106-20083-MT2 - PROBLEM (1} (2:3 points) The circuit shown...

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Unformatted text preview: PROBLEM (1} (2:3 points) The circuit shown in the l‘ieure has a )arallelv late ca )acitor whose Jlates are a I connected by identical conducting spritth (each with a force constant k) to a battery with emf V. With the switch 3 open, the plates are uncharged they are separated by a k Capacitor distance d, and the capacitor has a capacitance C. When the switch Sis closed and the d capacitor becomes fully charged, the distance between plates decreases to 5-. Express + ‘3’ l your answers in terms ofsome or all of the given quantities and related constants. (a) (5 pts) Find the amount of charge on each plate. . . . . . . . . . . . . . . . . . . . . . . . . , . . . , . . . . . . . . . . . . . . V . . , . . . . . . . . . . , . , . . . . . . . . . . . , . . . . . . . . . . . . . .. C: 29A w a! wise“ the, switch 5 i5; (Listed! (_ 39A . l (b) (8 pts) It is known that the force exerted on each plate by the other is F: find the spring constant for each spring. F: 9" aeéa Crwedg w»; 2¢A=CA p: 5?"! fl tacv)‘:t{c‘=v‘° 2c3 - 2C5 Zcel Zeva F: a (c) (5 pts) Find the energy stored in the capacitor. ..... .. U 532 m [g3 ‘ {LCVP “ ac.’ ~ Eta-0) I“ ‘th 7 523 i!- to D Q a; 280A 50) we, {Agave '. cam“ tai- 4* i‘: =3;— :: 2“ Cm..." L ’1 a V it W—ll—I Each SPY‘IU'W? give};wa 1:7 a gamma. where A is the plate area. Using this fact. Nit-s (d) (7 pts) With the switch 3 desed, a dielectric with dielectric constant K was inserted between the plates such that it fills all the volume between the plates. Find the induced charge density on the dielectric surface. ,r act} a. (I t \ 071=a~(1~—Li—"R(~.L ‘ ‘ A t N l Ci d‘~ : _ _L l L A R l C-cl c = E211 —a A = 3"“ a 9 Phys 106 Second Midterm Examination Page 3 Saturday, Aug O‘l, 2009 H _m~l.. PROBLEM (2) {25 points) A cylindrical glass rod has 3. length 1C. and a diameter Di as shown in the figure It becomes a conductor when heated to at particular temperature T and its resistivity \zu'ies with position I; measured from the center of the md :15 4 ptfl=flnjt Where p” is a p05:lt\c cnnstant. impress )ttur answers in terms of some 01' all of the giten quantities and related constants. Solve the emblem with the glass rod at the particular temperature T. (a) (12 pts] Find the resistance of the glass rod between its two ends. . . t . . . . . . , . . . . . . . _ . . _ . . . . . . . A . . . . . . . . , . . . . _ . . . . t . t . . . . . . t , , . . t . t .. Let's‘ ‘73 "fi‘uitsx I 6‘ fig‘lfi‘liflu '35., rFyufimt inlay? $644.5“! all? m’ L - M 1 l ma, {Va 1"“!«1‘51; rfnqlgfxr,.u-'tf$} cite. " W 9 “ml c w ‘5" 31:33:? f (It: (a L; fur T1, iflfltn . Li";- H strafing : ‘lgt §?Wé ' "MB? .2 i 1 .vaa ; l - I 3" l; l {a _ gigs 3'5 “K2. , {3.133.351 , ‘ newn- ‘ i ‘t N l t fil‘ "‘ 5 “5’2 1 R_ figure ALP ‘EHLI'Q‘ 32- (b) (8 pts) A voltage V is applied by a battery between the two ends of the glass rod. Find the current density and the steady- state electric field in the glass rod. | Eagjt z” mu apt-u...” Q»: seruamm c. Mgr: veg WNW I j = 3a- ! MEL - "y—E I Wkfl'l‘fifi & ‘-’ "as"; a“ ti AWE-*3... it? M“ 2-93 E7“ ' 2;; “5'8 l ‘53 v j: ! ngfimmL: (e) (5 pts) Find the electrical power dissipated in the glass rod in part (b) . , . . . . _ . . . . . . . . . . . . . , . . . . . , t . . A t . . . . t . . . . . . . t , . . . . . . . . . . . . .. P: 1% = (EAJZQ z: E‘A‘ ta A :n(.31.j2.: mt. A}: fight F‘ wow Etta 30L 3;" L?" 201'”)?