 —'-"" 2 Ad 4/; Problem 321 Show that RC has the dimensions of time. (4) r. V ,_ V T I Q C = 42 \ll 5 o l2 C: = ‘L.’ \ 52, Q V I. w yteeol. \ . . var (RC (haw/*5 (DlM—QqSlotLig 6;? . w‘<.. Problem 3b Write down the physical bases for Kirchoff’ s rules. (8) I100}: Quip; ~. Pa-I'efly‘CQ/Q p5 :DQJNQM 13‘0”" QWJUQ $29 I)”: Vat/PM a}? aura; PAW“? ‘waab m QNW” m. ‘i‘om‘ 6X4“? 0% PD'l—e—vx/(ick/Q CM (1 {WK/LAI" (be gag!) I Z AV: 0,. Lop/"3 JuNCTtroN ‘Qjfifa CM‘YVZWt- V5 €2sz bf; C/V/wuwjg de (2&th “g (Dis/\xgégx/UQA 50 ‘bDl-zz/Q (>th 8437‘“? (”N/WM, Wm (g. \MC/‘lgTOn ”W73? (:12. “egzler/Q ’ ‘ ‘ («*wa 47) (15M— blZ/t “A (final/v.2 — g louse“, : 21 a; N» _-//2 Gem Fla/wag, (LE/036d [COP 5/7 | Problem 30 In the circuit shown which resistor has i) the largest current, ii) the smallest current, when the switch is closed. I loco! 000(12— .‘L 8 E '2. 5 Problem 3d ‘ S W Shown are two circuits F" , R, =10kr2 i - _ C1 =1#F C ' 62 R2 =1k£2 ‘ R 02 =lO/1F E. 2. . E1 = E2 =10V If you close both switches 'at t=0, which capacitor reaches 5V first? Why? (5) qua. Pb/raq/V'a/Q Mag (‘3 ‘pmwf Walk? — b lame 51: E}: IOV Q‘CI : loéx :56: lf'arflez. 3 ,5 ’2- Ie‘LCz: ID XID z [D J—ec, kw (Mu: (”62W 5V 0/6 SON dim. Problem 4a You are given a charge q, how would you discover the presence of a {3 field? (5) Gl‘v‘ev a; Oij -€. q @69qu (1 UeXEQQ‘QOf V a 948 Ole Mpdmgwqgg q dam/C42. ”feivpCemC/U “-9 A Cake/L “gt 'U‘ CilAd am \ ‘5 {W73 (7 (.0 L27 [Au/j a 31/; Problem 4b A current I flowing through a conductor 91 produces a 13 field at 1”. given by AB = 51 [41:65 _' 47r r Show that the g field circulates around the current. (12) flare: ("A‘Wwéaflez flwm .1:/\n> Ea ,4? (£4 75’5“}: Problem 40 Write down the dimensions of i) Magnetic moment ii) Dielectric constant iii) B-field iv) Capacitance ll) [‘3 I AW? [(9. QTflLZ if k; .4; u D’NQM’AUMQM 31.070 “:1 HQ’IT‘I’ (/l’) Fa“ jfgxéj '3'?CP T'l A 69221";le U”) C: a flag” ...
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