106-20082-FIN - PROBLEM (I) (20 points) A iioneontiueting...

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Unformatted text preview: PROBLEM (I) (20 points) A iioneontiueting infinite Sl;ib(llkc.1:l infinitely [Lii’gcplastic V sheet] with thickness 2;? is uniformly Charged with volume : I ‘u . Charge density t). Assume that 11>» 0, (Note: Whenever you use Gauss‘ law. Show the associated Gaussian surface clearly.) {a} (6 pts) Find the potential difference, VAR 2 VA 7 V3, between the points A and B. (C) (3 pts) Find the potential difference VAC = VA — VC between the points A and C. . . . . . . . . . . . . . . i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. gecqqse. line refieel‘iaut A Sémwme’ifi'cj ' 0L (camel, Wrig‘jtqufi (0%-!th) l (d) (5 pts) Now suppose that an electric dipole having a dipoleimoment with magnitude p is placed at point A in such a way that the moment vector makes an angle of 53° above the positive xiaxis. Find the work done by the electric field as the dipole rotates to its stable equilibrium position. : WWLL do“; {H E, [chi {fem 3: 1L0 JC 0. ; " 11—”? A 1 mail t“ u ’ eta/thafi WEN NW“ __...) . l”: i l . n. ta 53¢ a) gafl‘ AuzANF (d ’ | E l: ‘ ‘3 g I —--‘—:)"—F.E I Q— r” ul.:_£l: 52-5 Uf :5: ft :.—be¢5 E i :2; Hr w w :’ 7595 I @ lc‘ Phys 1.06 Final Examination rage 3 Monday, Jun 01, 2009 PROBLEM {2) (20 points) Tlte figure shows :1 paralleliiplate capacitor which is partially filled with a (lielecrrie maierial having dieleczrie constant K. The area of the. air—filled part lg one half of the area of the . _ . {2’ capacltor and [he :lnekncss 19 7;. ,\ssume that Kagr = l and the capacitor ls charged. (Note: Whenever you use Gauss’ IE A”. 4L<—A‘;2___N)N law, Show the associated Gaussian surface clearly.) , . . C . e . . . . . e. la) [5 pts) Fmd the raoo, F ofthe capacxtance C to the capaeltance Cn when [he eapaenor 13 completely a1rhlled. C :5 lla¢ Quiaalemh Carota'lg-mmcfi 4 Co ‘ l ,4...“ M m ‘_; A l K K e C - ‘19—— _ 50A __ .Jku—a 2—“ H1; 3- e - l Gig—fl: E"; AT: Cr l2 m (L H1 __. :2 6.5/1 9" $641 C3 K13: / - :K A Cl’ 5 £0— E CL (b) (5 pts) Find the ratio, E? , of electric fields at points 6 andf. ...................................................................... .. f . we USC 6“:is l“) §&?' 3“ QQLAL mfi—r’ : 'l‘ {<50 E m— eoEe'AA : 0‘ f i l (c) (5 pts) Find the ratio, 31 of the surface charge densities at points a and b. ............................................ A. . g ‘ . ’ f 45“L Mag/Wei i Liam l) 6.41%: walled cq‘mcclmse 2W1 Mall“:A t Hams Elcc hoe f“; r 0W- —-—"“_'"'—-_-_-—T E ‘ law hric‘o pf— ?a. (Q) l games A. AA AF ( ‘ ET "" 1:";— "’ ' C23 ‘ Full 5 K“ E b b l /1\ C13 \f :7 E5 : fig e :1 .CK/ZF)C° : l<‘kl . l (d) (5 p13) Find the ratio‘ i,of1he en’ g like} in}; E; ed wing? ‘ 0-b— E’ 2. Palme- A ; A : FVAkLS ‘ r-EiL ' “'9 ta 2|: 59' l 2 | ,) L3 : lLKE°E3 , K l4“)! 1??? l” 5‘: as, E; I 1““ Phys 106 Final Examinatlon Page 4 Monday, Jun Ol, 2009 PROBLEM (3) (30 points) The Figure shows an 1ntinite conducting cylindrical shcil With E t _ /’ . . inner mthns and outer radius R. The entrant flowmg on tho sholl IS nonuniform and IS given tha current denStty J:— r where A is 2t constant. The total current carried by the Rheli is I. (a) {5 pts) Find A (in terms of I and R). ’7 j j j A A P‘ at V j 3“. 2m" F (’ng _ f R f: 27W“ 3” fl/z r is; g 2: 27M f ‘4‘ I Y We (13) (5 pts) Find the vaiue of the integrai §Bdl for the circuiar closed integration path (also known as Amperian loop) shown . t. . . . .' . . 