Sample_Exa-_1990 - (B Physics 322 Hour Exam Do all four...

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Unformatted text preview: (B Physics 322 Hour Exam October 12, 1990 Do all four problems; they are of equal weight. Before beginning any long calculations, state briefly the principles you intend to use. /100 s = 8.85 x 10‘12 farad/meter O |e| = 1.6 x 10-19 Coulomb mel = 0.91 x10'30 kg .1— :- ("x\0a MW 20 _2_' 1) A spherical conductor of radius rO is surrounded by concentric spherical shells as foll ro<r<r1: vacuum r1<r<r2: dielectric K r2<r<r3: vacuum r3<r<r4: conductor r4<r : vacuum The sphere of radius rO has net.charge 0; there is no net charge on any of the other shells. a) Determine the location and amount of the screening and polarization charges. (13 pts) $W“‘*\ Cnfiiruiflxt><$wcmmép cdt kafiém WW ~—NV3 \“NVQUx *—<§émm. 8Uulgsxo wk) (JandlfiaAnuSsideLt (3" -= -— VLuwn’éX 57:: +~9L /(¢figflr\ mess swam sewn M, v-Eco mm erANg> AmmfiAL3\§§Psi> ‘ SMM ‘fi§{xwvfiA.V¥g{9;;%§Ag>« <3V“\E§QA. \y, mAuEgtkny\, Q53*“%§.‘§l&US&RuD Qf":. a\-(E: - Qé’ b) Determine the elec "RQ *3 FE: (bx—0D,, (Ts-s ~\'\>\= '0“ RYE/41m}- ‘yv" * WV” U"3\a\"€qm% ‘. =. 1w a} Ge”. "10 “TD ‘14 P - Lean}, 6‘? ’v “U I« 'i‘ 12?: tric field E in each region. (12 pts) [vulva 3%va E = ‘L/uwscoa Vanni" E = ‘L/ UN Kama-X E 5 CU Law Sfisfl C) Ei‘z abAifiéongg , —3- 2) A parallel plate capacitor (each plate of area A and total spacing d) is filled with 2 slabs of dielectric constant K1 and K2; charges 0 and —0 are placed on the conducting plates. Find the capacitance C = Q/(voltage difference) for each of the following geometries d‘iA/L‘ _L QN\M cozuvxww a) (13 pts) S /// fit: “’4 b '7' Se '3 Q1“ WWVN‘ Q K‘ KL Q WK“ E1”— .Dvggu: {Kit} ~ m . A A , 13;?“ "r (“W / K130 6‘ A7. 7’ d\E\+ 6162': "ED dT‘Zf -.- c3 '.... Q @P: WQOK‘K\+ C = —- —— Lfigo Li 3 184% Cd k /EJ_\'<{* KL“ b) (12 ms) __ E W4: a (mm -4- 3) (25 pts) A uniform electric field E0 is applied externally to a conducting spherical shell a<r<b which has a charge 0 at its center. Determine the electrostatic potential and electric field in all regions. m B: ‘33 Egg Mmhm E” :0 mt “do (1(0/ E-fit $3. I K%w\ . . N 1to‘ a . _4" g”: 67%? m 833,, (Kwaom‘>hm\ “M “44”” “8““4‘ M Q do ate, k m gain \Sm meat. was”) La<m \ Q a, sum $.35) §= %‘«80Uot“ Ta * meson» = 5SM 4? §E_c, (T R.CG>E9 ~¥ ng} €3369\) ._ __ » ls E 3‘72; " E0 4‘ gift-£5“? m .k 4) mm g? v, WoBDAkkafim, ~3 ‘\ E ..—. .2. v? 0 “P: *st U‘) E" ~? my” ’6? w -5- 4) A spherical balloon is made of (light) conducting material; charge is placed on the surface to keep it spherical. The balloon has radius 10 cm (0.1m) and the breakdown electric field of the surounding air is 3x106 Volts/m. a) (8 pts) Find the maximum charge which can be placed on the balloon before breakdown. E = Few . e - L z (a «e » GEM: Meios- um’: Kmmtohxam M“ = 3.33m*"cm& b) (9 pts) Find the electrostatic force per unit area on the surface of the balloon, at maximum charge. _.‘(. 9 GE, E J 835M“: <3351~16‘7'd3>a\b(*31 (.gjs Egg, é‘721 Q“ 1 7L CWW m \SW L9“ 7' Nhflhm “ML avaoanxn1 ¥A<L c) (8 pts) Find the electric field energy, at maximum charge. "‘6 £§3¥1 ,soe. We, 00 mm“ mm H: Sch, E55. : flgflki 7'8 “33.. ‘i "i L'Wx'Eb Q. n.“ = if. -.=-. Ohm; x ‘4‘} ‘3 MN“ m 0‘5 ML ¥ = " 3.9. —,-_ V cc‘gmlmx” ww‘ W " ' Reflsl 7. k4VEed°\ (rams. 93% m. {L 2. SSL_ z =: i2;- Egtu) tuox-!) F/A '5 Via-o: ‘ {1k 46609 2' X g a - v '3 A —_— A \ (1— . ‘ I —-... (f m '\' 9 Rafi + (Q -—--ns 5 B a Q quak W A k , ‘ .. " ') .L’b <1, “’ TL $1.9 “' % N :{e + ‘1 ‘._E h “3'65.va P“ 4" manna he 8"“ e make'm‘g ‘fi —= '3 .LE‘. +1? I ARIO‘J‘VN “ rnmvfi 'w. i <\ > ‘ ‘11 ‘fi’bfi LAmf‘SvAABL —\r—~-—2 —-L V2 ': @261“ ‘31 + rESwS B ~53 n‘wb cQ , n + ~A ’ §W\\Zg& '= (Ag-k “Be,th +U\\ m 453‘“) £6 LG- 8.) *r kkLm‘ 4r Ella-A qme-Jmavw Mmfll ...
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This note was uploaded on 03/27/2008 for the course PHYS 322 taught by Professor Bruch during the Spring '08 term at University of Wisconsin.

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Sample_Exa-_1990 - (B Physics 322 Hour Exam Do all four...

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