Sample_Exa-_1994

Sample_Exa-_1994 - Name > PHYSICS 322 Hour Exam...

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Unformatted text preview: Name > PHYSICS 322 Hour Exam March 2, 1994 Do all four problems; they are of equal weight. Before beginning any long calculations, state briefly the principles you intend to use. 5‘59?” /100 so = 8.85 x 10"12 fared/meter [e] = 1.6 x 10‘19 Coulomb me; = 0.91 x 10"30 kg 1 =9x109 41reo V 1.a)( 12 pts) State Gauss’s law of electrostatics in integral form and in differential form. C“ ,. 1“ SVEL'AE = Ciwmk lgo SV= We QMQWUVJLM ‘ E3: like"; QWCK‘: QW‘R Q AQ\\ W‘ Z '5 b(13 pts) A spherical conductor of radius R and charge Q is surrounded by a concentric (thin) M spherical shell at radius 1.953. to 2R. The shell has net charge -2Q. Te Find the charge densities on the furfaces at R, 1.95R and 2R. R .. ' e— : 01:7»63 /U—rw K13 ’ “shun \R‘ak Maw —Qz K°9~Klbvmkwkowmxshm W 8’ —; _. clien- (maxik’fl 'me Mt c.\r\°~"°e N am”: «m ‘SQ NW Mama RAM. v ~k~m=~®< ' Lg 6"-< —Cx/Q*W"‘Kkl Find the electric field at radius 1.5R and at radius 3R from the center of the concentric spheres. 4. E U, mm“ bk MQW usch w glelnmxmg S '\ 62 E khga —.—. n, ___._. E ' kggfu = "q k“@ 2.(25 pts) A long cylindrical conducting shell, of inner and outer radii 0.95a. and 1.03. is placed , _ t. in an initiale uniform elecnc field £30. The direction of E0 is perpendicular to the 4 cylinder axis. © 4% Find the potential at points interior and exterior to the shell. 3.2; 7: 'Pxo+ ’BQQmm + kp‘xk‘r $05 ems-Q4 \clv'x ‘ Q lachmm no (Ma y 0 ll E5 L“ _L_ emgmak rev-Doe \ 0:;i\ ,‘ ('7 66 V m; 2 szvoriks OQWW (\ 4% so \g) (k, N -— Eomcflg P‘\‘= “Eu Ev‘ —. F" ’L k> CL. \5) 6; = [\b .\. Begum + 0339 05\%‘\L5\L°\ W K§=- SVufil“ ‘5‘; = W" (éktx\ ‘5 RD S K Me bkqw‘n mwgwm7 0; ~‘BL “W— ? mp_ §:,LQ L 3. Two point charges q] I i; Bi : E :7 and qz are placed at positions R“ 7 (ml '42) ’ (L1 (0,0,L1) and (xz,y2,L2) 1‘ ‘ ‘ 'r A \ __.__ -8211‘813-‘13 relative to a conducting plane at z=0, as shown in the sketch. a(10 pts) Find the electrostatic potential at a point (x,y,z), z>0. W1” M QSeM‘emM K1 W Wmtk W Xx *%1 M S\’\\i\N\’\ _ ‘\ L. —- a) L '7: * -—::,——- " ff” WW 8‘, _ 83 gm“ ( ,MSW “5,91 \( “mu (Q‘X‘AHL \\ * ‘11 “l‘::/ -— L . H,” \l UP‘LQ'LNUKUB-hIx—VZ: “L25” \{Ga-XzXl-x— M‘s-“XLX‘tLQfiE b(10 pts) What is the electrostatic energy of this distribution, taken relative to q1,q2 at infinite separation from each other and from the plane? bxjéivk‘m one“ F352,: .QMHQE W ‘ \KA £50 ’m‘kmfi 1 L3 “a a8 g’gkm «laws v- iiKGL‘Q U9 * cng‘M l fifit‘wg 3 \ -—.- ' I .— 3 L...- 05 W / ~ 3—— 133. + k 32,. + ,1, ‘_ \W\ “\9 (‘6‘ 2- R Cfifisx DEA-":73 Ub—JL'A HM— EU _ _ g .. exam 06L + 1 L 52L + L“ (1‘5 K” CE?) crew‘s“ ‘k‘ “‘86 m“: \ I " *” cu \ . °9W \ V9. -“;_\\ \‘kz' ,1 ¢\%Q~3* _ CS\% * 7‘. q E L ‘ %\ 1 “Eva "W-A 8K 83 (3-1—3 $1122. 7-1-1 reg; {a JUL) c(5 pts) What is the net charge on the conducting plane? /~ " 4. A spherical capacitor is constructed from two concentric metal s heres of outer radius a and inner radius b (a<b). There are 2 shells of dielectric in the space between the spheres, with dielectric constant K1 for a<r<c and with dielectric constant K2 for c<r<b. The inner sphere has total ~ charge Q. a(8 pts) Find the (free) charge densities on the spherical conducting surfaces at r=a and ‘ r=b. 6.5 DA = & 6“" 93,) (A 1) hm ‘ V‘D h" (7* “A a. Mm W 3 x M so “’ . m 53;. 0a. —_—. -— Gum m b(8 pts) Find'the surface polarization charge densities on the dielectrics at r=a1 and r=b, "D W «(NL‘O =2 {i N and r=c. qr“ n} ‘ D u= as; weave. = 8.3m: 9 3—.— 0-"sz @ ~ C K) finite A A " h \ a «v: +n~ 3120‘ m a: "“ \D GWL—Or'figr ’L '3 m'k .L. ? T“ m (rpm: U “(D “moi [C(Q pts) Find the potential difference between r=a. and r=b. 3 0e: (Luc— EA ® 3x: —R. A So 6'? L33 1: 31.x?”ch *" m’ Eu “:3 g ‘ ‘ \ z a‘mLU-{zv u-‘efl’ w R Kx $52on "v wan Q ’9 1' ' Q i— -— ’— 9; L *J' W. Kink L O“ c\ “W‘EuKz C“ b x x _. “D A L‘} A \ 'm . " ‘5'” *9 V378 +RREM® “a SQ‘Wflw =" 3 LIB “% : g 's~ V ‘3 = 1 F +1 V _*, "E ~ \x in mg, x {:1 3 .Le3 (g. F ‘ "o - '3 =.— _ —-- _. ._L ‘9 ‘3“ “' 4' mewe '69 “8 5 Fe '* masks :5qu “I 57mm?“ a“ «fa—8V9 4' ‘c-tv-t 2. _ __\__'B 1'3 L '3’ -91 7 L ‘1': '3 43m? Axéubétc (LIAN sweée'éq -= mém‘ié 4a V1541 0 EB“ £A0_+B‘i\ ~+ LEW“ me + (kz‘3+§£\%m§o ~‘~.) ‘ +~> wqu ' ' '= LAc-K' Be,th +U’u m +34“) «.6» LG- 80 *' my “r Bag-X mxe~0g~~~ mefl ...
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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 Wisconsin.

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Sample_Exa-_1994 - Name &amp;gt; PHYSICS 322 Hour Exam...

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