21? in the hgura. The closed intcgratton path 15 coamal With the shell and has {‘3de PO“; 1601C \ j A lac: J (Fl—fir if WI 23113 for which 5‘, = .) J (c) (10 pts) Find two points at which the magnetic field B is one-third of the field at the outer surface. (In other words, find r A? LET:- ( giant, {5 h____._._-—é-———*—'—"’_‘ Phys 706 Final Examination K Page 5 Monday, Jun 0?, 2009 PROBLEM (:1) (20 points) The figure shows two identical lowshaped wires inside a uniform magnetic field I}:3i5)-i-'T. One of them is held at rest while the other is pulled by a force in such a Wily that it slides over the other with the constant velocity B:(4;'+3;0 this. The resistance per unit length of the wires is 30 Slime Both comers have been at the same point at the initial time t: 0. Assume that the arms are very long and there is no gravity. (a) (10 pts) Find the current passing through the circuit at time I. Also, show its direction in the. figure given and explain how you have found it. No credit will be civen if there is n0 explanation. : D i a, lCMdii/to Jl‘hQ. clcreclfioq (5% We, CUUUA— At tame E S” V 'g l l i .i ei-eoaaéav» lee - i 7 I I ll ‘ i (saluted ’l’l"C infral 9‘3” ( 3a '5 0“ {CL Chem 9?? limit/xi OthMa line. Chose“ "rc alt’” «an. ,_ . - - -. 1 iii .are_ (mad A :3 l5 a noun or . WA he“ "l ,, fiestas-qvu-e‘ -; Walt" : 'll‘ ' i _ ‘ i "1 9” . ct, curmyll‘? omnaa=écrw : rmimmes R . y _ i , » . _ 7_ I A 1 I _. at}; __ ‘ ‘ 73.) Curfwlsildr Clockwcse' ~ - j n c1'nf9’ffiffltf Ea Lents \qw , k ' hf; cloelegijgse. 7‘. (b) (4 pts) Find the appiied force 1?? at time t: 0.10 s and express it in unit vector notation. . . . , . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. _3 ¥lfl€i : ‘3 becif‘x \ffl‘lecfi-J‘Bacfi M—SL. lxl%l*G‘7) (Imi Nate-l one if are hair loqroillel ; , Q4 15 5i“ (c) (6 pts) Find the rate of energy supplied by the force F and the rate of energy dissipated in the resistor at time I : 0‘10 3. Compare them and explain. No credit will be given ifthere is no explanation. _ ____5 A A A h _, P J (L. 2 R 7 PP: Pf? :04 (swfijlvl‘etgll This we etel / r' / l J; .romeem (Will—39K EMF 0M1 3 10,}K1qzl58W i a l cl;— Jilpe, Fmofigleclfofgrfzf . 7, ‘ A I 52R 1 (LA) (#2 Korlfif) force Jr? l’l/ie 335%?“ is I’m («*0 \ner—r‘r 0.4 like rests F. : 46-8 W- nwkerefl Qige this energy; Phys 106 Final Examination Page 6 Monday, Jun 01, 2009 PROBLEM (5) [20 points) In the circuit shown the switch 5 has been closed for a long time and it is suddenly opened at time I = U. (a) (5 pts) Find the potential difference, Vito : V“ —— Vb. at time {=0 ct l—h-lM/H; loe{<f€. {$0 ll“ % Ki it) mirevxl- E ovc <2 Y LE3! {ride («incl-9’ ‘Li 2 5* LE! i Lew-“6‘;— L‘ l “2:” 35L : \\=-L1A' gab-4L cuw’wl' will ' {:{gm {'MMLdCQlfll (54le Six Orfimeczl '“r (b) (5 pts) Find the rate of change of the current in the inductor V :5: (feign lfiai elm Gig a We. inclafclrsr it it I f , AC ,VL, LI]: 0m _.— _.-‘ #13 (01) (c) (5 pts) When does the current in R2 become equal to 2.0 A? (“Wei/\l- On ‘21 :1" _ t 3/: 4“th l; '1 :2 110)) e I f ,t/ 2: it e t aide: Q- (d) (5 pts) The inductor is a solenoid with cross—sectional are magnitude ofthe magnetic field inside the solenoid at time I: 0. W Wefsxf AME ?_ .7. , (I, : lg— .) ‘2'} IADL’iL Phys 106 Final Examination 3 Vt. Jig—,- Laflia‘ : MEL/v91) : axis-13 ‘l. 0’! ,namely —,attimet=0. ................................... d; l ,9 4:, b2: .06? £10025 I '5 a A: 3.2><l0’4 m2 and length I: 0.40 m. Find the average 'i. 'i r 8315*“) c. rv T o S "- fllfldo a Z0'|?T Ofl’i'v'i-l— Monday, Jun 01, 2009 ...
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This note was uploaded on 04/09/2012 for the course MATH 120 taught by Professor Onurfen during the Spring '12 term at Middle East Technical University.

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106-20082-FIN - PROBLEM (I) (20 points) A iioneontiueting...

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