- Phys 106 Second Midterm Examination Page 4 Saturday, Aug 01, 2009 PROBLEM (3) (25 points) For the circuit shown. the switch 5 is at position 2 for a long time and the capacitor is totally discharged. At the time I: 0. the switch 3 is moved to position 1 and the capacitor is being 8 charged. Express your answers in terms of some or all of the given quantities and reiated constants. (a) (8 pts) Write an expression for the charge on the capacitor as a function oftime t. . . . . _ . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . .. CQPa,r:l"i‘ar~ g}, all-rarjin-j wi‘i‘k W 'i‘e~°t;t4a mower-i“ {‘1 :geg‘l': €£R+£+&}Q: QR; air-.3; (a “gt/e) Q5=Ci I g “t fl'iflc. ‘3 ‘ ii=¢«€trc )[ (b) (7 pts) Find the voltage across the resistor 2R as a function oftime I. . . . . . . . . . . . . . . . , . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. LNt) “:VO We a mess res-ééequR i ate) = Maze i = d‘fiQt) CE, ~‘t/‘ific At. Lia; , , -e/ec. !. (t) h‘ "a; «Eu-hum: - Io 5- 2 a “ H I! P g: It 0 I] at (c) (10 pts) After the capacitor is fuiiy charged, the switch 5 is moved to position 2 at a new time I = 0 and the capacitor is discharging. Draw graphs of the charge versus time and the current versus time for this discharging process. In each graph indicate the values of charge and current at the time I = O. . F'uit L ‘ r . it ~ = ‘ {*3 ‘1 Ca W12? 6: :i Water +94“ :63“; easeieafigvij . hit} with the. image sews ems-:12" * i» T—Efiefitfiifiafi. gfl Ewe +3»? {gems t5“; UMQMAS , t manta—>1, i n earn-mt'em— . i “MW” e. O ‘ cf 2. *7?“ 5‘ :3 a» . . i "an; m3“!qu u ...- ; “pqu run was: cum mO‘O t Phys 106 Second Midterm Examination Damn -: c r ' - M *“ ‘ ‘ PROBLEM {-1) (25 points) The magnetic field of the Earth at a certain place is uniform and IV directed \ ertically downward. with a magnitude off-0.0 ng. A proton Pmmn ~~ "—AE W is moving horizontally in this magnetic field toward west with a H; _ X B (uniform) speed of 6.20 x it)6 m/s, as shown in the figure. The proton has a S mass of 1.67 X 10’27 kg . Neglect gravity. (View from top) (a) (7 pts) Find the magnitude and direction of the magnetic force the field exerts on this proton. . . . . . . , , . . . . . . . . . . . . . . . . . , . . . . . .. a, ' i" w: *1 C‘ll'lm “’3; :9 tr- ig G; twterig'tfi M we- I e = .. Q l ‘3 i, 3-, l: = lffié» 3‘: E 0"” M +cw'mcé wail: wwmwmnaga—M;-¢=M.Rm ' ’ Jaw", ‘ _ w live-W ’l’h‘fi $51451 ii? {1-th E ’5 dive: in“ (b) (7' pts) Find the radius of the circular are followed by this proton. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . , . . . . . . . . . , . . . . . ._ nu! “ya at .i. g _,_...m...t.........,..--..\ Pee-~59 :4: fi’tasi‘ie/s Mani ll!“ 2 i2. 3 (3 PM: .i mi time? a Fifi!“ UCM W) 2.: “‘W i. w 2: New F P e F b m agenda?"Keenan‘s}; Hrttfamé'f‘?‘ (c) {6 pts) At the instant the proton is moving horizontally to the west, find the electric field {magnitude and direction) required «EQNQ-V’Cl WGFT'H l uh , "www.m‘... to make the net force on it zero. Essrewc 1, ‘2’ rug-HA . q n rm ' I Hie rl “4:41? E... r". : J j l in“ "" «- 3W5 l ’93" ea "‘3’ ‘5": =1" Te.» “‘3‘ ‘1‘”? a l g... ;.%:{g ‘ v. “,169 ,-‘vp w- - T.»— .,.. v X-TJ | w: “a -m=flW-rpqilie.4c—gmm “W? E g C. cm .4 N, .J . Kfifé-loxsoflifhfiifififo“) ; (d) (5 pts} How does the kinetic energy of the proton changes as it moves under the action of the magnetic force? Give your answer with your reasons. No credits ifthere is no reason. a? i I F a e "u: K r? l 5‘3: W 6* “figmflmmflwfi v5 ~11 , “'9 E - 'L U“ ul- l: ninety": a; l: LUV: WC" Cmufo-"amf l K1—Z'Hi"; '5 next-“fit: W. the. éu-Lve.c.viwu 3*? “defines 3 332*“ “Mi! “. , r- ' ,L Arias“ H. We sistcné‘a-stjl‘wfl. Jew-:9“ $08: «1:? {Ir-’A-C‘véfil U“ : u- .. . 0 cm ' o" r; omega i _ ,, t i I» “t i u w c. ! Phys 106 Second Midterm Examination Page 6 Satiirdnv, Arm m 7006) ...
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106-20083-MT2 - PROBLEM (1} (2:3 points) The circuit shown...

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