PHYS 211 Exam 2 with Solution, Fall 2011

PHYSICS 211 Quiz n TIME: 60 minutes December l5,20ll DO NOT OPEN THIS EXAM BEFORE YOU ARE TOLD TO IDNumber Useful infonnation eo=8. 85x1 o-12 c2lN.m2. E Check if solution is continued on the back. Score: l. (18%) Consider abattery producing a current /flowing in a long cylindrical wire with resistivity p,lengfh / and diameter D. [AIl the onswenr below should be given as a function of these parametersl a- (6%) Start from the definition of a current to show that l=nqv6A and use this calculation to define, ft, e,vdandA. dt 1.= A )82 N1 ,,,ln*. al E II.. 'L*'J"V fo nl* b ,l-t > AV lc'[ttnr/a'cc t- t4 , ^-,4 'J(*> v c- (6%) What is the enerry per unit volnme dissipated in the wire in I second? Y1* "l^s*iyJ.d 1)ouuL .'^ ilt n?'v{sf,u z L ?. R&? z # -:+ vt/z fzL't t" t-s =+ rva p$;ir, fr" =) d$t, c lt t- l/. rl*,r /*'fr Nz nV J** ) u t Ut nol'L'n' 2 Q'* +&.n1A*< =+ E--rf *s "1Ant'q ,-I"u* cttl A l/^ /t"'f t/r";k b- (60/0) Does the potential drop across the resistor depends on l, justifi. 0l-," 4D: b{e ?3- ut R,= ?+ d^J?=n1urA =) AV' f lnlUl tr.t( fu6 AJIT efVr*"( /72 n . E Check if solution is continued on the back. Score:_ 2. (s2%) l- (8v:) u:ing Ampere's raw, show that the magnetic field generated at a distance a from the wire has tle expressionhpol/2i. enycLu's -4,a', ,$6.U ,1+f;o 1l* flm"pottbn H 1n,.t.) i o crbc,l, arJL--l o* Il*, Lrd. ,,r/A'*2;^ n. -, ..a, . =>h"BE z $aas z B fotd o+',r}a ch'beL On.t dA.L "rrya-:+ a(rr.):Va E :t =M 7Ba, )a W.tru Z L ,'^, €4/*ll;b,ur^,rn :i Zf -O \ rF. E* d sA,n'Yryltr q ='i,Z.'l-j , E ncr*' $' !- i^il^ *t: obbt'h'^ :> i w tn tL - a - Alnea[U^ B,t 4 2x* u:e Ltv+ E] Ctrectifsolutioniscontinuedontheback. 3 n/^rilY -aoC and direction necessary to keep the *ir" Z tom current Jn is laid horizontally in free space at a distance a from the wire I which i, f"yio! Jro h. "Lr*rUy_on the ground as shown io m-, ng_. to the right. Determine the cunent.l" "roptitoO, Score:-- - fr;::ffi: at a distancey from wire I is moving at a constant u!g.rr, v inthe a- (6%) Determine the distance it has to have with 0t?. t so as its frajectoryisnotmodifiedwhenyca a tO , ,, ?/ //' e ; .r7zd *^d " /" A: oLhc /is- 7> # *,ai' u'-J 'A t *"ot /' d/>e b'4 d,wtJ"/ t" l'l' w =) zF +0 -t c. notmoving at all, justiS? z:o Ef Check if solution is continued on the back. 4 ry *',o * ;,,a*l*, 'leclron-elm-be placed to stay in equilibrium if it was justiS? b ilr. *- a7t )r, "r/aze or{"o" //, Q^ttf, /"rr+ Score: 3. Q$o/o) A vertical parallel-plate capacitor with area A and distance d between the plates, is half filled with a dielectic for which the dielectric constant is rc (figure (a) below). tl t l ffim atK ffi (a)(6%)Determine tn" "quiuadl capacitance oiJn. ,yrt"- when the two plates are 'j:'1"5""fr:r;fi8U a^lltno,cc E /./, o*. ? /,/. 7{/t/ t/t/'@ , 4? f^ bc ra*'e'aluzed he ftn ry cr Jz'{?u'rrl' z) Coq= (t t cz = 4- K& z/q\ gS fr -rl A zL7)7 (b)(6%', Determine the equivalent capacitance of the system when the two plates are positioned horizontally and filled up to a heistrfdwhere/is the fraction ofthe filling. tl,€^-'lwo ca/rt*r/ya- uv S, oelvt24 + h .t Lr t 0'-) r, Arr?tW.tZt -t' x,3 A-o< -l-*l- cr eL ?b(,etz4/ T'* % rc bL" tt - = t retl , = - 8'.0. 91- = 2( .1t* D)T (c)(8%) When this capacitor is positioned horizontally, determine the fraction/it should be filled with the same dielectoic (r) in order for the two capacitors to have equal capacitance? ca,,s L.r, )e$},,ffi T (ant)fd - vc(, &) tl l+K 6= z) EI Check if solution is continued on the back Score: 4. Q0%\ Kirchhoffs rules G' -r -l t \ l (a) (4%) State the two rules of Kirchhoffand what each of them represents. ,fffin*rffi),, * = o ; i oo/c t^ffi- ylu- ir^rl,wao./, o (zZ)rn= Gd)*t t'!o;yfus"'"I* (b) (13%) find the cunent jn each resistor in the Fieure aboye. w. chztne ilt alrtn"k "D6;fu/rr/C :> TL 21r*.'J,V-' nt/' =>Vrtry4 U 11. Li bf ""'/^ : b\V+ blJ'or+ 0V..' + 6Y'6*bV6o=o z) +2, + tL 24 bVah 2l ? 3,= \ 77= ( 7t= t 0 Zz t?, L. f?,8, = o I ry' { 6V,rr + b{on =o t 44 P,4:o ={ 0,3 ( s ,,^fl ?.G1 ' # 3.0V ,n ff E Check ifsolution is continued on the back. Score: ftfi"l?ffi*l; potential difference berween points c ndfwhich point is ar the Nl. -- Vc - V : blrc, * oY rd z) vf ; ++i* ,Hfr'" =-6a'zv (c)Q%) Find the potential b,etween points e andf ,t'+ce ,?& c/*rn*-l ; ,h L/'rrc.n ( */ / z5 bV"6 - o (e) (5y0 compare the power dissipated to the power generated and comment. 7L< fln u, A o8srVol"1 bA l* ));A- ; ?,= P.8' . *ag<:l&/ z o, zq6 oo{. ?=?ot'. ?{.h6 rnn\o ?. - ?6 rm\I/' (*trnrnt'nq ll" t"^du^'^ */r^ /" u',na/ d "l il, ztffi? r" d^h, ol€* :> 2f ,r"A o'h a'^ d 6e'Lu26lcr' ,&^ 7t D il" "h t/ ^{/ a/ da < a'#4blb'' :u) A ?rr=+&,bv,z+&2, =26.q5 7, .= +f,qa\45 = EzZ+ .= 915.2 ?r, .' + Sr AVo '-2.2, = t g4-r' -D C\**rfr/ 7dr,u* : ?r = z/,2 W Err*nlA 1 -, ?, t 2h2 W dr>e N El ctrect if solution is continued on the back. 7 score: